Lousto CO
Max-Planck-Institut fur Gravitationsphysik, Albert-Einstein-Institut, Am Muhlenberg 1, D-14476 Golm, Germany, and Instituto de Astronomia y Fisica del Espacio-CONICET, Buenos Aires, Argentina.
Phys Rev Lett. 2000 Jun 5;84(23):5251-4. doi: 10.1103/PhysRevLett.84.5251.
We study the relativistic orbit of binary black holes in systems with small mass ratio. The trajectory of the smaller object (another black hole or a neutron star), represented as a particle, is determined by the geodesic equation on the perturbed massive black hole spacetime. Here we study perturbations around a Schwarzschild black hole using Moncrief's gauge invariant formalism. We decompose the perturbations into l multipoles to show that all l-metric coefficients are C0 at the location of the particle. Summing over l, to reconstruct the full metric, gives a formally divergent result. We succeed in bringing this sum to a Riemann's zeta-function regularization scheme and numerically compute the first-order geodesics.
我们研究了质量比小的系统中双黑洞的相对论轨道。较小天体（另一个黑洞或中子星）的轨迹被表示为一个粒子，它由扰动的大质量黑洞时空上的测地线方程决定。在这里，我们使用蒙克里夫规范不变形式研究围绕史瓦西黑洞的扰动。我们将扰动分解为l阶多极子，以表明所有l度规系数在粒子位置处都是C0连续的。对l求和以重建完整度规，会得到一个形式上发散的结果。我们成功地将这个和引入黎曼ζ函数正则化方案，并数值计算了一阶测地线。
