Related papers: General Relativistic Shock Waves that Exhibit Cosm…
Starting with the periodic waves earlier constructed for the gravity Whitham equation, we parameterise the solution curves through relative wave height, and use a limiting argument to obtain a full family of solitary waves. The resulting…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a…
We study test-body orbits in the gravitational field of a static spherically symmetric object in presence of a minimally coupled nonlinear scalar field. We generated a two-parametric family of scalar field potentials, which allow finding…
We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein…
A spherically symmetric comoving fluid solution of Einstein's equations is adapted for cosmological application by extending the geometry of standard FRW cosmology using a generalised curvature term. The resulting model retains many of the…
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…
The geometry of solutions to the higher dimensional Einstein vacuum equations presents aspects that are absent in four dimensions, one of the most remarkable being the existence of stably trapped null geodesics in the exterior of…
These lecture notes, based on a course given at the Zurich Clay Summer School (June 23-July 18, 2008), review our current mathematical understanding of the global behaviour of waves on black hole exterior backgrounds. Interest in this…
Propagation of strong shock wave in the expanding universe is studied using approximate analytic, and exact numerical solution of self-similar equations. Both solutions have similar properties, which change qualitatively, depending on the…
We present and analyze exact solutions of the Einstein-Maxwell equations in higher dimensions which form a large subclass of the Kundt family of spacetimes. We assume that the cosmological constant may be nonvanishing, and the matter…
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically…
Axisymmetric numerical simulations of rotating stellar core collapse to a neutron star are performed in the framework of full general relativity. The so-called Cartoon method, in which the Einstein field equations are solved in the…
We present a one-parameter family of exact solutions to Einstein equations that may be used to study the nature of the Green-Wald backreaction framework. Our explicit example is a family of Einstein-Rosen waves coupled to a massless scalar…
In this paper we describe in full details a new family of recently found exact solutions of relativistic, perfect fluid dynamics. With an ansatz, which generalizes the well-known Hwa-Bjorken solution, we obtain a wide class of new exact,…
Geometrical shock dynamics, also called CCW theory, yields approximate equations for shock propagation in which only the conditions at the shock appear explicitly; the post-shock flow is presumed approximately uniform and enters implicitly…
We test the validity of Isaacson's formula which states that high frequency and low amplitude gravitational waves behave as a radiation fluid on average. For this purpose, we numerically construct a solution of the vacuum Einstein equations…
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 show the stability of the geometric optics approximation in general relativity by constructing a family $(g_\lambda)_{\lambda\in(0,1]}$ of high-frequency metrics solutions to the Einstein vacuum equations in 3+1 dimensions without any…
The growth rate of long wavelength kinetic instabilities arising due to the interaction of a collimated beam of relativistic particles and a cold unmagnetized plasma are calculated in the ultra relativistic limit. For sufficiently…