Palatini Kalb-Ramond引力中的精确黑洞解
Exact black hole solutions in Palatini Kalb-Ramond gravity
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中文总结 AI 辅助
该研究在Palatini Kalb-Ramond引力中求得精确静态球对称黑洞解，推导修正场方程并验证热力学定律，通过水星进动等观测给出洛伦兹破缺参数的最强约束。
中文摘要 AI 辅助
我们研究了Palatini Kalb-Ramond引力中的静态球对称黑洞，其中Kalb-Ramond场的非零真空期望值自发破缺了局域洛伦兹对称性。将度规和无挠仿射联络视为独立变量，我们推导了修正场方程，并获得了包含宇宙学常数$\Lambda$为正、零和负值的一族精确解。与相应的纯度规表述不同，Palatini理论一致地允许两个洛伦兹破缺参数$\ell_1$和$\ell_2$同时非零。利用Iyer-Wald形式，我们确定了黑洞解的守恒质量。对于$\Lambda\leq0$区域，我们进一步验证了第一定律和Smarr关系，将守恒质量识别为热力学焓。然后我们将$\Lambda=0$解与水星近日点进动、太阳光线偏折和Shapiro时间延迟进行对比。一旦中心质量参数通过行星动力学校准，这些可观测量仅通过$q\equiv\ell_2/(1-\ell_1)$约束洛伦兹破缺参数。在这些测试中，水星近日点进动给出了最严格的约束，$-7.4\times10^{-12} \leq q \leq 3.7\times10^{-11}$。
英文摘要
We investigate static and spherically symmetric black holes in Palatini Kalb-Ramond gravity, where a nonzero vacuum expectation value of the Kalb-Ramond field spontaneously breaks local Lorentz symmetry. Treating the metric and the torsion-free affine connection as independent variables, we derive the modified field equations and obtain an exact family of solutions encompassing positive, vanishing, and negative values of the cosmological constant $Λ$. Unlike the corresponding purely metric formulation, the Palatini theory consistently allows both Lorentz-violating parameters $\ell_1$ and $\ell_2$ to be nonzero. Using the Iyer-Wald formalism, we determine the conserved mass of the black hole solutions. For the $Λ\leq0$ sector, we further verify the first law and the Smarr relation, identifying the conserved mass as the thermodynamic enthalpy. We then confront the $Λ=0$ solution with Mercury's perihelion precession, solar light deflection, and the Shapiro time delay. Once the central mass parameter is calibrated by planetary dynamics, these observables constrain the Lorentz-violating parameters only through $q\equiv\ell_2/(1-\ell_1)$. Among these tests, Mercury's perihelion precession yields the most stringent constraint, $-7.4\times10^{-12} \leq q \leq 3.7\times10^{-11}$.
发表机构
- School of Physical Science and Technology, Southwest University（西南大学物理科学与技术学院）
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