Temperature and thermodynamic structure of Einstein's equations for a cosmological black hole

Abstract

It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime. Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity. In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time. To single out the correct one we find the temperature by studying the Hawking effect in the tunnelling formalism. This leads to time dependent structure. After identifying the correct one, the Einstein's equations are written on the horizon and we show that this leads to the first law of thermodynamics. In this process the expressions for horizon entropy and energy, obtained earlier by explicit calculations, are being used. This provides the evidence that Einstein's equations have thermodynamic structure even for a cosmological black hole spacetime. Moreover, this study further clarifies the correctness of the expressions for the thermodynamic quantities; like temperature, entropy and internal energy.

Comments added, to appear in Phys. Rev. D

References in corpus (12)

• Hawking Radiation of Apparent Horizon in a FRW Universe
• Anomalies, Hawking Radiations and Regularity in Rotating Black Holes
• Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies
• Temporal contribution to gravitational WKB-like calculations
• Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
• Quantum Tunneling and Trace Anomaly
• Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
• Black Hole Evaporation in an Expanding Universe
• Hawking Radiation as Quantum Tunneling in Rindler Coordinate
• The Hawking temperature of expanding cosmological black holes
• Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy
• Near horizon hidden symmetry and entropy of Sultana-Dyer black hole: A time dependent case

Cited by in corpus (16)

• Foliation dependence of black hole apparent horizons in spherical symmetry
• Thermogeometric description of the van der Waals like phase transition in AdS black holes
• Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• Regular black holes with $\Lambda >0$ and its evolution in Lovelock gravity
• Hawking-Like Radiation as Tunneling from a Cosmological Black Hole in Modified Gravity: Semiclassical Approximation and Beyond
• Hawking radiation in a non-covariant frame: the Jacobi metric approach
• Cosmological applications of the Brown-York quasilocal mass
• Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation
• Tolman-Ehrenfest's criterion of thermal equilibrium extended to conformally static spacetimes
• Abbott-Deser-Tekin like conserved quantities in Lanczos-Lovelock gravity: beyond Killing diffeomorphisms
• Spacetime mappings of the Brown-York quasilocal energy
• Tunneling from the past horizon
• Thermodynamic parameters of fluids on conformally connected spacetimes
• Scalar particles tunneling radiation in the Demianski-Newman spacetime with influences of quantum gravity
• The Accurate Modification of Tunneling Radiation of Fermions with Arbitrary Spin in Kerr-de Sitter Black Hole Space-time