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Asymptotics of d-dimensional Kaluza-Klein black holes: beyond the newtonian approximation

Yi-Zen Chu1, Walter D. Goldberger1 and Ira Z. Rothstein2

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We study the thermodynamics of small black holes in compactified spacetimes of the form Rd−1 × S1. This system is analyzed with the aid of an effective field theory (EFT) formalism in which the structure of the black hole is encoded in the coefficients of operators in an effective worldline Lagrangian. In this effective theory, there is a small parameter λ that characterizes the corrections to the thermodynamics due to both the non-linear nature of the gravitational action as well as effects arising from the finite size of the black hole. Using the power counting of the EFT we show that the series expansion for the thermodynamic variables contains terms that are analytic in λ, as well as certain fractional powers that can be attributed to finite size operators. In particular our operator analysis shows that existing analytical results do not probe effects coming from horizon deformation. As an example, we work out the order λ2 corrections to the thermodynamics of small black holes for arbitrary d, generalizing the results in the literature.

Keywords

Black Holes

Classical Theories of Gravity

Extra Large Dimensions

 

E-print Number: hep-th/0602016

Cited: by |

Refers: to

PACS

04.50.-h Higher-dimensional gravity and other theories of gravity

11.10.Ef Lagrangian and Hamiltonian approach

04.25.Nx Post-Newtonian approximation; perturbation theory; related approximations

04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics

Subjects

Gravitation and cosmology

Particle physics and field theory

Dates

Issue 03 (March 2006)

Received 3 February 2006, accepted for publication 6 February 2006

Published 2 March 2006



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