Related papers: On the Singularity Structure and Stability of Plan…
The possibility that the universe may have a fundamental and positive cosmological constant has motivated an interesting cosmological model, in which initially the universe is in a cosmological constant sea, then the local quantum…
General relativity can be formally derived as a flat spacetime theory, but the consistency of the resulting curved metric's light cone with the flat metric's null cone has not been adequately considered. If the two are inconsistent, then…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
Scalar and gravity wave subcurvature fluctuations are calculated for a background approximating the Hawking and Turok open universe model. The gravity wave cosmic microwave background contribution is finite and it appears that a…
Our spacetime is filled with gravitational wave backgrounds that constitute a fluctuating environment created by astrophysical and cosmological sources. Bounds on these backgrounds are obtained from cosmological and astrophysical data but…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds.…
We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves…
This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain…
To understand an oft-observed but poorly understood phenomenon in which a solitary wave in a dispersive equation slowly deteriorates due to a persistent emission of radiation (i.e. a ``radiating solitary wave''), we propose a bare-bones…
In this this paper the stochastic background of gravitational waves (SBGWs) is analyzed with the auxilium of the WMAP data. We emphasize that, in general, in previous works in the literature about the SBGWs, old COBE data were used. After…
The stability of cosmological event and Cauchy horizons of spacetimes associated with plane symmetric domain walls are studied. It is found that both horizons are not stable against perturbations of null fluids and massless scalar fields;…
For a special time-dependent homogeneous plane wave background that includes a null singularity we construct the closed string propagators. We carry out the summation over the oscillator modes and extract the worldsheet spacetime structures…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
We prove the linear and nonlinear instability of the water line solitary waves with respect to transverse perturbations.
Key issues of classical and quantum strings in gravitational plane waves, shock waves and spacetime singularities are synthetically understood. This includes the string mass and mode number excitations, energy-momentum tensor, scattering…
Wave maps (or Lorentzian-harmonic maps) from a $1+1$-dimensional Lorentz space into the $2$-sphere are associated to constant negative Gaussian curvature surfaces in Euclidean 3-space via the Gauss map, which is harmonic with respect to the…
We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of…
We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of…
General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the…