发表机构
University of Hradec Králové（赫拉德茨克拉洛韦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究共形魏尔引力中曼海姆-卡扎纳斯黑洞的德西特分支，分析其视界存在条件，比较不同温度约定并计算沃尔德熵，提出局域视界热力学描述。
AI 中文摘要
共形魏尔引力中的静态黑洞与爱因斯坦引力中的对应黑洞存在简单但重要的差异：曼海姆-卡扎纳斯几何由巴赫平直的 lapse 函数描述，其径向依赖关系比史瓦西-德西特几何更为丰富。我们在史瓦西规范下研究该解的德西特分支，保留特征线性项与二次德西特项。在与正质量史瓦西-德西特时空连续连接的分支中，当满足以下条件时，黑洞视界与宇宙学视界之间存在规则静态区域：-1/3 < βγ < 2/3，0 < κ < (1+3βγ)/(27β²)。在该参数窗口内，原点处的奇点被隐藏，两个正视界满足0 < r_b < 3β < r_c，极限端点为纳里亚几何。其热力学解释比根结构更为微妙：两个视界通常具有不同温度，且静态片不存在可选择唯一时间归一化的渐近区域。因此，我们比较了基林温度、布索-霍金归一化温度、托尔曼局域温度以及双视界有效温度约定，并计算了纯魏尔平方作用量对应的沃尔德熵。所得结果为局域视界热力学描述，其将几何事实与全局第一定律所需的依赖系综的选择相分离。
英文摘要
Static black holes in conformal Weyl gravity differ from their Einstein counterparts in a simple but important way: the Mannheim--Kazanas geometry is encoded in a Bach-flat lapse function whose radial dependence is richer than that of Schwarzschild--de Sitter. We study the de Sitter branch of this solution in the Schwarzschild gauge, keeping the characteristic linear term together with the quadratic de Sitter term. In the branch continuously connected to the positive-mass Schwarzschild--de Sitter spacetime, a regular static region between a black-hole horizon and a cosmological horizon exists precisely when \[ -\frac{1}{3}<βγ<\frac{2}{3}, \qquad 0<κ<\frac{1+3βγ}{27β^{2}}. \] In this window the singularity at the origin is hidden, the two positive horizons obey $0<r_b<3β<r_c$, and the limiting endpoint is the Nariai geometry. The thermodynamic interpretation is subtler than the root structure: the two horizons generally have different temperatures, and the static patch has no asymptotic region that would select a unique normalization of time. We therefore compare the Killing, Bousso--Hawking normalized, Tolman local, and effective two-horizon temperature conventions, and we compute the corresponding Wald entropy for the pure Weyl-squared action. The result is a local horizon thermodynamic description that keeps the geometric facts separate from the ensemble-dependent choices needed for any global first law.
Comments11 pages, 3 figures
Journal refInternational Journal of Gravitational and Theoretical Physics 2(3), 3 2026
DOI：10.53941/ijgtp.2026.100017
