General relativity is atheory ofgravitation developed byAlbert Einstein between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping ofspacetime.
By the beginning of the 20th century,Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses. In Newton's model, gravity is the result of an attractive force between massive objects. Although even Newton was troubled by the unknown nature of that force, the basic framework was extremely successful at describing motion.
Experiments and observations show that Einstein's description of gravitation accounts for several effects that are unexplained by Newton's law, such as minute anomalies in theorbits ofMercury and otherplanets. General relativity also predicts novel effects of gravity, such asgravitational waves,gravitational lensing and an effect of gravity on time known asgravitational time dilation. Many of these predictions have been confirmed by experiment or observation,most recently gravitational waves.
General relativity has developed into an essential tool in modernastrophysics. It provides the foundation for the current understanding ofblack holes, regions of space where the gravitational effect is strong enough that even light cannot escape. Their strong gravity is thought to be responsible for the intenseradiation emitted by certain types of astronomical objects (such asactive galactic nuclei ormicroquasars). General relativity is also part of the framework of the standardBig Bang model ofcosmology.
Although general relativity is not the only relativistic theory of gravity, it is the simplest one that is consistent with the experimental data. Nevertheless, a number of open questions remain, the most fundamental of which is how general relativity can be reconciled with the laws ofquantum physics to produce a complete and self-consistent theory ofquantum gravity.
In September 1905,Albert Einstein published his theory ofspecial relativity, which reconcilesNewton's laws of motion withelectrodynamics (the interaction between objects withelectric charge). Special relativity introduced a new framework for all of physics by proposing new concepts ofspace and time. Some then-accepted physical theories were inconsistent with that framework; a key example was Newton's theory ofgravity, which describes the mutual attraction experienced by bodies due to their mass.
Several physicists, including Einstein, searched for a theory that would reconcile Newton's law of gravity and special relativity. Only Einstein's theory proved to be consistent with experiments and observations. To understand the theory's basic ideas, it is instructive to follow Einstein's thinking between 1907 and 1915, from his simplethought experiment involving an observer in free fall to his fully geometric theory of gravity.[1]
A person in afree-falling elevator experiencesweightlessness; objects either float motionless or drift at constant speed. Since everything in the elevator is falling together, no gravitational effect can be observed. In this way, the experiences of an observer in free fall are indistinguishable from those of an observer in deep space, far from any significant source of gravity. Such observers are the privileged ("inertial") observers Einstein described in his theory ofspecial relativity: observers for whomlight travels along straight lines at constant speed.[2]
Einstein hypothesized that the similar experiences of weightless observers and inertial observers in special relativity represented a fundamental property of gravity, and he made this the cornerstone of his theory of general relativity, formalized in hisequivalence principle. Roughly speaking, the principle states that a person in a free-falling elevator cannot tell that they are in free fall. Every experiment in such a free-falling environment has the same results as it would for an observer at rest or moving uniformly in deep space, far from all sources of gravity.[3]
Most effects of gravity vanish infree fall, but effects that seem the same as those of gravity can beproduced by anaccelerated frame of reference. An observer in a closed room cannot tell which of the following two scenarios is true:
Conversely, any effect observed in an accelerated reference frame should also be observed in a gravitational field of corresponding strength. This principle allowed Einstein to predict several novel effects of gravity in 1907(see§ Physical consequences, below).
