Gravitational Field of a Particle Falling in a Schwarzschild Geometry Analyzed in Tensor Harmonics

Sources of Gravitational Waves: Theory and Observations

“…(6.1) with η µν replaced by the background metric g µν and the higher-order terms Λ µν neglected.] Those equations were derived in 1950's and 1970's for the metric perturbations by Regge-Wheeler and Zerilli (RWZ) [202,203] in the Schwarzschild case, and for the curvature perturbations by Teukolsky [204] in the Kerr case. Using suitable gauges, those equations (or variants of them [205]) can be integrated analytically, for quasi-circular orbits, by PN expansion in powers of v/c, v being the velocity of the small body, obtaining the gravitational radiation and luminosity at very high PN orders.…”

“…Concretely, they used the EOB formalism to compute the trajectory followed by an object spiraling and plunging into a much larger BH, and then used that trajectory in the source term of either the time-domain RWZ [202,203] or Teukolsky equation [204]. Solving those equations is significantly less expensive than evolving a BH binary in full numerical relativity.…”

Hybrid approach to black hole perturbations from extended matter sources

“…In the RWZ approach [1,2], the equations describing the radial behavior of the perturbations of a Schwarzschild black hole are reduced to two wave equations after expanding all perturbed tensors in tensorial spherical harmonics and after separating the radial from the angular part. In particular, they are expressed for two suitable combinations of the components of the perturbed metric tensor and which are referred to as the Zerilli function, Z 'm , and the Regge-Wheeler function,Z ÿ 'm , respectively.…”

“…The first one is by F. Zerilli [2], who derived the radial equation governing the polar perturbations of a Schwarzschild black hole, thus completing the work of Regge and Wheeler (see [3] for a recent review). The second one is by S. Teukolsky [4], who achieved the formidable task of reducing the equations for the perturbations of a Kerr black hole to a master radial equation.…”

Hot plasma waves surrounding the Schwarzschild event horizon in a Veselago medium

“…Regge and Wheeler [1] concluded that the Schwarzschild singularity remains stable when a small non-spherical odd-parity perturbation is introduced. Zerilli [2] explored the same stability problem by considering an even parity perturbation. The behavior of electric field generated by a charged particle at rest near the Schwarzschild black hole was discussed by Hanni and Ruffini [3].…”