Related papers: The wave equation on Schwarzschild-de Sitter space…
We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy…
We study spherically symmetric solutions of semilinear wave equations in the case where the nonlinearity satisfies the null condition on extremal Reissner--Nordstrom black hole spacetimes. We show that solutions which arise from…
Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein…
We study solutions to the linear wave equation on the cosmological region of Schwarzschild-de Sitter spacetimes. We show that all sufficiently regular finite-energy solutions to the linear equation possess a particular finite-order…
We analyze in detail the geometry and dynamics of the cosmological region arising in spherically symmetric black hole solutions of the Einstein-Maxwell-scalar field system with a positive cosmological constant. More precisely, we solve, for…
We investigate the Schwarzschild-(anti) de Sitter spacetime with the anisotropic metric ansatz. The Wheeler-DeWitt equation for such a metric is solved numerically. In the presence of the cosmological constant $\Lambda$, we show that two…
We present an elementary physical space argument to establish local integrated decay estimates for the perturbed wave equation $\Box_g \phi = \epsilon \beta^a \partial_a \phi$ on the exterior of the Schwarzschild geometry $(\mathcal{M},g)$.…
We prove Price's law with an explicit leading order term for solutions $\phi(t,x)$ of the scalar wave equation on a class of stationary asymptotically flat $(3+1)$-dimensional spacetimes including subextremal Kerr black holes. Our precise…
We consider smooth solutions of the wave equation, on a fixed black hole region of a subextremal Reissner-Nordstr\"om (asymptotically flat, de Sitter or anti-de Sitter) spacetime, whose restrictions to the event horizon have compact…
The massive wave equation $\Box_g \psi - \alpha\frac{\Lambda}{3} \psi = 0$ is studied on a fixed Kerr-anti de Sitter background $(\mathcal{M},g_{M,a,\Lambda})$. We first prove that in the Schwarzschild case (a=0), $\psi$ remains uniformly…
Motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS spacetimes, we initiate the study of massive scalar waves satisfying $\Box_g \psi - \mu \psi =0$ on the interior of Anti-de Sitter (AdS) black holes. We prescribe…
Let G(x) be a C^0 function such that |G(x)|\le K|x|^{p} for |x|\le c, for constants K,c>0. We consider spherically symmetric solutions of \Box_g\phi=G(\phi) where g is a Schwarzschild or more generally a Reissner-Nordstrom metric, and such…
In this paper, the real scalar field equation in Schwarzschild-de Sitter spacetime is solved numerically with high precision. A method called polynomial approximation is introduced to derive the relation between the tortoise coordinate x…
We consider Kerr spacetimes with parameters a and M such that |a|<< M, Kerr-Newman spacetimes with parameters |Q|<< M, |a|<< M, and more generally, stationary axisymmetric black hole exterior spacetimes which are sufficiently close to a…
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…
This work studies solutions of the scalar wave equation \[\Box_g\phi=0\] on a fixed subextremal Reissner-Nordstr\"{o}m spacetime with non-vanishing charge $q$ and mass $M$. In a recent paper, Luk and Oh established that generic smooth and…
We consider the Cauchy problem for the (non-linear) Maxwell-Charged-Scalar-Field equations with spherically symmetric initial data, on a sub-extremal Reissner--Nordstr\"{o}m or Schwarzschild exterior space-time. We prove that the solutions…
We study scattering solutions $\phi$ of the linear wave equation on extremal Reissner-Nordstr\"{o}m spacetimes, satisfying the following properties: i) $\phi$ attains a prescribed radiation field $\psi_{\mathcal{I}}$ through future null…
We study the behaviour of smooth solutions to the wave equation, $\square_g\psi=0$, in the interior of a fixed Schwarzschild black hole. In particular, we obtain a full asymptotic expansion for all solutions towards $r=0$ and show that it…
In this paper, we derive the early-time asymptotics for fixed-frequency solutions $\phi_\ell$ to the wave equation $\Box_g \phi_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from the no incoming radiation condition on…