An observer in an accelerated reference frame must introduce what physicists callfictitious forces to account for the acceleration experienced by the observer and objects around them. In the example of the driver being pressed into their seat, the force felt by the driver is one example; another is the force one can feel while pulling the arms up and out if attempting to spin around like a top. Einstein's master insight was that the constant, familiar pull of the Earth's gravitational fieldis fundamentally the same as these fictitious forces.[4] The apparent magnitude of the fictitious forces always appears to be proportional to the mass of any object on which they act – for instance, the driver's seat exerts just enough force to accelerate the driver at the same rate as the car. By analogy, Einstein proposed that an object in a gravitational field should feel a gravitational force proportional to its mass, as embodied inNewton's law of gravitation.[5]
In 1907, Einstein was still eight years away from completing the general theory of relativity. Nonetheless, he was able to make a number of novel, testable predictions that were based on his starting point for developing his new theory: the equivalence principle.[6]
The first new effect is thegravitational frequency shift of light. Consider two observers aboard an accelerating rocket-ship. Aboard such a ship, there is a natural concept of "up" and "down": the direction in which the ship accelerates is "up", and free-floating objects accelerate in the opposite direction, falling "downward". Assume that one of the observers is "higher up" than the other. When the lower observer sends a light signal to the higher observer, the acceleration of the ship causes the light to bered-shifted, as may be calculated fromspecial relativity; the second observer will measure a lowerfrequency for the light than the first sent out. Conversely, light sent from the higher observer to the lower isblue-shifted, that is, shifted towards higher frequencies.[7] Einstein argued that such frequency shifts must also be observed in a gravitational field. This is illustrated in the figure at left, which shows a light wave that is gradually red-shifted as it works its way upwards against the gravitational acceleration. This effect has been confirmed experimentally, as describedbelow.
This gravitational frequency shift corresponds to agravitational time dilation: Since the "higher" observer measures the same light wave to have a lower frequency than the "lower" observer, time must be passing faster for the higher observer. Thus, time runs more slowly for observers the lower they are in a gravitational field.
It is important to stress that, for each observer, there are no observable changes of the flow of time for events or processes that are at rest in his or her reference frame. Five-minute-eggs as timed by each observer's clock have the same consistency; as one year passes on each clock, each observer ages by that amount; each clock, in short, is in perfect agreement with all processes happening in its immediate vicinity. It is only when the clocks are compared between separate observers that one can notice that time runs more slowly for the lower observer than for the higher.[8] This effect is minute, but it too has been confirmed experimentally in multiple experiments, as describedbelow.
In a similar way, Einstein predicted thegravitational deflection of light: in a gravitational field, light is deflected downward, to the center of the gravitational field. Quantitatively, his results were off by a factor of two; the correct derivation requires a more complete formulation of the theory of general relativity, not just the equivalence principle.[9]
The equivalence between gravitational and inertial effects does not constitute a complete theory of gravity. When it comes to explaining gravity near our own location on the Earth's surface, noting that our reference frame is not in free fall, so thatfictitious forces are to be expected, provides a suitable explanation. But a freely falling reference frame on one side of the Earth cannot explain why the people on the opposite side of the Earth experience a gravitational pull in the opposite direction.
A more basic manifestation of the same effect involves two bodies that are falling side by side towards the Earth, with a similar position and velocity. In a reference frame that is in free fall alongside these bodies, they appear to hover weightlessly – but not exactly so. These bodies are not falling in precisely the same direction, but towards a single point in space: namely, the Earth'scenter of gravity. Consequently, there is a component of each body's motion towards the other (see the figure). In a small environment such as a freely falling lift, this relative acceleration is minuscule, while forskydivers on opposite sides of the Earth, the effect is large. Such differences in force are also responsible for thetides in the Earth's oceans, so the term "tidal effect" is used for this phenomenon.
The equivalence between inertia and gravity cannot explain tidal effects – it cannot explain variations in the gravitational field.[10] For that, a theory is needed which describes the way that matter (such as the large mass of the Earth) affects the inertial environment around it.
While Einstein was exploring the equivalence of gravity and acceleration as well as the role of tidal forces, he discovered several analogies with thegeometry ofsurfaces. An example is the transition from an inertial reference frame (in which free particles coast along straight paths at constant speeds) to a rotating reference frame (in whichfictitious forces have to be introduced in order to explain particle motion): this is analogous to the transition from aCartesian coordinate system (in which the coordinate lines are straight lines) to acurved coordinate system (where coordinate lines need not be straight).
