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Gauss-Bonnet AdS平面和球对称黑洞热力学及全息

Gauss-Bonnet AdS planar and spherical black hole thermodynamics and holography

Souvik Paul, Sunandan Gangopadhyay, Ashis Saha

备注：
v1: 17 pages LaTex, v2: 23 pages & multiple new figures, to appear in Classical and Quantum Gravity
发表信息：
Classical and Quantum Gravity 41 (2024) 235010
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AI总结：

本研究扩展JHEP11(2022)013，利用AdS/CFT对偶和Gauss-Bonnet修正，建立球对称与平面Schwarzschild黑洞在AdS边界附近的Tolman温度关系，并计算共形流体能量密度，验证其与温度成正比。

摘要：

在本工作中，我们扩展了JHEP11(2022)013中的研究，结合AdS/CFT对偶，在引力作用中加入Gauss-Bonnet曲率修正，建立了靠近AdS边界的大（AdS）球对称和（AdS）平面Schwarzschild黑洞的局部温度（Tolman温度）之间的关系。我们证明了由于在体中加入Gauss-Bonnet项，高阶曲率修正出现在局部温度关系中。通过将度规变换为Fefferman-Graham形式，我们计算了边界处共形流体的能量密度。所得结果包含有限耦合修正，这些修正是由体理论中的Gauss-Bonnet曲率修正全息诱导的。遵循流体/引力对偶的已知方法，将边界处共形流体的能量密度与黑体辐射能量密度进行比较。比较表明，能量密度与共形流体的温度成正比。然后证明共形流体的温度与黑洞的Tolman温度相关，这最终帮助我们建立了在Gauss-Bonnet引力中靠近AdS边界的大球对称和平面Schwarzschild黑洞之间的Hawking温度和Tolman温度关系。

英文摘要：

In this work, we extend the study in \href{https://link.springer.com/article/10.1007/JHEP11(2022)013}{JHEP11(2022)013} incorporating the AdS/CFT duality to establish a relationship between the local temperatures (Tolman temperatures) of a large (AdS) spherical and a (AdS) planar Schwarzschild black hole near the AdS boundary considering Gauss-Bonnet curvature correction in the gravitational action. We have shown that the higher curvature corrections appear in the local temperature relationship due to the inclusion of Gauss-Bonnet term in the bulk. By transforming the metric into Fefferman-Graham form, we have calculated the energy density of the conformal fluid at the boundary. The obtained result contains finite coupling corrections which are holographically induced by the Gauss-Bonnet curvature correction in the bulk theory. Following the well known approach of fluid/gravity duality, the energy density of the conformal fluid at the boundary is then compared with the black body radiation energy density. This comparison shows that the energy density is proportional to the temperature of the conformal fluid. The temperature of the conformal fluid is then shown to be related to the Tolman temperature of the black hole which then eventually helps us to establish both the Hawking temperature and Tolman temperature relationship between large spherically symmetric and planar Schwarzschild black holes in Gauss-Bonnet gravity near the AdS boundary.

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