Black hole evaporation in Lovelock gravity with diverse dimensions

Abstract

We investigate the black hole evaporation process in Lovelock gravity with diverse dimensions. By selecting the appropriate coefficients, the space-time solutions can possess a unique AdS vacuum with a fixed cosmological constant Λ=−(d−1)(d−2)2ℓ2. The black hole solutions can be divided into two cases: d>2k+1 and d=2k+1. In the case of d>2k+1, the black hole is in an analogy with the Schwarzschild AdS black hole, and the life time is bounded by a time of the order of ℓd−2k+1, which reduces Page's result on the Einstein gravity in k=1. In the case of d=2k+1, the black hole resembles the three dimensional black hole. The black hole vacuum corresponds to T=0, so the black hole will take infinite time to evaporate away for any initial states, which obeys the third law of thermodynamics. In the asymptotically flat limit ℓ→∞, the system reduces to the pure Lovelock gravity that only possesses the highest k-th order term. For an initial mass M0, the life time of the black hole is in the order of M0d−2k+1d−2k−1.