Thermodynamics of Asymptotically Conical Geometries

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA and Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia

DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA, LE STUDIUM, Loire Valley Institute for Advanced Studies, Tours and Orleans, France, and 3Laboratoire de Mathematiques et de Physique Theorique, Universite de Tours, Tours, France

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA and National Center for Physics, Quaid-i-Azam University, Shahdara valley road, Islamabad, Pakistan

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Phys. Rev. Lett.114, 231301 –Published 10 June, 2015

DOI:https://doi.org/10.1103/PhysRevLett.114.231301

Abstract

We study the thermodynamical properties of a class of asymptotically conical geometries known as “subtracted geometries.” We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.