Related papers: Spacelike matching to null infinity
Normal modes, quasi-normal modes and super-radiant modes are studied to clarify the total dynamics for complex scalar fields in Kerr anti-de Sitter black hole spacetime. Orthonormal relations and quasi-orthonormal relations are obtained for…
This short paper derives the constant of motion of a scalar field in the gravitational field of a Kerr black hole which is associated to a Killing tensor of that space-time. In addition, there is found a related new symmetry operator S for…
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…
Quasinormal modes and power-law late-time decay tails of a charged scalar field on a charged black hole have been considered in the literature, and here we use the hyperboloidal formalism to present an independent comparison to prior…
This brief report presents analytical solutions to the equations of motion of a null string. The background spacetime is a magnetically charged Kaluza-Klein black hole. The string coordinates are expanded with the world-sheet velocity of…
A heuristic method to find asymptotic solutions to a system of non-linear wave equations near null infinity is proposed. The non-linearities in this model, dubbed good-bad-ugly, are known to mimic the ones present in the Einstein field…
We obtain an exact Kerr-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation…
Zero and normal modes for scalar and spinor fields in Kerr-anti de Sitter spacetime are studied as bound state problem with Dirichlet and Neumann boundary conditions. Zero mode is defined as the momentum near the horizon to be zero: $p_{\rm…
We study the global decay properties of solutions to the linear wave equation in 1+3 dimensions on time-dependent, weakly asymptotically flat spacetimes. Assuming non-trapping of null geodesics and a local energy decay estimate, we prove…
We consider the long-time behavior of the massless Dirac equation coupled to a Coulomb potential. For nice enough initial data, we find a joint asymptotic expansion for solutions near the null and future infinities and characterize…
We consider necessary and sufficient conditions for photons emitted from an arbitrary spacetime position of the extremal Kerr black hole to escape to infinity. The radial equation of motion determines the necessary conditions for photons…
We prove uniqueness theorems for asymptotically flat, stationary, extremal, vacuum black hole solutions, in four and five dimensions with one and two commuting rotational Killing fields respectively. As in the non-extremal case, these…
This article examines the analytic solutions of isotropic spacetime with the minimal coupling of scalar field and matter in the context of energy-momentum squared gravity. The scalar field includes quintessence and phantom dark energy…
In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…
We describe a new numerical algorithm for ray tracing in the external spacetimes of spinning compact objects characterized by arbitrary quadrupole moments. Such spacetimes describe non-Kerr vacuum solutions that can be used to test the…
This manuscript is a lightly reformatted version of my 2017 PhD thesis. I am posting it on arXiv at the request of my advisor, Sergiu Klainerman, who noted that it has been useful to some students. The content largely reflects the thesis in…
We study propagation of high-frequency electromagnetic and gravitational waves in the gravitational field of a rotating black hole. Due to the interaction of the spin of the field with the spacetime curvature, the standard geometric optics…
The Klein-Gordon equations were recently solved in general relativity for the case of a plane-symmetric static massless scalar field with cosmological constant. By analytic continuation, time-dependent solutions can be obtained that…
We derive alternate and new closed-form analytic solutions for the non-equatorial eccentric bound trajectories, $\{ \phi \left( r, \theta \right)$, $\ t \left( r, \theta \right),\ r \left( \theta \right) \}$, around a Kerr black hole by…
We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…