Related papers: Generating static perfect-fluid solutions of Einst…
A new exact static interior solution of the Einstein equations is obtained for a gravitating ball filled with a Pascal perfect fluid . The solution is an extension of the well-known interior solution with a parabolic distribution of mass…
We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption…
The trace-free Einstein equations contain one equation less than the complete field equations. In a static and spherically symmetric spacetime, the number of field equations is thus reduced to two. The equation of pressure isotropy of…
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases…
The symmetry method is used to derive solutions of Einstein's equations for fluid spheres using an isotropic metric and a velocity four vector that is non-comoving. Initially the Lie, classical approach is used to review and provide a…
The space of the solutions of the differential equations resulting from considering matter fluids of scalar field type or perfect fluid in Einstein-aether theory is analyzed. The Einstein-aether theory of gravity consists of General…
We establish the existence of a class of asymptotically Euclidean solutions to Einstein's constraint equations, whose asymptotic behavior at infinity is arbitrarily prescribed. The proposed seed-to-solution method relies on iterations based…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
We show that a flow (timelike congruence) in any type $B_{1}$ warped product spacetime is uniquely and algorithmically determined by the condition of zero flux. (Though restricted, these spaces include many cases of interest.) The flow is…
The exact interior static solution of Einstein-Maxwell equations in Bondi's coordinates for the electrically charged fluid ball is obtained as a source of the Reissner-Nordstr\"om solution.
Analytic gravitational collapse and expansion solutions with anisotropic pressure are generated. Metric functions are found by requiring zero heat flow scalar. It emerges that a single function generates the anisotropic solutions. Each…
A new class of plane symmetric solution sourced by a perfect fluid is found in our recent work. An n-dimensional ($n\geq 4$) global plane symmetric solution of Einstein field equation generated by a perfect fluid source is investigated,…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise…
In this work, we show that if the bumblebee field in the Einstein-bumblebee theory is given by its vacuum expectation value ($B_{\mu}=b_{\mu}$) and it is not dynamical ($\partial_{\mu}B_{\nu}-\partial_{\nu}B_{\mu}=0$), then these conditions…
We investigate an exact solution that describes the embedding of the four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein spacetime. The effective metric of the 4D perfect fluid as a hypersurface with induced matter is…
We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The…
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such…
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…