Related papers: Nonlinear Wave Dynamics in Black Hole Spacetimes
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to…
We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation…
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…
We study the initial value problem for a defocusing semi-linear wave equation with spatially growing nonlinearity. By employing Moser-Trudinger type inequalities and Strichartz estimates, we establish global well-posedness in the energy…
Improved semiclassical techniques are developed and applied to a treatment of a real scalar field in a $D$-dimensional gravitational background. This analysis, leading to a derivation of the thermodynamics of black holes, is based on the…
Quantitative versions of mode stability type statements for the wave equation on Kerr-Newman black holes are proven for the full sub-extremal range. The mode stability result on the real axis is then applied to prove integrated local energy…
In this manuscript we investigate the Benjamin-Feir (or modulation) instability for the spatial evolution of water waves from the perspective of the discrete, spatial Zakharov equation, which captures cubically nonlinear and resonant wave…
In calculations of the inspiral of binary black holes an intermediate approximation is needed that can bridge the post-Newtonian methods of the early inspiral and the numerical relativity computations of the final plunge. We describe here…
This article is an extended version of a presentation given at KOZWaves 2024: The 6th Australasian Conference on Wave Science, held in Dunedin, New Zealand. Soliton methods were initially introduced to study equations such as the…
We establish boundedness and polynomial decay results for the Teukolsky system in the exterior spacetime of very slowly rotating and strongly charged sub-extremal Kerr-Newman black holes, with a focus on axially symmetric solutions. The key…
Based on the covariant hamiltonian formalism, we study the dynamics of spinning test bodies in the Kerr and Schwarzschild spacetimes. For the first time, we derive the exact solution of circular orbits in the Kerr plane without truncating…
The gravitational field around an astrophysical black hole (BH) is thought to be described by the Kerr spacetime, which is a solution of the Einstein equation. Signatures of binary black hole (BBH) coalescence in gravitational waves (GW)…
We show that the leading-order term in the late-time asymptotics of solutions to the linear wave equation on radially symmetric stationary perturbations of $(2 + 1)$-dimensional Minkowski space is proportional to $u^{-1/2}v^{-1/2}$ (which…
We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation…
Here we are interested to study the spin-1 particle i.e., electro-magnetic wave in curved space-time, say around black hole. After separating the equations into radial and angular parts, writing them according to the black hole geometry,…
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…
In this paper we consider a semi-linear, defocusing, shifted wave equation on the hyperbolic space \[ \partial_t^2 u - (\Delta_{{\mathbb H}^n} + \rho^2) u = - |u|^{p-1} u, \quad (x,t)\in {\mathbb H}^n \times {\mathbb R}; \] and introduce a…
The close limit approximation of binary black hole is a powerful method to study gravitational-wave emission from highly non-linear geometries. In this work, we use it as a tool to model black hole spacetimes in theories of gravity with a…
In this paper, we consider the Cauchy problem for semi-linear wave equations with structural damping term $\nu (-\Delta)^2 u_t$, where $\nu >0$ is a constant. As being mentioned in [8,10], the linear principal part brings both the diffusion…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…