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In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we…
In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching…
We extend the theory of non-thermal fixed points to the case of anomalously slow universal scaling dynamics according to the sine-Gordon model. This entails the derivation of a kinetic equation for the momentum occupancy of the scalar field…
We obtain explicit characterization of spectral and orbital stability of solitary wave solutions to the $\mathbf{U}(1)$-invariant Klein--Gordon equation in one spatial dimension coupled to an anharmonic oscillator. We also give the complete…
In the present paper, we show that the global solution to (partially) damped Klein-Gordon equation on the three dimensional Euclidean space with small data decays exponentially. The key ingredients in the proof are: Morawetz-type estimates…
Modulation spaces have received considerable interest recently as it is the natural function spaces to consider low regularity Cauchy data for several nonlinear evolution equations. We establish global well-posedness for 3D…
We study the focusing, cubic, nonlinear Klein-Gordon equation in 3D with large radial data in the energy space. This equation admits a unique positive stationary solution, called the ground state. In 1975, Payne and Sattinger showed that…
We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the…
Here we prove a global existence theorem for sufficiently small however fully nonlinear perturbations of a family of background solutions of the $`n+1$' vacuum Einstein equations in the presence of a positive cosmological constant…
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and…
Oscillating solutions to the effective equations of Loop Quantum Cosmology have been suggested for the role of an `eternal seed', providing a possible starting point for the emergent universe scenario. We investigate the stability of a…
Several models within the framework of Einstein-Gauss-Bonnet gravities are considered with regard their late-time phenomenological viability. The models contain a non-minimally coupled scalar field and satisfy a constraint on the scalar…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
We prove global completeness in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form $\Sigma \times S^{1}\times R$ where $\Sigma $ is a compact surface of genus $G>1.$ The Cauchy data are…
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation $u_{tt}-u_{xx}+V'(u)=0$, where $u$ is a scalar-valued function of $x$ and $t$, and the…
We give a new proof of the recent result by Fournodavlos-Schlue on the nonlinear stability of the expanding region of Kerr-de Sitter spacetimes as solutions of the Einstein vacuum equations with positive cosmological constant. Our gauge is…
Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz [Ann. H. Poincar\'e 16, 2059 (2015)], in this article we show how to construct a system of quasilinear wave equations for the geometric fields…
We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge…
We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with a nonlinear Klein-Gordon equation on a star graph. The proof of the well-posedness uses a classical fixed point…
We study the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime. We focus attention on modes with zero speed of propagation and conjecture…