Related papers: General Relativistic Shock Waves that Exhibit Cosm…
A large class of solutions of the Einstein-conformal scalar equations in D=2+1 and D=3+1 is identified. They describe the collisions of asymptotic conformal scalar waves and are generated from Einstein-minimally coupled scalar spacetimes…
We prove that the essential smoothness of the gravitational metric at shock waves in GR, a PDE regularity issue for weak solutions of the Einstein equations, is determined by a geometrical condition which we introduce and name the {\it…
We introduce what we call a locally inertial Godunov method with dynamical time dilation, and use it to simulate a new one parameter family of general relativistic shock wave solutions of the Einstein equations for a perfect fluid. The…
This article is the first of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. The results of the present article concern the asymptotic behaviour of solutions to linear systems of…
A linear second order wave equation is presented based on cosmological general relativity, which is a space-velocity theory of the expanding Universe. The wave equation is shown to be exactly solvable, based on the Gaussian hypergeometric…
We construct the simplest solution of the Einstein equations that incorporates a shock-wave into a standard Friedmann-Robertson-Walker metric whose equation of state accounts for the Hubble constant and the microwave background radiation…
Self-similar solutions to the problem of a strong imploding relativistic shock wave are calculated. These solutions represent the relativistic generalisation of the Newtonian Gouderley-Landau-Stanyukovich problem of a strong imploding…
We have examined the properties of shock waves in simulations of large scale structure formation for two cosmological scenarios (a SCDM and a LCDM with Omega =1). Large-scale shocks result from accretion onto sheets, filaments and Galaxy…
We prove a stable shock formation result for a large class of systems of quasilinear wave equations in two spatial dimensions. We give a precise description of the dynamics all the way up to the singularity. Our main theorem applies to…
We study gravitational shock waves using scattering amplitude techniques. After first reviewing the derivation in General Relativity as an ultrarelativistic boost of a Schwarzschild solution, we provide an alternative derivation by…
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves…
In an influential 1964 article, P. Lax studied $2 \times 2$ genuinely nonlinear strictly hyperbolic PDE systems (in one spatial dimension). Using the method of Riemann invariants, he showed that a large set of smooth initial data lead to…
We prove in this paper that the Schwarzschild famiily of black holes are linearly stable as a family of solutions to the system of equations that result from expressing the Einstein vacuum equations in a generalised wave gauge. In…
We introduce a new asymptotic ansatz for spherical perturbations of the Standard Model of Cosmology (SM) which applies during the $p=0$ epoch, and prove that these perturbations trigger instabilities in the SM on the scale of the supernova…
This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the…
In a recent seminal paper \cite{D-H-R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this…
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…
The self-similarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. In this context, the validity of the corresponding hypothesis…
We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the distance from the surface, there…
The process of cosmic ray first-order Fermi acceleration at relativistic shock waves is studied with the method of Monte Carlo simulations. The simulations are based on numerical integration of particle equations of motion in a turbulent…