相关论文: A note on boundary value problems for black hole e…

In numerical computations of Einstein's equations for black hole spacetimes, it will be necessary to use approximate boundary conditions at a finite distance from the holes. We point out here that ``tails,'' the inverse power-law decrease…

A well-known open problem in general relativity, dating back to 1972, has been to prove Price's law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation flux on…

Schwarzschild black holes evolve toward their static configuration by emitting gravitational waves, which decay over time following a power law at fixed spatial positions. We derive this power law analytically for the second-order even…

A numerical study of the evolution of a massless scalar field in the background of rotating black holes is presented. First, solutions to the wave equation are obtained for slowly rotating black holes. In this approximation, the background…

We prove the global leading-order late-time asymptotic behaviour of solutions to inhomogeneous wave equations on dynamical black hole exterior backgrounds that settle down to Schwarzschild backgrounds with arbitrarily small decay rates. In…

Price's Law states that linear perturbations of a Schwarzschild black hole fall off as $t^{-2\ell-3}$ for $t \to \infty$ provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially…

The evolution of scalar, electromagnetic and gravitational fields around spherically symmetric black hole surrounded by quintessence are studied with special interest on the late-time behavior. In the ring down stage of evolution, we find…

We consider a spherically symmetric characteristic initial value problem for the Einstein-Maxwell-scalar field equations. On the initial outgoing characteristic, the data is assumed to satisfy the Price law decay widely believed to hold on…

Power law tails induced by nonlinearities of General Relativity (``sourced'' or ``nonlinear'' tails) were recently shown to dominate the late time waveform of Schwarzschild black hole ringdowns. We extend the analytical results regarding…

Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field…

We studied the eigenvalue problem of scalar fields in the (2+1)-dimensional BTZ black hole spacetime. The Dirichlet boundary condition at infinity and the Dirichlet or the Neumann boundary condition at the horizon are imposed. Eigenvalues…

We study the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved…

We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry…

We introduce a general method for understanding the late time tail for solutions to wave equations on asymptotically flat spacetimes with odd space dimensions. In particular, for a large class of equations, we prove that the precise late…

We prove sharp pointwise $t^{-3}$ decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates…

Nonlinear tails in black hole perturbations, arising from second-order effects, present a distinct departure from the well-known Price tail of linear theory. We present an analytical derivation of the power law indices and amplitudes for…

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the…

This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…

Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known to possess (monopole) scalar hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as a neutron…

The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…