Abstract
The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (e.g. Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this ‘black hole surface’ (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for ‘black droplets’, i.e. black holes localized at the boundary of AdS, and for non-uniform black strings.
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ArXiv ePrint: 1504.06489
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Emparan, R., Shiromizu, T., Suzuki, R. et al. Effective theory of black holes in the 1/D expansion. J. High Energ. Phys. 2015, 159 (2015). https://doi.org/10.1007/JHEP06(2015)159
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DOI: https://doi.org/10.1007/JHEP06(2015)159