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The large D limit of General Relativity

Roberto Emparan
(
)
,
Ryotaku Suzuki
(
- Kyoto U.
)
,
Kentaro Tanabe
(
- Barcelona U., Dept. Fund. Phys. and
- ICC, Barcelona U.
)

Feb 26, 2013

48 pages

Published in:

JHEP 06 (2013) 009

e-Print:

1302.6382 [hep-th]

DOI:

10.1007/JHEP06(2013)009

View in:

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Abstract: (Springer)

General Relativity simplifies dramatically in the limit that the number of spacetime dimensions D is infinite: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor absorb radiation of any finite frequency. Non-trivial black hole dynamics occurs at length scales that are 1/D times smaller than the horizon radius, and at frequencies D times larger than the inverse of this radius. This separation of scales at large D, which is due to the large gradient of the gravitational potential near the horizon, allows an effective theory of black hole dynamics. We develop to leading order in 1/D this effective description for massless scalar fields and compute analytically the scalar absorption probability. We solve to next-to-next-to-leading order the black brane instability, with very accurate results that improve on previous approximations with other methods. These examples demonstrate that problems that can be formulated in an arbitrary number of dimensions may be tractable in analytic form, and very efficiently so, in the large D expansion.

Note:

50 pages, 2 figures; v3: improved discussion of conceptual points

black brane: stability
space-time: dimension
field theory: scalar: massless
higher-order: 2
higher-order: 0
black hole
general relativity
perturbation theory
dimension: infinite
scalar particle: absorption

References(50)

Figures(2)

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