Related papers: A new method to integrate (2+1)-wave equations wit…
The Klein-Gordon equation for a massive scalar field in the background of a rapidly-rotating Kerr black hole is studied analytically. In particular, we derive a simple formula for the stationary (marginally-stable) resonances of the field…
A (2+1)-static black hole solution with a nonlinear electric field is derived. The source to the Einstein equations is a nonlinear electrodynamics, satisfying the weak energy conditions, and it is such that the energy momentum tensor is…
This work aims to initiate a discussion on finding solutions to non-homoge\-neous differential equations in terms of generalized functions. For simplicity, we conduct the analysis within the specific context of the stationary Klein-Gordon…
We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can…
We investigate two-dimensional higher derivative gravitational theories in a Riemann-Cartan framework and obtain the most general static black hole solutions in conformal coordinates. We also consider the hamiltonian formulation of the…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
I review the classical and quantum properties of the (2+1)-dimensional black hole of Ba{\~n}ados, Teitelboim, and Zanelli. This solution of the Einstein field equations in three spacetime dimensions shares many of the characteristics of the…
We obtain the four-derivative corrections to the Kerr-Sen solution in heterotic supergravity, which includes the Gibbons-Maeda-Garfinkle-Horowitz-Strominger solution as a limiting case. In particular, we first embed the Kerr solution into…
It is generally believed that tidal deformations of a black hole in an external field, as measured using its gravitational field multipoles, vanish. However, this does not mean that the black hole horizon is not deformed. Here we shall…
We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic…
In the Randall-Sundrum two-brane model (RS1), a Kerr black hole on the brane can be naturally identified with a section of rotating black string. To estimate Kaluza-Klein (KK) corrections on gravitational waves emitted by perturbed rotating…
We study numerically in the time domain the linearized gravitational waves emitted from a plunge into a nearly extremal Kerr black hole by solving the inhomogeneous Teukolsky equation. We consider spinning black holes for which the specific…
These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the…
The Dirac equation governs the behaviour of spin-1/2 particles. The equation's separability into decoupled radial and angular differential equations is a crucial step in analytical and numerical computations of quantities like eigenvalues,…
Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired…
We develop a numerical solver, that extends the computational framework considered in [Phys. Rev. D 65, 084016 (2002)], to include scalar perturbations of nonrotating black holes. The nonlinear Einstein-Klein-Gordon equations for a massless…
We study the scalar and spinor perturbation to Kerr-NUT space-time, that is, Klein-Gordan and Dirac equation therein. The equations are invariant under duality transformation between the gravitational electric (M) and magnetic (l) charge,…
In this work we extend the so--called Minimal Geometric Deformation method in $2+1$ dimensional space--times with cosmological constant in order to deal with the gravitational decoupling of two circularly symmetric sources. We find that,…
We study the massless Klein-Gordon equation in the background of the most general rotating dyonic AdS black hole in gauged $\mathcal{N}=2$, $U(1)^{2}$ gauged supergravity in $D=4$, given by Chow and Comp\`{e}re [Phys. Rev. D\textbf{89}…
In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…