Thermodynamics of Sultana-Dyer Black Hole

Abstract

The thermodynamical entities on the dynamical horizon are not naturally defined like the usual static cases. Here I find the temperature, Smarr formula and the first law of thermodynamics for the Sultana-Dyer metric which is related to the Schwarzschild spacetime by a time dependent conformal factor. To find the temperature ($T$), the chiral anomaly expressions for the two dimensional spacetime are used. This shows an application of the anomaly method to study Hawking effect for a dynamical situation. Moreover, the analysis singles out one expression for temperature among two existing expressions in the literature. Interestingly, the present form satisfies the first law of thermodynamics. Also, it relates the Misner-Sharp energy ($\bar{E}$) and the horizon entropy ($\bar{S}$) by an algebraic expression $\bar{E}=2\bar{S}T$ which is the general form of the Smarr formula. This fact is similar to the usual static black hole cases in Einstein's gravity where the energy is identified as the Komar conserved quantity.

typos corrected, to appear in JCAP

References in corpus (10)

• General Relativity from a Thermodynamic Perspective
• Hawking Radiation and Covariant Anomalies
• Statistical Origin of Gravity
• Black Hole Evaporation in an Expanding Universe
• Hawking Radiation, Covariant Boundary Conditions and Vacuum States
• The Hawking temperature of expanding cosmological black holes
• Hawking radiation from the quantum Lemaitre-Tolman-Bondi model
• Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions
• Horizon thermodynamics and spacetime mappings
• Emergent gravity: From statistical point of view

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• Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy
• Near horizon hidden symmetry and entropy of Sultana-Dyer black hole: A time dependent case
• Cosmological applications of the Brown-York quasilocal mass
• Covariant approach to the thermodynamic structure of a generic null surface
• Black hole mechanics and thermodynamics in the light of Weyl transformations
• Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation
• Vacuum condition and the relation between response parameter and anomaly coefficient in (1+3) dimensions
• 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
• Thermal scalar field stress tensor on a two dimensional black hole and its near horizon properties