arXiv subjects

Alessandro D. A. M. Spallicci

Publications and source records attributed to Alessandro D. A. M. Spallicci.

38 records · Page 3Linked to original sources

arXiv1999

Analytic solution of the Regge-Wheeler differential equation for black hole pertubations in radial coordinate and time domains

An analytic solution of the Regge-Wheeler (RW) equation has been found via the Frobenius method at the regular singularity of the horizon 2M, in the form of a time and radial coordinate dependent series. The RW partial differential equation, derived from the Einstein field equations, represents the first order perturbations of the Schwarzschild metric. The known solutions are numerical in time domain or approximate and asymptotic for low or high frequencies in Fourier domain. The former is of scarce relevance for comprehension of the geodesic equations for a body in the black hole field, while the latter is mainly useful for the description of the emitted gravitational radiation. Instead a time domain solution is essential for the determination of radiation reaction of the falling particle into the black hole, i.e. the influence of the emitted radiation on the motion of the perturbing mass in the black hole field. To this end, a semi-analytic solution of the inhomogeneous RW equation with the source term (Regge-Wheeler-Zerilli equation) shall be the next development.

gr-qc↗

arXiv1998

On the perturbed Schwarzschild geometry for determination of particle motion

A novel method for calculation of the motion and radiation reaction for the two-body problem (body plus particle, the small parameter m/M being the ratio of the masses) is presented. In the background curvature given by the Schwarzschild geometry rippled by gravitational waves, the geodesic equations insure the presence of radiation reaction also for high velocities and strong field. The method is generally applicable to any orbit, but radial fall is of interest due to the non-adiabatic regime (equality of radiation reaction and fall time scales), in which the particle locally and immediately reacts to the emitted radiation. The energy balance hypothesis is only used (emitted radiation equal to the variation in the kinetic energy) for determination of the 4-velocity via the Lagrangian and normalization of divergencies. The solution in time domain of the Regge-Wheeler-Zerilli-Moncrief radial wave equation determines the metric tensor expressing the polar perturbations, in terms of which the geodesic equations are written and shown herein.

gr-qc↗