标题： 偶宇称引力理论中黑洞扰动 显示英文标题

标题： Even-parity black hole perturbations in Minimal Theory of Bigravity

摘要： 我们研究最小双引力理论(MTBG)中偶宇称黑洞扰动。 我们考虑在自加速分支中以空间平坦坐标写出的施瓦茨希尔德解作为背景解。 我们明确了在联合保叶微分同胚变换下，$\ell=0$、$1$和$\geq2$模式的规范变换，其中$\ell$是角多重极矩。 要求物理和参考部分的渐近区域共享相同的闵可夫斯基真空，$\ell=0$扰动的解可以通过重新定义施瓦茨希尔德背景来吸收。 为了分析$\ell=1$和$\geq 2$模式，为简化起见，我们专注于有效无质量的情况，其中测量两个部分之间固有时比的常数参数被设为1，且运动方程中的有效质量项消失。 我们还发现，当在空间无穷远处施加正则性条件时，所有的$\ell=1$摄动都消失。 对于每个$\ell\geq 2$模式，在有效无质量的情况下，我们强调了预期的两个传播模式和四个瞬时模式的存在。 显示英文摘要

摘要： We study even-parity black hole perturbations in Minimal Theory of Bigravity (MTBG). We consider the Schwarzschild solution written in the spatially-flat coordinates in the self-accelerating branch as the background solution. We clarify the gauge transformations for the $\ell=0$, $1$, and $\geq2$ modes with $\ell$ being the angular multipole moments under the joint foliation-preserving diffeomorphism transformation. Requiring that the asymptotic regions in the physical and fiducial sectors share the same Minkowski vacua, the solution to the $\ell=0$ perturbations can be absorbed by a redefinition of the Schwarzschild background. In order to analyze the $\ell=1$ and $\geq 2$ modes, for simplicity we focus on the effectively massless case, where the constant parameter measuring the ratio of the proper times between the two sectors is set to unity and the effective mass terms in the equations of motion vanish. We also find that as a particular solution all the $\ell=1$ perturbations vanish by imposing their regularity at spatial infinity. For each of the $\ell\geq 2$ modes, in the effectively massless case, we highlight the existence of the expected two propagating modes and four instantaneous modes.