Universality of Black Hole Entropy

A range of supermassive black holes lights up this new image from NASA’s NuSTAR. All of the dots are active black holes tucked inside the hearts of galaxies, with colors representing different energies of X-ray light.

It was not until the past few decades that physicists have made remarkable experimental advancements in the study of black holes, such as with the Event Horizon Telescope and the Laser Interferometer Gravitational-Wave Observatory.

On the theoretical side, there are still lingering questions regarding the thermodynamics of these objects. It is well known that black holes have a simple formula for their entropy. It was first postulated by Jacob Bekenstein and Stephen Hawking that the entropy is proportional to the area of its event horizon. The universality of this formula is quite impressive and has stood the test of time.

However, there is more to the story of black hole thermodynamics. Even though the entropy is proportional to its area, there are sub-leading terms that also contribute. Theoretical physicists like to focus on the logarithmic corrections to this formula and investigate whether it is just as universal as the leading term.

Examining a certain class of black holes in four dimensions, Hristov and Reys have shown such a universal result may exist. They focused on a set of spacetimes, that asymptote for large radial distance, to a negatively curved spacetime, called Anti-de Sitter. These Anti-de Sitter spacetimes have been at the forefront of high energy theory due to the AdS/CFT correspondence.

Moreover, they found that the logarithmic term is proportional to its Euler Characteristic, a topologically invariant quantity, and a single dynamical coefficient, that depends on the spacetime background. Their work is a stepping stone in understanding the structure of the entropy for these asymptotically AdS black holes.

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