Can Bekenstein's area law prevail in modified theories of gravity?

TL;DR

This paper argues that the Bekenstein area law for black hole entropy can hold in certain modified theories of gravity when symmetries are properly accounted for, challenging previous assumptions about its limitations.

Contribution

It demonstrates that logarithmic corrections in 4D Gauss--Bonnet gravity are due to ignoring shift symmetry, and shows the area law can be preserved in these theories with proper modifications.

Findings

Logarithmic corrections vanish when shift symmetry is considered.

The first law remains valid with a modified temperature definition.

The area law can hold in higher-dimensional Lovelock gravities with temperature adjustments.

Abstract

According to Bekenstein's area law, the black hole entropy is identified holographically -- with one quarter of the horizon area. However, it is commonly believed that such a law is only valid in Einstein's theory and that higher curvature corrections generically give rise to its modifications. This is for example the case of black holes in Lovelock gravities, or their four-dimensional cousins in the recently discovered 4D scalar-tensor Gauss--Bonnet gravity where one naively `finds' (classical) logarithmic corrections to the Bekenstein's law. In this Letter we argue that such logarithmic corrections originate from ignoring the shift symmetry of the 4D Gauss--Bonnet gravity. When this symmetry is properly taken into account, there is no longer any departure from the area law in this theory. Moreover, the first law remains valid upon modifying the black hole temperature, which can be derived via the Euclidean grand canonical ensemble (Brown--York) procedure, but is no longer given by the surface gravity. Interestingly, we show that upon similar modification of the black hole temperature the area law can also prevail for black holes in higher-dimensional Lovelock gravities.