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arXiv 2012.02723gr-qcastro-ph.HEhep-th
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量子度规涨落引起的修正引力下的黑洞解

Black hole solutions in modified gravity induced by quantum metric fluctuations

Jin-Zhao Yang, Shahab Shahidi, Tiberiu Harko, Shi-Dong Liang

摘要:

在几何作用量中包含度规的量子涨落是理解引力量子性质的一个有希望的途径。在这种方法中,度量被分解为经典和波动部分的和,量子起源,其通常可以表示为任意的二阶张量,从度量构造,并从描述物质场的热力学量。本文研究了量子涨落对由变分原理得到的修正场方程的球对称静态黑洞解的影响,假设量子修正张量由标量场与度规张量的耦合给出.通过引入一个合适的独立径向坐标系,将场方程转化为无量纲形式,得到了它们的数值解。我们检测到的形成一个黑洞从存在的奇异性的度量张量分量。几种模型,对应于不同的功能形式的标量场潜力,被认为是。研究了黑洞解的热力学性质(视界温度、比热、熵和Hawking光度蒸发时间)。

英文摘要:

The inclusion of the quantum fluctuations of the metric in the geometric action is a promising avenue for the understanding of the quantum properties of gravity. In this approach the metric is decomposed in the sum of a classical and of a fluctuating part, of quantum origin, which can be generally expressed in terms of an arbitrary second order tensor, constructed from the metric, and from the thermodynamic quantities describing matter fields. In the present paper we investigate the effects of the quantum fluctuations on the spherically symmetric static black hole solutions of the modified field equations, obtained from a variational principle, by assuming that the quantum correction tensor is given by the coupling of a scalar field to the metric tensor. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, we obtain their solutions numerically. We detect the formation of a black hole from the presence of a singularity in the metric tensor components. Several models, corresponding to different functional forms of the scalar field potential, are considered. The thermodynamic properties of the black hole solutions (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also investigated.

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