论文标题
Kerr黑洞的稳定性在广义杂交公制 - 帕拉蒂尼重力
Stability of Kerr black holes in generalized hybrid metric-Palatini gravity
论文作者
论文摘要
结果表明，KERR解决方案存在于广义杂交公制 - 帕拉蒂尼重力理论中，并且对于函数的某些选择$ f（r，\ mathcal r）$，该理论的特征是稳定的，Kerr解决方案可以稳定在理论的标量自由度上扰动。我们首先验证哪些是函数$ f（R，\ Mathcal r）$的最通用条件，该函数允许一般相对论KERR解决方案也成为该理论的解决方案。我们在度量张量的轨迹中执行标量扰动，这又在RICCI和Palatini标量曲线中施加了扰动。要在扰动中的第一阶，可以根据扰动$ΔR$的第四阶波方程来重写运动方程，即与RICCI和Palatini曲率标量相关的场方程和方程，可以将其分解为两个第二阶质量质量波动方程的相同变量。使用通常的ANSATZ和分离方法，并获得RICCI标量扰动的有效质量的稳定性界限。这些稳定性制度是根据情况研究的，并获得了允许稳定的KERR解决方案存在的函数$ f（R，\ Mathcal R）$的特定形式。
It is shown that the Kerr solution exists in the generalized hybrid metric-Palatini gravity theory and that for certain choices of the function $f(R,\mathcal R)$ that characterizes the theory, the Kerr solution can be stable against perturbations on the scalar degree of freedom of the theory. We start by verifying which are the most general conditions on the function $f(R,\mathcal R)$ that allow for the general relativistic Kerr solution to also be a solution of this theory. We perform a scalar perturbation in the trace of the metric tensor, which in turn imposes a perturbation in both the Ricci and Palatini scalar curvatures. To first order in the perturbation, the equations of motion, namely the field equations and the equation that relates the Ricci and the Palatini curvature scalars, can be rewritten in terms of a fourth-order wave equation for the perturbation $δR$ which can be factorized into two second-order massive wave equations for the same variable. The usual ansatz and separation methods are applied and stability bounds on the effective mass of the Ricci scalar perturbation are obtained. These stability regimes are studied case by case and specific forms of the function $f(R,\mathcal R)$ that allow for a stable Kerr solution to exist within the perturbation regime studied are obtained.