A deeper analogy relates tidal forces with a property of surfaces calledcurvature. For gravitational fields, the absence or presence of tidal forces determines whether or not the influence of gravity can be eliminated by choosing a freely falling reference frame. Similarly, the absence or presence of curvature determines whether or not a surface isequivalent to aplane. In the summer of 1912, inspired by these analogies, Einstein searched for a geometric formulation of gravity.[11]
The elementary objects ofgeometry –points,lines,triangles – are traditionally defined in three-dimensionalspace or on two-dimensionalsurfaces. In 1907,Hermann Minkowski, Einstein's former mathematics professor at the Swiss Federal Polytechnic, introducedMinkowski space, a geometric formulation of Einstein'sspecial theory of relativity where the geometry included not onlyspace but also time. The basic entity of this new geometry is four-dimensionalspacetime. The orbits of moving bodies arecurves in spacetime; the orbits of bodies moving at constant speed without changing direction correspond to straight lines.[12]
The geometry of general curved surfaces was developed in the early 19th century byCarl Friedrich Gauss. This geometry had in turn been generalized to higher-dimensional spaces inRiemannian geometry introduced byBernhard Riemann in the 1850s. With the help of Riemannian geometry, Einstein formulated a geometric description of gravity in which Minkowski's spacetime is replaced by distorted, curved spacetime, just as curved surfaces are a generalization of ordinary plane surfaces. Embedding diagrams are used to illustrate curved spacetime in educational contexts.[13][14]
After he had realized the validity of this geometric analogy, it took Einstein a further three years to find the missing cornerstone of his theory: the equations describing howmatter influences spacetime's curvature. Having formulated what are now known asEinstein's equations (or, more precisely, his field equations of gravity), he presented his new theory of gravity at several sessions of thePrussian Academy of Sciences in late 1915, culminating in his final presentation on November 25, 1915.[15]
ParaphrasingJohn Wheeler, Einstein's geometric theory of gravity can be summarized as:spacetime tells matter how to move; matter tells spacetime how to curve.[16] What this means is addressed in the following three sections, which explore the motion of so-calledtest particles, examine which properties of matter serve as a source for gravity, and, finally, introduce Einstein's equations, which relate these matter properties to the curvature of spacetime.
In order to map a body's gravitational influence, it is useful to think about what physicists call probe ortest particles: particles that are influenced by gravity, but are so small and light that we can neglect their own gravitational effect. In the absence of gravity and other external forces, a test particle moves along a straight line at a constant speed. In the language ofspacetime, this is equivalent to saying that such test particles move along straightworld lines in spacetime. In the presence of gravity, spacetime isnon-Euclidean, orcurved, and in curved spacetime straight world lines may not exist. Instead, test particles move along lines calledgeodesics, which are "as straight as possible", that is, they follow the shortest path between starting and ending points, taking the curvature into consideration.
A simple analogy is the following: Ingeodesy, the science of measuring Earth's size and shape, a geodesic is the shortest route between two points on the Earth's surface. Approximately, such a route is asegment of agreat circle, such as aline of longitude or theequator. These paths are certainly not straight, simply because they must follow the curvature of the Earth's surface. But they are as straight as is possible subject to this constraint.
