Related papers: General Relativistic Shock Waves that Exhibit Cosm…
From a classical analysis, it is shown that the nondiffractive accelerating gravitational Airy wave packets are solutions of Einstein equations for their linearized tensor modes in a Friedmann-Lema\^itre-Robertson-Walker cosmological…
The so called gamma metric corresponds to a two-parameter family of axially symmetric, static solutions of Einstein's equations found by Bach. It contains the Schwarzschild solution for a particular value of one of the parameters, that…
We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a…
We show that the Nariai-Bertotti Petrov type D, homogeneous solution of Einstein's vacuum field equations with a cosmological constant describes the space-time in the interaction region following the head-on collision of two homogeneous,…
Astrophysical explosions are accompanied by the propagation of a shock wave through an ambient medium. Depending on the mass and energy involved in the explosion, the shock velocity $V$ can be non-relativistic ($V \ll c$, where $c$ is the…
We give a definitive characterization of the instability of the pressureless ($p=0$) critical ($k=0$) Friedmann spacetime to smooth radial perturbations. We use this to characterize the global accelerations away from $k\leq0$ Friedmann…
The derivation of the equation of one-dimensional movement of a solitary shock wave is given. This derivation shows, that the differential equation of movement of a solitary plane shock wave in the channel with variable area, is exact, if…
We show that the maximal globally hyperbolic development of near-FLRW initial data for the Einstein scalar-field Vlasov system exhibits stable Big Bang formation in the collapsing direction. The solutions exhibit stable Kretschmann scalar…
The main interest of the work exposed in this thesis is to explore hairy black holes in a more general framework than General Relativity by taking into account the presence of a cosmological constant, of higher dimensions, of exotic matter…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized…
Gravitational waves provide a unique window into gravity, cosmology, and high-energy physics, enabling the exploration of fundamental phenomena across a wide range of scales. This review presents a coherent and pedagogical framework that…
We study the behaviour of smooth solutions to the wave equation, $\square_g\psi=0$, in the interior of a fixed Schwarzschild black hole. In particular, we obtain a full asymptotic expansion for all solutions towards $r=0$ and show that it…
In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordstr\"om…
We consider an imperfect relativistic fluid which develops a shock wave and discuss its structure and thickness, taking into account the effects of viscosity and heat conduction in the form of sound absorption. The junction conditions and…
Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We derive a new formulation of the relativistic Euler equations that exhibits remarkable properties. This new formulation consists of a coupled system of geometric wave, transport, and elliptic equations, sourced by nonlinearities that are…
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…