The spacetime is independent of the entropy

Physics: borderline case for black holes

Based on the assumption that black holes can disintegrate, the four physicists made the far-reaching conjecture that gravity is the weakest force in any possible universe. That means: objects with Q > M. always exist for all types of cargo Q, regardless of whether the objects are particles like electrons (which in fact carry far more electrical charge than mass) or small black holes.

This »weak gravity conjecture« became enormously influential and inspired a number of other ideas about quantum gravity. But Arkani-Hamed, Motl, Nicolis and Vafa have by no means proven that Q > M. applies or extremal black holes disintegrate. The quantum gravity corrections could also have a different sign - a negative instead of a positive one. Then small black holes would carry even less charge per mass than large ones. Extreme specimens did not disintegrate, nor would the weak gravity conjecture hold. The researchers therefore had to find out whether the sign of the corrections in quantum gravity is positive or negative.

The question of such corrections has arisen earlier, in a different, apparently unrelated branch of black hole studies. In the 1970s, the physicists Jacob Bekenstein and Stephen Hawking independently discovered that the entropy of a black hole is directly proportional to its surface area. Entropy is generally considered to be a measure of disorder. More precisely, it stands for the number of ways in which the components of an object can be rearranged without changing the overall state. The findings of Bekenstein and Hawking thus connected the smallest internal components of a black hole with its exterior. Thus the "law of area of ​​entropy" became an important anchor on the way to a theory of quantum gravity.

Bekenstein and Hawking derived their law by applying Einstein's gravitational equations along with the laws of thermodynamics to the surface of the black hole. They treated these as smooth and ignored any structure at short distances.

In 1993, the physicist Robert Wald from the University of Chicago showed how to do it more precisely. He used a few tricks to deduce the small effects without having to know a full description. His tactic, which the theoretical physicist Kenneth Wilson had developed in a different context, was to write down every possible physical effect. Wald showed how you can add a number of additional terms to Einstein's equations - the main thing is that they have the correct physical dimensions and units and contain all the relevant variables. The hope was that some of them would describe the unknown properties of the surface of a black hole over short distances.

The individual constructs from the numerous variables are becoming increasingly confusing, but fortunately the series can be broken off after a few terms, since the more complicated parts hardly contribute to the final answer. Even many of the leading terms can be deleted because they have the wrong symmetries or violate consistency conditions. After all, there are only a few terms of importance that modify Einstein's equations of gravity. The solution of the equations supplemented in this way then provides more precise statements about the properties of black holes.