Quantum Tunneling, Blackbody Spectrum and Non-Logarithmic Entropy Correction for Lovelock Black Holes

Abstract

We show, using the tunneling method, that Lovelock black holes Hawking radiate with a perfect blackbody spectrum. This is a new result. Within the semiclassical (WKB) approximation the temperature of the spectrum is given by the semiclassical Hawking temperature. Beyond the semiclassical approximation the thermal nature of the spectrum does not change but the temperature undergoes some higher order corrections. This is true for both black hole (event) and cosmological horizons. Using the first law of thermodynamics the black hole entropy is calculated. Specifically the $D$-dimensional static, chargeless black hole solutions which are spherically symmetric and asymptotically flat, AdS or dS are considered. The interesting property of these black holes is that their semiclassical entropy does not obey the Bekenstein-Hawking area law. It is found that the leading correction to the semiclassical entropy for these black holes is not logarithmic and next to leading correction is also not inverse of horizon area. This is in contrast to the black holes in Einstein gravity. The modified result is due to the presence of Gauss-Bonnet term in the Lovelock Lagrangian. For the limit where the coupling constant of the Gauss-Bonnet term vanishes one recovers the known correctional terms as expected in Einstein gravity. Finally we relate the coefficient of the leading (non-logarithmic) correction with the trace anomaly of the stress tensor.