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We study here the structure of singularity forming in gravitational collapse of spherically symmetric inhomogeneous dust. Such a collapse is described by the Tolman-Bondi-Lema{\^i}tre metric, which is a two-parameter family of solutions to…
We analyze the null geodesic equations in five dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equation…
We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of radial null geodesics.…
We consider static circularly symmetric solution of three-dimensional Einstein's equations with negative cosmological constant (the BTZ black hole). The case of zero cosmological constant corresponding to the interior region of a black hole…
Using the Sparling form and a geometric construction adapted to spacetimes with a 2-dimensional isometry group, we analyse a quasi-local measure of gravitational energy. We then study the gravitational radiation through spacetime junctions…
This is the second in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the class of solutions to the…
We study the quantum gravitational collapse of spherically symmetric pressureless dust. Using an effective equation derived from a polymer quantization in the connection-triad phase space variables of general relativity, we find…
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 survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and…
In this paper, we take dust matter and investigate static spherically symmetric solution of the field equations in metric f(R) gravity. The solution is found with constant Ricci scalar curvature and its energy distribution is evaluated by…
The Einstein equations with a positive cosmological constant are coupled to the pressureless perfect fluid matter in plane symmetry. Under suitable restrictions on the initial data, the resulting Einstein-dust system is proved to have a…
Time-symmetric initial data for two-body solutions in three dimensional anti-deSitter gravity are found. The spatial geometry has constant negative curvature and is constructed as a quotient of two-dimensional hyperbolic space. Apparent…
Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. In particular, these include all the solutions of dust and…
Multi-parameter solutions to the Einstein equations in 2+1 dimensions are presented, with stress-energy given by a rotating dust with negative cosmological constant. The matter density is uniform in the corotating frame, and the ratio of…
We investigate the circumstances under which gravitationally collapsing dust can form a black hole in three-dimensional spacetime.
The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued…
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the…
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$…
The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles,…
We investigate the spherically symmetric gravitational collapse of an incoherent dust cloud by considering a LTB type space-time in third order Lovelock Gravity without cosmological constant, and give three families of LTB-like solutions…