Is gravitational entropy quantized ?

TL;DR

This paper argues that in general Lanczos-Lovelock theories of gravity, horizon entropy, not area, has an equally spaced quantum spectrum, extending the concept of quantization beyond Einstein's gravity.

Contribution

It provides a general proof that entropy, rather than area, is quantized in all Lanczos-Lovelock gravity theories, supported by explicit calculations in Gauss-Bonnet gravity.

Findings

Entropy has an equally spaced spectrum in Lanczos-Lovelock theories.

In Gauss-Bonnet gravity, quasi-normal modes support entropy quantization.

Area quantization is not universal across all gravity theories.

Abstract

In Einstein's gravity, the entropy of horizons is proportional to their area. Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equally spaced spectrum for large quantum numbers. But in more general theories (like, for e.g, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is \emph{not} proportional to area and the question arises as to which of the two (if at all) will have this property. We give a general argument that in all Lanczos-Lovelock theories of gravity, it is the \emph{entropy} that has equally spaced spectrum. In the case of Gauss-Bonnet gravity, we use the asymptotic form of quasi normal mode frequencies to explicitly demonstrate this result. Hence, the concept of a quantum of area in Einstein Hilbert (EH) gravity needs to be replaced by a concept of \emph{quantum of entropy} in a more general context.