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Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
Some future global properties of cosmological solutions for the Einstein-Vlasov-Maxwell system with surface symmetry are presented. Global existence is proved, the homogeneous spacetimes are future complete for causal trajectories, and the…
We study the asymptotic behavior of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein- Gauss-Bonnet action. We show that in general the scalar field that parametrizes…
We prove the existence of static, spherically symmetric solutions of the stellar dynamic Vlasov-Poisson and Vlasov-Einstein systems, which have the property that their spatial support is a finite, spherically symmetric shell with a vacuum…
We derive exact magnetically charged, static and spherically symmetric black hole solutions of the four-dimensional Einstein-Born-Infeld-dilaton gravity. These solutions are neither asymptotically flat nor (anti)-de Sitter. The properties…
The paper establishes the result that solutions of the type described in the title of the article are only those that have been already presented in the literature. The procedure adopted in the paper is somewhat novel - while the usual…
We study smooth, global-in-time solutions of the relativistic Vlasov-Maxwell system that possess arbitrarily large charge densities and electric fields. In particular, we construct spherically symmetric solutions that describe a thin shell…
Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on…
We construct the first smooth bubbling geometries using the Weyl formalism. The solutions are obtained from Einstein theory coupled to a two-form gauge field in six dimensions with two compact directions. We classify the charged Weyl…
We find new static, spherically symmetric, and asymptotically flat vacuum solutions without horizon in Starobinsky's quadratic f(R) gravity. We systematically classify these solutions by an asymptotic analysis around the origin and find…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
The occurrence of a spacetime singularity indicates the breakdown of Einstein gravitation theory in these extreme regimes. We consider here the singularity issue and various black hole paradoxes at classical and quantum levels. It is…
The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented…
We discuss spherically symmetric static solutions of the Einstein-Klein-Gordon equations for a real scalar field with a mass and a quartic self-interaction term. As for the massless case the solutions have a naked singularity at the origin.…
We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are…
The results on local existence and continuation criteria obtained by G. Rein in [4] are extended to the case with a non-zero cosmological constant. It is also shown that for the spherically symmetric case and a positive cosmological…
A large family of inhomogeneous non-static spherically symmetric solutions of the Einstein equation for null fluid in higher dimensions has been obtained. It encompasses higher dimensional versions of many previously known solutions such as…
We prove the existence of a class of plane symmetric perfect-fluid cosmologies with a (-1/3, 2/3, 2/3) Kasner-like singularity. These solutions of the Einstein equations depend on two smooth functions of one space coordinate. They are…
Spherical dust collapse generally forms a shell focusing naked singularity at the symmetric center. This naked singularity is massless. Further the Newtonian gravitational potential and speed of the dust fluid elements are everywhere much…
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field equations sourced by a topological defect, \ie~a singularity of a very specific form, the result is a localised…