Effective matter sectors from modified entropies

TL;DR

This paper develops a formalism linking modified entropy functions to effective matter sectors in spacetime, providing a way to interpret entropy modifications as emergent anisotropic fluids within general relativity.

Contribution

It introduces a general method to derive effective matter sectors from various modified entropies, connecting thermodynamics with spacetime geometry and matter content.

Findings

Derived explicit correspondence between entropy derivative and metric function.

Applied formalism to multiple modified entropies, analyzing resulting effective matter sectors.

Identified conditions under which effective matter satisfies energy conditions.

Abstract

We present a general formalism linking modified entropy functions directly to a modified spacetime metric and, subsequently, to an effective matter sector of entropic origin. In particular, within the framework of general relativity, starting from the first law of black-hole thermodynamics we establish an explicit correspondence between the entropy derivative and the metric function, which naturally leads to an emergent stress-energy tensor representing an anisotropic effective fluid. This backreaction effect of horizon entropy may resolve possible inconsistencies recently identified in black hole physics with modified entropies. As specific examples, we apply this procedure to a wide class of modified entropies, such as Barrow, Tsallis-Cirto, Renyi, Kaniadakis, logarithmic, power-law, loop-quantum-gravity, and exponential modifications, and we derive the associated effective matter sectors, analyzing their physical properties and energy conditions.