Generalized Entropy Implies Varying-G: Horizon Area Dependent Field Equations and Black Hole-Cosmology Coupling

Abstract

When the Bekenstein-Hawking entropy is modified, ambiguity often arises concerning whether the Hawking temperature or the thermodynamic mass should be modified. The common practice, however, is to keep the black hole solution the same as that in general relativity. On the other hand, if Jacobson's method of deriving Einstein equations from thermodynamic is valid in the general settings, then given a generalized entropy one should first derive the corresponding modified gravity, and then look for the compatible black hole solution before investigating its thermodynamics. We comment on some properties and subtleties in this approach. In particular, we point out that generically generalized entropy would lead to a varying effective gravitational "constant" theory, where $G_{\text{eff}}$ depends on the horizon area. We discuss in what ways such theories are discernible from general relativity despite its seemingly jarring differences, and how to make sense of area-dependent field equations. As a consequence we show that in the Jacobson's approach, the standard quantum gravitational logarithmic correction to Bekenstein-Hawking entropy is equivalent to a running gravitational "constant". A horizon area dependent $G_{\text{eff}}$ could also lead to a coupling between black hole masses and cosmological expansion, a scenario that has been studied recently in the literature, but so far lacks strong theoretical motivation. In the Tsallis case, we show that the thermodynamic mass for a Schwarzschild black hole is just a constant multiple of its ADM mass, which is considerably simpler than the approach not utilizing the Jacobson's method.

Minor changes; also added/fixed some references; published version

References in corpus (35)

• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Kaniadakis holographic dark energy and cosmology
• A rapid transition of $G_{\mathrm{eff}}$ at $z_t\simeq 0.01$ as a solution of the Hubble and growth tensions
• Observational evidence for cosmological coupling of black holes and its implications for an astrophysical source of dark energy
• Area-law versus Rényi and Tsallis black hole entropies
• Cosmological apparent and trapping horizons
• Alternative entropies and consistent black hole thermodynamics
• A Preferential Growth Channel for Supermassive Black Holes in Elliptical Galaxies at z<2
• Observational constraints of the modified cosmology through Barrow entropy
• An exploration of an early gravity transition in light of cosmological tensions
• Equilibrium Temperature for Black Holes with Nonextensive Entropy
• How Barrow Entropy Modifies Gravity: With Comments on Tsallis Entropy
• Running Newton Coupling, Scale Identification and Black Hole Thermodynamics
• Can varying the gravitational constant alleviate the tensions ?
• Surfaces away from horizons are not thermodynamic
• Notes on thermodynamics of Schwarzschild-like bumblebee black hole
• A Critique on Some Aspects of GUP Effective Metric
• The third law of thermodynamics, non-extensivity, and energy definition in black hole physics
• Effective field equations and scale-dependent couplings in gravity
• Thermodynamics and decay of de Sitter vacuum
• Variance of Newtonian constant from local gravitational acceleration measurements
• Statistical approaches and the Bekenstein bound conjecture in Schwarzschild black holes
• Constraints on cosmologically coupled black holes from gravitational wave observations and minimal formation mass
• A generalized mass-to-horizon relation: a new global approach to entropic cosmologies and its connection to $\Lambda$CDM
• Constraining the evolution of Newton's constant with slow inspirals observed from spaceborne gravitational-wave detectors
• Observational implications of cosmologically coupled black holes
• Let's talk about varying G
• Probe the gravitational constant variation via the propagation of gravitational waves
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• Mergers of primordial black holes in extreme clusters and the $H_0$ tension
• The effect of the gravitational constant variation on the propagation of gravitational waves
• Upper Bound of Barrow Entropy Index from Black Hole Fragmentation
• General mass formulas for charged Kerr-AdS black holes
• Can Bekenstein's area law prevail in modified theories of gravity?

Cited by in corpus (8)

• Importance of being nonminimally coupled: Scalar Hawking radiation from regular black holes
• Black Hole Thermodynamics via Tsallis Statistical Mechanics
• GUP Effective Metric Without GUP: Implications for the Sign of GUP Parameter and Quantum Bounce
• Do Black Holes With Generalized Entropy Violate Bekenstein Bound?
• Geometry-Information Duality: Quantum Entanglement Contributions to Gravitational Dynamics
• Shadow of rotating black holes with consistent thermodynamics
• Mass-to-Horizon Relation and Entropy Beyond the Bekenstein-Hawking Limit
• Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence