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

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.