Related papers: A slightly less grand challenge: Colliding Black H…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
We evaluate how much energy can be converted into gravitational radiation in head-on collision of black holes. We estimate it by the area theorem of black hole horizon incorporating merging entropy of colliding black holes from a viewpoint…
The close-limit method has given approximations in excellent agreement with those of numerical relativity for collisions of equal mass black holes. We consider here colliding holes with unequal mass, for which numerical relativity results…
Perturbative calculations of gravitational radiation near the horizons of rotating black holes in the frequency domain have been plagued by divergence issues. We resolve this longstanding obstacle by constructing a nonsingular source term…
We present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of…
Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.
A powerful technique to calculate gravitational radiation from binary systems involves a perturbative expansion: if the masses of the two bodies are very different, the "small" body is treated as a point particle of mass $m_p$ moving in the…
In this paper, perturbations of an accretion disk by a star orbiting around a black hole are studied. We report on a numerical experiment, which has been carried out by using a parallel-machine code originally developed by D\"{o}nmez…
We present the derivation and the solutions to the coupled electromagnetic and gravitational perturbations with sources in a charged black hole background. We work in the so called ghost gauge and consider as source of the perturbations the…
This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes…
Largely motivated by the development of highly sensitive gravitational-wave detectors, our understanding of merging compact binaries and the gravitational waves they generate has improved dramatically in recent years. Breakthroughs in…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
We summarize the state of the art of the ``close approximation'' to black hole collisions. We discuss results to first and second order in perturbation theory for head-on collisions of momentarily-stationary and non-stationary black holes…
The major source of ground-based gravitational wave detectors, the inspiral and merger of comparable mass binary black holes (BBH), consists of a slow quasicircular inspiral, a merger to form a single remnant hole, and the quasinormal…
Motivated by neutrino astronomy, we consider a plane wave of coupled and massive flavours, scattered by a static black hole, and describe analytically and numerically the corresponding oscillation probability in the surrounding space. Both…
We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close-approximation perturbative calculations but they reveal…
We discuss the initial value problem of general relativity in its recently unified Lagrangian and Hamiltonian pictures and present a multi-domain pseudo-spectral collocation method to solve the resulting coupled nonlinear partial…
Homotopy perturbation is one of the newest methods for numerical analysis of deferential equations. We have used for solving wave equation around a black hole. Our conclusions have this method far reaching consequences for comparison of…
Within the effective field theory approach to gravity, deviations from general relativity can be systematically described by higher-curvature operators. However, computing the resulting corrections to black hole quasinormal mode spectra…
We develop a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it…