String theory: Difference between revisions

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=== Derivation within string theory ===

In a paper from 1996, [[Andrew Strominger]] and [[Cumrun Vafa]] showed how to derive the Beckenstein–HawkingBekenstein–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>