非对易施瓦西黑洞的热力学及其量子修正

Thermodynamics and its quantum correction of non-commutative Schwarichild black hole

为了探讨量子引力效应对黑洞量子性质的影响,本文研究了非对易黑洞的热力学及其量子修正.首先,利用修正的黑洞热力学第一定律,对非对易施瓦西黑洞的热力学量进行了计算.结果表明,利用修正的热力学第一定律得到的非对易黑洞温度与利用表面引力和隧穿方法得到的温度相同,而且黑洞熵符合贝肯斯坦-霍金面积定律.对得到的黑洞热容进行分析,发现在视界半径与非对易参数满足一定条件时,热容可以为正值,非对易黑洞可以具有热力学稳定性.其次,讨论了广义不确定原理对非对易施瓦西黑洞热力学的影响,给出了广义不确定原理修正的黑洞温度、熵和热容表达式,其中得到的黑洞熵包含面积对数项.在忽略广义不确定原理效应的情况下,修正的黑洞熵可以回到贝肯斯坦-霍金面积定律的情况.同样,修正的黑洞温度和热容也可以在忽略量子引力效应时回到通常施瓦西黑洞的情况.

Black hole thermodynamics establishes a deep and satisfying link to gravity, thermodynamics, and quantum theory. And, the thermodynamic property of black hole is essentially a quantum feature of gravity. In this paper, in order to study the influence of the quantum gravity effect on the quantum properties of black hole, we study the thermodynamics and its quantum correction to a non-commutative black hole. First of all,the temperature of the non-commutative Schwarichild black hole is calculated by using three different methods:surface gravity, tunneling effects and the first law of black hole thermodynamics. It is found that the same hole temperature is obtained by means of the surface gravity and tunneling effects. However, by using the first law of black hole thermodynamics, different results are derived from the first two methods. Therefore, we incline to the result obtained by surface gravity and tunneling effects, and the temperature obtained by the thermodynamic law needs modifying. That is, for the non-commutative black hole, there is a contradiction to the first law of thermodynamics. To calculate the temperature and other thermodynamic quantities for the noncommutative Schwarichild black hole, we use the corrected first law of black hole thermodynamics proposed in the literature. It is found that the black hole temperature derived by the corrected first law is the same as the temperature obtained by the surface gravity and the tunneling model, and the black hole entropy still follows Beckenstein-Hawking area law. Also, the heat capacity of the black hole is obtained and analyzed. It is seen that when the horizon radius and non-commutative parameter satisfy the particular conditions, the heat capacity is positive and the non-commutative black holes are thermodynamically stable. This is a different result from that of the usual Schwarichild black hole. Further, by studying the influence of generalized uncertainty principle on non-commutative black hole thermodynamics, the quantum corrections from generalized uncertainty principle for temperature, entropy and heat capacity of the non-commutative Schwarzschild black hole are given. It is found that with considering this quantum gravity effect, the obtained black hole entropy contains the item of are alogarithm. If the effect of the generalized uncertainty principle is neglected, the corrected black hole entropy can return to that in the usual case of Beckenstein-Hawing area law.Similarly, the corrected black hole temperature and heat capacity can also return to their counterparts in the case of usual Schwarzschild black hole when this quantum gravity effect is ignored.