Related papers: Quasilinear wave equations on Schwarzschild-de Sit…
We derive precise late-time asymptotics for solutions to the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes including as special cases the Schwarzschild and Reissner-Nordstrom families of black holes.…
A class of nonstationary spacetimes is obtained by means of a conformal transformation of the Schwarzschild metric, where the conformal factor $a(t)$ is an arbitrary function of the time coordinate only. We investigate several situations…
Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in…
We apply a new analytic scheme, developed in a preceding paper, in order to calculate the late time behavior of scalar test fields evolving outside a Schwarzschild black hole. The pattern of the late time decay at future null infinity is…
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…
By using a quasi-stationary approach, we consider the mass evolution of Schwarzschild black holes in the presence of a nonminimally coupled cosmological scalar field. The mass evolution equation is analytically solved for generic coupling,…
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…
It has long been suggested that solutions to linear scalar wave equation $$\Box_g\phi=0$$ on a fixed subextremal Reissner-Nordstr\"om spacetime with non-vanishing charge are generically singular at the Cauchy horizon. We prove that generic…
Time evolution of a black hole lattice universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of opposite faces. Defining…
Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain…
We present a fully analytic treatment of Schwarzschild--de~Sitter (SdS) black-hole evaporation in two-dimensional dilaton gravity with anomaly-induced backreaction. Starting from the spherical reduction of four-dimensional Einstein gravity…
We present a systematic method for constructing static, spherically symmetric regular spacetimes in general relativity satisfying the weak energy condition. Our approach relies on physically reasonable assumptions on the matter energy…
In this note, we use an elementary argument to show that the existence and unitarity of radiation fields implies asymptotic partition of energy for the corresponding wave equation. This argument establishes the equipartition of energy for…
In this article, we investigate the blow-up for local solutions to a semilinear wave equation in the generalized Einstein - de Sitter spacetime with nonlinearity of derivative type. More precisely, we consider a semilinear damped wave…
We investigate the late-time behavior of the massive vector field in the background of the Schwarzschild and Schwarzschild-de Sitter black holes. For Schwarzschild black hole, at intermediately late times the massive vector field is…
We establish global existence in 3+1 dimensions of small-amplitude solutions of quasilinear Dirichlet-wave equations satisfying the null condition outside of star-shapped obstacles.
In this paper we define the radiation field for the wave equation on the Schwarzschild black hole spacetime. In this context it has two components: the rescaled restriction of the time derivative of a solution to null infinity and to the…
Quasi-local energies for constantly accelerating observers in Ba\~nados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological…
We construct spherically symmetric, static solutions to the Einstein-Vlasov system with non-vanishing cosmological constant $\Lambda$. The results are divided as follows. For small $\Lambda>0$ we show existence of globally regular solutions…
We consider the problem of small data global existence for quasilinear wave equations with null condition on a class of Lorentzian manifolds $(\mathbb{R}^{3+1}, g)$ with \textbf{time dependent} inhomogeneous metric. We show that…