C-Functions in Lovelock Gravity

TL;DR

This paper introduces multiple C-functions in Lovelock gravity for static, spherically symmetric spacetimes, demonstrating their monotonic behavior and relation to black hole entropy, highlighting differences from Einstein gravity.

Contribution

It defines two distinct C-functions in Lovelock gravity that are monotonic and coincide at the horizon, extending the concept beyond Einstein gravity.

Findings

C-functions are monotonically increasing with radius.

Two C-functions agree at the horizon and relate to black hole entropy.

Monotonicity depends on specific energy conditions.

Abstract

We present C-functions for static and spherically symmetric spacetimes in Lovelock gravity theories. These functions are monotonically increasing functions of the outward radial coordinate and acquire their minima when evaluated on the horizon. Unlike the case of Einstein gravity, where there is a single C-function, we find that this function is non-unique in the case of Lovelock gravity. We define two C-functions, which agree at the horizon giving the black hole entropy, and state the different energy conditions that must hold in order for these functions to satisfy the monotonicity condition.