标题： 二阶微扰的施瓦茨希尔德黑洞：包含奇宇称微扰 显示英文标题

标题： Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations

摘要： 我们考虑了史瓦西黑洞的扰动，这些扰动可以是偶宇称和奇宇称的，在扰动理论的二阶项范围内，针对$\ell=2$轴对称情况。 我们利用 Regge-Wheeler-Zerilli 方法推导了演化方程和辐射能量及波形的显式公式。 这种表述对于处理“接近极限近似”中反向旋转黑洞碰撞的情况是有用的。 显示英文摘要

摘要： We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the $\ell=2$ axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for the treatment in the ``close limit approximation'' of the collision of counterrotating black holes.