The properties of geodesics differ from those of straight lines. For example, on a plane, parallel lines never meet, but this is not so for geodesics on the surface of the Earth: for example, lines of longitude are parallel at the equator, but intersect at the poles. Analogously, the world lines of test particles in free fall arespacetime geodesics, the straightest possible lines in spacetime. But still there are crucial differences between them and the truly straight lines that can be traced out in the gravity-free spacetime of special relativity. In special relativity, parallel geodesics remain parallel. In a gravitational field with tidal effects, this will not, in general, be the case. If, for example, two bodies are initially at rest relative to each other, but are then dropped in the Earth's gravitational field, they will move towards each other as they fall towards the Earth's center.[17]
Compared with planets and other astronomical bodies, the objects of everyday life (people, cars, houses, even mountains) have little mass. Where such objects are concerned, the laws governing the behavior of test particles are sufficient to describe what happens. Notably, in order to deflect a test particle from its geodesic path, an external force must be applied. A chair someone is sitting on applies an external upwards force preventing the person fromfalling freely towardsthe center of the Earth and thus following a geodesic, which they would otherwise be doing without the chair there, or any other matter in between them and the center point of the Earth. In this way, general relativity explains the daily experience of gravity on the surface of the Earthnot as the downwards pull of a gravitational force, but as the upwards push of external forces. These forces deflect all bodies resting on the Earth's surface from the geodesics they would otherwise follow.[18] For objects massive enough that their own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how to move.[19]
InNewton's description of gravity, the gravitational force is caused by matter. More precisely, it is caused by a specific property of material objects: theirmass. In Einstein's theory and relatedtheories of gravitation, curvature at every point in spacetime is also caused by whatever matter is present. Here, too, mass is a key property in determining the gravitational influence of matter. But in a relativistic theory of gravity, mass cannot be the only source of gravity. Relativity links mass with energy, and energy with momentum.
The equivalence between mass andenergy, as expressed by the formula [[Mass–energy equivalence|E = mc‹ThetemplateSmallsup is beingconsidered for deletion.› 2]], is the most famous consequence of special relativity. In relativity, mass and energy are two different ways of describing one physical quantity. If a physical system has energy, it also has the corresponding mass, and vice versa. In particular, all properties of a body that are associated with energy, such as itstemperature or thebinding energy of systems such asnuclei ormolecules, contribute to that body's mass, and hence act as sources of gravity.[20]
In special relativity, energy is closely connected tomomentum. In special relativity, just as space and time are different aspects of a more comprehensive entity called spacetime, energy and momentum are merely different aspects of a unified, four-dimensional quantity that physicists callfour-momentum. In consequence, if energy is a source of gravity, momentum must be a source as well. The same is true for quantities that are directly related to energy and momentum, namely internalpressure andtension. Taken together, in general relativity it is mass, energy, momentum, pressure and tension that serve as sources of gravity: they are how matter tells spacetime how to curve. In the theory's mathematical formulation, all these quantities are but aspects of a more general physical quantity called thestress–energy tensor.[21]
Einstein's equations are the centerpiece of general relativity. They provide a precise formulation of the relationship between spacetime geometry and the properties of matter, using the language of mathematics. More concretely, they are formulated using the concepts ofRiemannian geometry, in which the geometric properties of a space (or a spacetime) are described by a quantity called ametric. The metric encodes the information needed to compute the fundamental geometric notions of distance and angle in a curved space (or spacetime).
A spherical surface like that of the Earth provides a simple example. The location of any point on the surface can be described by two coordinates: the geographiclatitude andlongitude. Unlike the Cartesian coordinates of the plane, coordinate differences are not the same as distances on the surface, as shown in the diagram on the right: for someone at the equator, moving 30 degrees of longitude westward (magenta line) corresponds to a distance of roughly 3,300 kilometers (2,100 mi), while for someone at a latitude of 55 degrees, moving 30 degrees of longitude westward (blue line) covers a distance of merely 1,900 kilometers (1,200 mi). Coordinates therefore do not provide enough information to describe the geometry of a spherical surface, or indeed the geometry of any more complicated space or spacetime. That information is precisely what is encoded in the metric, which is a function defined at each point of the surface (or space, or spacetime) and relates coordinate differences to differences in distance. All other quantities that are of interest in geometry, such as the length of any given curve, or the angle at which two curves meet, can be computed from this metric function.[22]
The metric function and its rate of change from point to point can be used to define a geometrical quantity called theRiemann curvature tensor, which describes exactly how theRiemannian manifold, the spacetime in the theory of relativity, is curved at each point. As has already been mentioned, the matter content of the spacetime defines another quantity, thestress–energy tensorT, and the principle that "spacetime tells matter how to move, and matter tells spacetime how to curve" means that these quantities must be related to each other. Einstein formulated this relation by using the Riemann curvature tensor and the metric to define another geometrical quantityG, now called theEinstein tensor, which describes some aspects of the way spacetime is curved.Einstein's equation then states that
i.e., up to a constant multiple, the quantityG (which measures curvature) is equated with the quantityT (which measures matter content). Here,G is thegravitational constant of Newtonian gravity, andc is thespeed of light from special relativity.
