Eur. Phys. J. C (2008) 58: 511-516
https://doi.org/10.1140/epjc/s10052-008-0743-y

Regular Article - Theoretical Physics

Truncated heat kernel and one-loop determinants for the BTZ geometry

¹ Departamento de Física, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina, Paraná, Brazil
² Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Niterói, RJ, Brazil

^* e-mail: abyts@uel.br

Received: 26 June 2008
Published online: 29 October 2008

Abstract

There is a special relation between the spectrum and the truncated heat kernel of the Euclidean BTZ black hole which entails the Patterson–Selberg zeta function. Using an orbifold description of this relation we calculate the on-shell corrections of the gravitational quantum fluctuations.