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BSSN formalism

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Formalism of general relativity

General relativity

G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }

Fundamental concepts

Phenomena

Spacetime
Kepler problem Gravitational lensing Gravitational redshift Gravitational time dilation Gravitational waves Frame-dragging Geodetic effect Event horizon Singularity Black hole
Spacetime diagrams Minkowski spacetime Einstein–Rosen bridge

Equations
Formalisms

Equations
Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon Hamilton–Jacobi–Einstein Raychaudhuri
Formalisms
ADM NP BSSN Post-Newtonian
Advanced theory
Kaluza–Klein theory Quantum gravity

Solutions

Scientists

TheBSSN formalism (Baumgarte, Shapiro, Shibata, Nakamura formalism) is aformalism ofgeneral relativity that was developed byThomas W. Baumgarte,Stuart L. Shapiro, Masaru Shibata and Takashi Nakamura between 1987 and 1999.^[1] It is a modification of theADM formalism developed during the 1950s.

The ADM formalism is aHamiltonian formalism that does not permit stable and long-term numerical simulations. In the BSSN formalism, the ADM equations are modified by introducing auxiliary variables. The formalism has been tested for a long-term evolution of linear gravitational waves and used for a variety of purposes such as simulating the non-linear evolution ofgravitational waves or the evolution and collision ofblack holes.^[2]^[3]

References

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^Jinho Kim (2008-07-28)."General Relativistic Hydrodynamics Using BSSN formalism"(PDF).Seoul National University. Archived fromthe original(PDF) on 2012-03-27. Retrieved2009-10-19.
^Masaru Shibata (October 2004)."Status of numerical relativity".Indian Academy of Sciences. Retrieved2009-10-19.
^Takashi Nakamura (2006)."Formation of black hole and emission of gravitational waves".Proceedings of the Japan Academy, Series B.82 (9):311–327.Bibcode:2006PJAB...82..311N.doi:10.2183/pjab.82.311.PMC 4338837.PMID 25792793.

Relativity

Special
relativity

Background	Principle of relativity (Galilean relativity Galilean transformation) Special relativity Doubly special relativity
Fundamental concepts	Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations Proper length Proper time Proper acceleration Relativistic mass
Formulation	Lorentz transformation Textbooks
Phenomena	Time dilation Mass–energy equivalence (E=mc²) Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Ladder paradox Twin paradox Terrell rotation
Spacetime	Light cone World line Minkowski diagram Biquaternions Minkowski space

General
relativity

Background	Introduction Mathematical formulation
Fundamental concepts	Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle
Formulation	ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation
Phenomena	Black hole Event horizon Singularity Two-body problem Gravitational waves:astronomy detectors (LIGO andcollaboration Virgo LISA Pathfinder GEO) Hulse–Taylor binary Other tests:precession of Mercury lensing (together withEinstein cross andEinstein rings) redshift Shapiro delay frame-dragging /geodetic effect (Lense–Thirring precession) pulsar timing arrays
Advanced theories	Brans–Dicke theory Kaluza–Klein Quantum gravity
Solutions	Cosmological:Friedmann–Lemaître–Robertson–Walker (Friedmann equations) Lemaître–Tolman Kasner BKL singularity Gödel Milne Spherical:Schwarzschild (interior Tolman–Oppenheimer–Volkoff equation) Reissner–Nordström Axisymmetric:Kerr (Kerr–Newman) Weyl−Lewis−Papapetrou Taub–NUT van Stockum dust discs Others:pp-wave Ozsváth–Schücking Alcubierre Ellis In computational physics:Numerical relativity

Scientists

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See also

References