Conformal entropy for generalised gravity theories as a consequence of horizon properties

TL;DR

This paper demonstrates that the microscopic entropy formula derived from Virasoro algebra can be obtained from horizon properties of stationary Killing horizons in general gravity theories, highlighting the role of Riemann tensor invariants.

Contribution

It extends the understanding of horizon entropy to Lagrangians with arbitrary Riemann tensor dependence and explores implications for theories with derivatives of Riemann tensor.

Findings

Entropy formula follows from horizon invariants in general theories.

Regularity of Riemann invariants constrains metric functions near the horizon.

Generalization to derivatives of Riemann tensor requires additional regularity assumptions.

Abstract

We show that microscopic entropy formula based on Virasoro algebra follows from properties of stationary Killing horizons for Lagrangians with arbitrary dependence on Riemann tensor. The properties used are consequence of regularity of invariants of Riemann tensor on the horizon. Eventual generalisation of these results to Lagrangians with derivatives of Riemann tensor, as suggested by an example treated in the paper, relies on assuming regularity of invariants involving derivatives of Riemann tensor. This assumption however leads also to new interesting restrictions on metric functions near horizon.