Thermodynamics on the Maximally Symmetric Holographic Screen and Entropy from Conical Singularities

TL;DR

This paper demonstrates that the thermodynamic interpretation of gravity extends beyond horizons to general maximally symmetric holographic screens, deriving consistent entropy formulas via multiple methods including conical singularities.

Contribution

It introduces a generalized first law of thermodynamics on maximally symmetric screens in Lovelock gravity and confirms the entropy formula through various approaches.

Findings

Thermodynamic relations hold on general symmetric screens.

Entropy formulas are consistent across static, dynamical, and conical singularity methods.

Gravity's thermodynamic interpretation applies beyond horizons.

Abstract

For a general maximally symmetric (spherically, plane or hyperbola symmetric) holographic screen, we rewrite the equations of motion of general Lovelock gravity into the form of some generalized first law of thermodynamics, under certain ansatz. With this observation together with other two independent ways, exactly the same temperature and entropy on the screen are obtained. So it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general maximally symmetric screen. Moreover, the formula of entropy is further checked in the (maximally symmetric) general static case and dynamical case. The entropy formula also holds for those cases. Finally, the method of conical singularity is used to calculate the entropy on such screen, and the result again confirms the entropy formula.