This equation is often referred to in the plural asEinstein's equations, since the quantitiesG andT are each determined by several functions of the coordinates of spacetime, and the equations equate each of these component functions.[23]A solution of these equations describes a particular geometry ofspacetime; for example, theSchwarzschild solution describes the geometry around a spherical, non-rotating mass such as astar or ablack hole, whereas theKerr solution describes a rotating black hole. Still other solutions can describe agravitational wave or, in the case of theFriedmann–Lemaître–Robertson–Walker solution, an expanding universe. The simplest solution is the uncurvedMinkowski spacetime, the spacetime described by special relativity.[24]
No scientific theory is self-evidently true; each is a model that must be checked by experiment.Newton's law of gravity was accepted because it accounted for the motion of planets and moons in theSolar System with considerable accuracy. As the precision of experimental measurements gradually improved, some discrepancies with Newton's predictions were observed, and these were accounted for in the general theory of relativity. Similarly, the predictions of general relativity must also be checked with experiment, and Einstein himself devised three tests now known as the classical tests of the theory:
Of these tests, only the perihelion advance of Mercury was known prior to Einstein's final publication of general relativity in 1916. The subsequent experimental confirmation of his other predictions, especially the first measurements of the deflection of light by the sun in 1919, catapulted Einstein to international stardom.[28] These three experiments justified adopting general relativity over Newton's theory and, incidentally, over a number ofalternatives to general relativity that had been proposed.
Further tests of general relativity include precision measurements of theShapiro effect or gravitational time delay for light, measured in 2002 by theCassini space probe. One set of tests focuses on effects predicted by general relativity for the behavior ofgyroscopes travelling through space. One of these effects,geodetic precession, has been tested with theLunar Laser Ranging Experiment (high-precision measurements of the orbit of theMoon). Another, which is related to rotating masses, is calledframe-dragging. The geodetic and frame-dragging effects were both tested by theGravity Probe B satellite experiment launched in 2004, with results confirming relativity to within 0.5% and 15%, respectively, as of December 2008.[29]
By cosmic standards, gravity throughout the solar system is weak. Since the differences between the predictions of Einstein's and Newton's theories are most pronounced when gravity is strong, physicists have long been interested in testing various relativistic effects in a setting with comparatively strong gravitational fields. This has become possible thanks to precision observations ofbinary pulsars. In such a star system, two highly compactneutron stars orbit each other. At least one of them is apulsar – an astronomical object that emits a tight beam of radiowaves. These beams strike the Earth at very regular intervals, similarly to the way that the rotating beam of a lighthouse means that an observer sees the lighthouse blink, and can be observed as a highly regular series of pulses. General relativity predicts specific deviations from the regularity of these radio pulses. For instance, at times when the radio waves pass close to the other neutron star, they should be deflected by the star's gravitational field. The observed pulse patterns are impressively close to those predicted by general relativity.[30]
One particular set of observations is related to eminently useful practical applications, namely tosatellite navigation systems such as theGlobal Positioning System (GPS) that are used for both precisepositioning andtimekeeping. Such systems rely on two sets ofatomic clocks: clocks aboard satellites orbiting the Earth, and reference clocks stationed on the Earth's surface. General relativity predicts that these two sets of clocks should tick at slightly different rates, due to their different motions (an effect already predicted by special relativity) and their different positions within the Earth's gravitational field. In order to ensure the system's accuracy, either the satellite clocks are slowed down by a relativistic factor, or that same factor is made part of the evaluation algorithm. In turn, tests of the system's accuracy (especially the very thorough measurements that are part of the definition ofuniversal coordinated time) are testament to the validity of the relativistic predictions.[31]
A number of other tests have probed the validity of various versions of theequivalence principle; strictly speaking, all measurements of gravitational time dilation are tests of theweak version of that principle, not of general relativity itself. So far, general relativity has passed all observational tests.[32]
Models based on general relativity play an important role inastrophysics; the success of these models is further testament to the theory's validity.
