Related papers: Some exact solutions in general relativity
The Tolman-Oppenheimer-Volkov [TOV] equation constrains the internal structure of general relativistic static perfect fluid spheres. We develop several "solution generating" theorems for the TOV, whereby any given solution can be "deformed"…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…
This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic…
We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian…
We develop here a new procedure within Einstein's theory of gravity to generate equilibrium configurations that result as the final state of gravitational collapse from regular initial conditions. As a simplification, we assume that the…
In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al.[1] algorithm. The anisotropic fluid solution so obtained join continuously to…
The various schemes for studying rigidly rotating perfect fluids in general relativity are reviewed. General conclusions one may draw from these are: (i) There is a need to restrict the scope of the possible ansatze, and (ii) the angular…
The Riemann, Ricci and Einstein tensors for N-dimensional spherically symmetric spacetimes in various systems of coordinates are studied, and the general metric for conformally flat spacetimes is given. As an application, all the…
Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
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,…
This paper concerns the construction and analysis of a new family of exact general relativistic shock waves. The construction resolves the open problem of determining the expanding waves created behind a shock-wave explosion into a static…
A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity.…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The…