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One of the unresolved problems in fundamental physics is how to understand black hole entropy microscopically with respect to black hole microstates. Gravitational theories proposing solutions to this problem often include additional higher-derivative terms to the Einstein-Hilbert action of general relativity. The question addressed in this talk is how these higher derivative terms and couplings modify the Bekenstein-Hawking entropy function for a particular type of black hole. We consider an extremal Reissner–Nordstrøm black hole possessing a near-horizon geometry which is given by the product of two-dimensional anti-de Sitter space and a 2-sphere. For this geometry, we use Ashoke Sen’s entropy function formalism to calculate the black hole’s entropy for a gravitational action containing the 4-derivative Gauss-Bonnet term as well as a 6-derivative term describing an electrogravitational coupling. The results of this macroscopic approach will permit comparisons to microscopic calculations provided, for instance, via Siegel modular forms in supergravity and string theories.
[Abstract (PDF)]
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