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) 2ℓ 2 . 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 ℓ d−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 M d−2k+1 d−2k−1 0 .

Black hole evaporation in Hořava–Lifshitz gravity

“…The black hole evaporation process in = 1 and d = 4, 5 is different from Schwarzschild-AdS because of the existence of the state T = 0 and the third law of the black hole thermodynamics. The black hole evaporation in HL gravity is different from the other higher derivative gravity theories, such as the conformal (Weyl) gravity [48,49] and the Lovelock gravity [50], because the black hole mass in HL gravity can be written as M ∼ d−3 , thus according to the Stefan-Boltzmann law, the lifetime is in the order of…”

“…The maximal value of f (r )/r 2 , which can be used to define the impact factor b c , depends on the exact form of f (r ). Once we obtained the impact factor, according to the Stefan-Boltzmann law, we conclude that in d-dimensional spacetime, the Hawking emission power is [8,50,[53][54][55]…”

“…Inserting the above formulas into the Stefan-Boltzmann law, we can also obtain the result that the lifetime of the black hole is bounded by a time of the order of d−1 [12,50]. In Fig.…”

“…Therefore, it is important to study the various properties of HL black holes. In this work, we shall consider the black hole evaporation process in HL gravity and compare the results with the AdS black hole in Einstein gravity [12] or higher derivative gravity theories [48][49][50].…”

Cosmic censorship and the evolution of d -dimensional charged evaporating black holes

“…Next we need to calculate the cross section of the effective emitting surface of the black hole. We shall assume that the emitted massless particle moves along null geodesics and following [15,28,29], we shall apply the geometrical optics approximation. Orienting the extra (d − 3) angular coordinates in dΩ 2 d−2 and normalizing the affine parameter λ, the geodesic equation of the massless quanta reads dr dλ…”