TY - JOUR

T1 - A dialogue of multipoles

T2 - Matched asymptotic expansion for caged black holes

AU - Gorbonos, Dan

AU - Kol, Barak

PY - 2004/6/1

Y1 - 2004/6/1

N2 - No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic "mirrors", and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the "Archimedes effect". The next order corrections will appear in a sequel. On the way we determine independently the static perturbations of the Schwarzschild black hole in dimension d ≥ 5, where the system of equations can be reduced to "a master equation" -a single ordinary differential equation. The solutions are hypergeometric functions which in some cases reduce to polynomials.

AB - No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic "mirrors", and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the "Archimedes effect". The next order corrections will appear in a sequel. On the way we determine independently the static perturbations of the Schwarzschild black hole in dimension d ≥ 5, where the system of equations can be reduced to "a master equation" -a single ordinary differential equation. The solutions are hypergeometric functions which in some cases reduce to polynomials.

KW - Black Holes

KW - Extra Large Dimensions

UR - http://www.scopus.com/inward/record.url?scp=8744309889&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2004/06/053

DO - 10.1088/1126-6708/2004/06/053

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AN - SCOPUS:8744309889

SN - 1029-8479

VL - 8

SP - 1311

EP - 1357

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 6

ER -