Since light is deflected in a gravitational field, it is possible for the light of a distant object to reach an observer along two or more paths. For instance, light of a very distant object such as aquasar can pass along one side of a massivegalaxy and be deflected slightly so as to reach an observer on Earth, while light passing along the opposite side of that same galaxy is deflected as well, reaching the same observer from a slightly different direction. As a result, that particular observer will see one astronomical object in two different places in the night sky. This kind of focussing is well known when it comes tooptical lenses, and hence the corresponding gravitational effect is calledgravitational lensing.[33]
Observational astronomy uses lensing effects as an important tool to infer properties of the lensing object. Even in cases where that object is not directly visible, the shape of a lensed image provides information about themass distribution responsible for the light deflection. In particular, gravitational lensing provides one way to measure the distribution ofdark matter, which does not give off light and can be observed only by its gravitational effects. One particularly interesting application are large-scale observations, where the lensing masses are spread out over a significant fraction of the observable universe, and can be used to obtain information about the large-scale properties and evolution of our cosmos.[34]
Gravitational waves, a direct consequence of Einstein's theory, are distortions of geometry that propagate at the speed of light, and can be thought of as ripples in spacetime. They should not be confused with thegravity waves offluid dynamics, which are a different concept.
In February 2016, the AdvancedLIGO team announced that they had directlyobserved gravitational waves from ablack hole merger.[35]
Indirectly, the effect of gravitational waves had been detected in observations of specific binary stars. Such pairs of starsorbit each other and, as they do so, gradually lose energy by emitting gravitational waves. For ordinary stars like the Sun, this energy loss would be too small to be detectable, but this energy loss was observed in 1974 in abinary pulsar calledPSR1913+16. In such a system, one of the orbiting stars is a pulsar. This has two consequences: a pulsar is an extremely dense object known as aneutron star, for which gravitational wave emission is much stronger than for ordinary stars. Also, a pulsar emits a narrow beam ofelectromagnetic radiation from its magnetic poles. As the pulsar rotates, its beam sweeps over the Earth, where it is seen as a regular series of radio pulses, just as a ship at sea observes regular flashes of light from the rotating light in a lighthouse. This regular pattern of radio pulses functions as a highly accurate "clock". It can be used to time the double star's orbital period, and it reacts sensitively to distortions of spacetime in its immediate neighborhood.
The discoverers of PSR1913+16,Russell Hulse andJoseph Taylor, were awarded theNobel Prize in Physics in 1993. Since then, several other binary pulsars have been found. The most useful are those in which both stars are pulsars, since they provide accurate tests of general relativity.[36]
Currently, a number of land-basedgravitational wave detectors are in operation, and a mission to launch a space-based detector,LISA, is currently under development, with a precursor mission (LISA Pathfinder) which was launched in 2015. Gravitational wave observations can be used to obtain information about compact objects such as neutron stars and black holes, and also to probe the state of the earlyuniverse fractions of a second after theBig Bang.[37]
When mass is concentrated into a sufficientlycompact region of space, general relativity predicts the formation of ablack hole – a region of space with a gravitational effect so strong that not even light can escape. Certain types of black holes are thought to be the final state in theevolution of massivestars. On the other hand,supermassive black holes with the mass ofmillions orbillions ofSuns are assumed to reside in the cores of mostgalaxies, and they play a key role in current models of how galaxies have formed over the past billions of years.[38]
Matter falling onto a compact object is one of the most efficient mechanisms for releasingenergy in the form ofradiation, and matter falling onto black holes is thought to be responsible for some of the brightest astronomical phenomena imaginable. Notable examples of great interest to astronomers arequasars and other types ofactive galactic nuclei. Under the right conditions, falling matter accumulating around a black hole can lead to the formation ofjets, in which focused beams of matter are flung away into space at speeds nearthat of light.[39]
