Editing String theory (section)

=== Derivation within string theory ===

In a paper from 1996, [[Andrew Strominger]] and [[Cumrun Vafa]] showed how to derive the Bekenstein–Hawking formula for certain black holes in string theory.<ref name="Strominger and Vafa 1996"/> Their calculation was based on the observation that D-branes—which look like fluctuating membranes when they are weakly interacting—become dense, massive objects with event horizons when the interactions are strong. In other words, a system of strongly interacting D-branes in string theory is indistinguishable from a black hole. Strominger and Vafa analyzed such D-brane systems and calculated the number of different ways of placing D-branes in spacetime so that their combined mass and charge is equal to a given mass and charge for the resulting black hole. Their calculation reproduced the Bekenstein–Hawking formula exactly, including the factor of {{math|1/4}}.<ref>[[#Yau|Yau and Nadis]], pp. 190–192</ref> Subsequent work by Strominger, Vafa, and others refined the original calculations and gave the precise values of the "quantum corrections" needed to describe very small black holes.<ref name=MSW/><ref name=OST/>

The black holes that Strominger and Vafa considered in their original work were quite different from real astrophysical black holes. One difference was that Strominger and Vafa considered only [[extremal black hole]]s in order to make the calculation tractable. These are defined as black holes with the lowest possible mass compatible with a given charge.<ref>[[#Yau|Yau and Nadis]], pp. 192–193</ref> Strominger and Vafa also restricted attention to black holes in five-dimensional spacetime with unphysical supersymmetry.<ref>[[#Yau|Yau and Nadis]], pp. 194–195</ref>

Although it was originally developed in this very particular and physically unrealistic context in string theory, the entropy calculation of Strominger and Vafa has led to a qualitative understanding of how black hole entropy can be accounted for in any theory of quantum gravity. Indeed, in 1998, Strominger argued that the original result could be generalized to an arbitrary consistent theory of quantum gravity without relying on strings or supersymmetry.<ref name=Strominger1998/> In collaboration with several other authors in 2010, he showed that some results on black hole entropy could be extended to non-extremal astrophysical black holes.<ref name=Guica/><ref name=CMS/>