In this work, we extend the study in Bilic and Fabris (2022 J. High Energy Phys. 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 (GB) 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 GB 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 GB 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 GB gravity near the AdS boundary.

中文翻译：

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Gauss-Bonnet AdS 平面和球面黑洞热力学和全息术


在这项工作中，我们扩展了 Bilic 和 Fabris （2022 J. High Energy Phys. JHEP11（2022）013） 的研究，结合了 AdS/CFT 对偶性，以建立大型 （AdS） 球形黑洞和 （AdS） 平面施瓦西黑洞在 AdS 边界附近的局部温度（托尔曼温度）之间的关系考虑到引力作用中的高斯-邦尼特 （GB） 曲率校正。我们已经证明，由于本体中包含 GB 项，因此在局部温度关系中出现较高的曲率校正。通过将度量转换为 Fefferman-Graham 形式，我们计算了边界处保形流体的能量密度。所得结果包含有限耦合校正，这些校正是由体理论中的 GB 曲率校正全息引起的。遵循众所周知的流体/重力对偶方法，然后将边界处保形流体的能量密度与黑体辐射能量密度进行比较。该比较表明，能量密度与保形流体的温度成正比。然后显示保形流体的温度与黑洞的托尔曼温度有关，这最终帮助我们在 AdS 边界附近的 GB 引力中建立大型球对称和平面史瓦西黑洞之间的霍金温度和托尔曼温度关系。