There are several properties that make black holes the most promising sources of gravitational waves. One reason is that black holes are the most compact objects that can orbit each other as part of a binary system; as a result, the gravitational waves emitted by such a system are especially strong. Another reason follows from what are calledblack-hole uniqueness theorems: over time, black holes retain only a minimal set of distinguishing features (these theorems have become known as "no-hair" theorems), regardless of the starting geometric shape. For instance, in the long term, the collapse of a hypothetical matter cube will not result in a cube-shaped black hole. Instead, the resulting black hole will be indistinguishable from a black hole formed by the collapse of a spherical mass. In its transition to a spherical shape, the black hole formed by the collapse of a more complicated shape will emit gravitational waves.[40]
One of the most important aspects of general relativity is that it can be applied to theuniverse as a whole. A key point is that, on large scales, our universe appears to be constructed along very simple lines: all current observations suggest that, on average, the structure of the cosmos should be approximately the same, regardless of an observer's location or direction of observation: the universe is approximatelyhomogeneous andisotropic. Such comparatively simple universes can be described by simple solutions of Einstein's equations. The currentcosmological models of the universe are obtained by combining these simple solutions to general relativity with theories describing the properties of the universe'smatter content, namelythermodynamics,nuclear- andparticle physics. According to these models, our present universe emerged from an extremely dense high-temperature state – theBig Bang – roughly 14billionyears ago and has beenexpanding ever since.[41]
Einstein's equations can be generalized by adding a term called thecosmological constant. When this term is present,empty space itself acts as a source of attractive (or, less commonly, repulsive) gravity. Einstein originally introduced this term in his pioneering 1917 paper on cosmology, with a very specific motivation: contemporary cosmological thought held the universe to be static, and the additional term was required for constructing static model universes within the framework of general relativity. When it became apparent that the universe is not static, but expanding, Einstein was quick to discard this additional term. Since the end of the 1990s, however, astronomical evidence indicating anaccelerating expansion consistent with a cosmological constant – or, equivalently, with a particular and ubiquitous kind ofdark energy – has steadily been accumulating.[42]
General relativity is very successful in providing a framework for accurate models which describe an impressive array of physical phenomena. On the other hand, there are many interesting open questions, and in particular, the theory as a whole is almost certainly incomplete.[43]
In contrast to all other modern theories offundamental interactions, general relativity is aclassical theory: it does not include the effects ofquantum physics. The quest for a quantum version of general relativity addresses one of the most fundamentalopen questions in physics. While there are promising candidates for such a theory ofquantum gravity, notablystring theory andloop quantum gravity, there is at present no consistent and complete theory. It has long been hoped that a theory of quantum gravity would also eliminate another problematic feature of general relativity: the presence ofspacetime singularities. These singularities are boundaries ("sharp edges") of spacetime at which geometry becomes ill-defined, with the consequence that general relativity itself loses its predictive power. Furthermore, there are so-calledsingularity theorems which predict that such singularitiesmust exist within the universe if the laws of general relativity were to hold without any quantum modifications. The best-known examples are the singularities associated with the model universes that describe black holes and thebeginning of the universe.[44]
Other attempts to modify general relativity have been made in the context ofcosmology. In the modern cosmological models, most energy in the universe is in forms that have never been detected directly, namelydark energy anddark matter. There have been several controversial proposals to remove the need for these enigmatic forms of matter and energy, by modifying the laws governing gravity and the dynamics ofcosmic expansion, for examplemodified Newtonian dynamics.[45]
Beyond the challenges of quantum effects and cosmology, research on general relativity is rich with possibilities for further exploration: mathematical relativists explore the nature of singularities and the fundamental properties of Einstein's equations,[46] and ever more comprehensive computer simulations of specific spacetimes (such as those describing merging black holes) are run.[47]More than one hundred years after the theory was first published, research is more active than ever.[48]
Additional resources, including more advanced material, can be found inGeneral relativity resources.
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