Hořava–Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter \(0\leqslant \epsilon ^2\leqslant 1\). We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with \(d=4,5\) behave differently from \(d\geqslant 6\). For the case of \(\epsilon =0\), in \(d=4,5\), the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As \(d\geqslant 6\), however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of \(\ell ^{d-1}\), similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to \(\epsilon ^2=1\)), though for the latter this holds for all \(d\geqslant 4\). The case of \(0<\epsilon ^2<1\) is also qualitatively similar with \(\epsilon =0\).

中文翻译：

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Hořava–Lifshitz重力中的黑洞蒸发

制定Hořava–Lifshitz（HL）引力，是为了解决爱因斯坦引力的非重归一化问题和高导数引力理论中的鬼影问题，这是通过违反洛伦兹不变性来解决的。在这项工作中，我们考虑了在不同时空尺寸d下的HL重力下的球对称中性AdS黑洞蒸发过程，并且具有详细的平衡违反参数\（0 \ leqslant \ epsilon ^ 2 \ leqslant 1 \）。我们发现在霍金蒸发条件下黑洞的寿命与尺寸有关，\（d = 4,5 \）的行为与\（d \ geqslant 6 \）不同。对于\（\ epsilon = 0 \）的情况，在\（d = 4,5 \）中，黑洞允许处于零温度状态，并且黑洞的寿命始终是无限的。这种现象符合黑洞热力学的第三定律，并暗示黑洞在蒸发结束时变成有效的残余物。但是，作为\（d \ geqslant 6 \），黑洞的寿命不会随任何初始黑洞质量而发散，并且其受时间限制为\（\ ell ^ {d-1} \），类似于爱因斯坦引力中Schwarzschild-AdS的情况（对应于\（\ epsilon ^ 2 = 1 \）），尽管对于后者，这适用于所有\（d \ geqslant 4 \）。的情况下\（0 <\小量^ 2 <1 \）也与性质上相似\（\小量= 0 \） 。