Related papers: Remarks on Papapetrou Class of Vacuum Solutions of…
Axisymmetric Solutions of the vacuum Einstein equations are found in the Papapetrou-Weyl gauge. The solutions depend on two pairs of functionals, each pair of two functions depends on a different arbitrarily chosen function of one variable.…
The gravitational properties of the {\em only} static plane-symmetric vacuum solution of Einstein's field equations without cosmological term (Taub's solution, for brevity) are presented: some already known properties (geodesics, weak field…
A vacuum solution of the Einstein gravitational field equation is given that follows from a general ansatz but fails to follow from it if a certain symmetric matrix is assumed to be in diagonal form from the beginning.
The Newtonian theory of gravitation and electrostatics admit equilibrium configurations of charged fluids where the charge density can be equal to the mass density, in appropriate units. The general relativistic analog for charged dust…
Introducing the well known Papapetrou field as the gravitoelectromagnetic field tensor, we express the Maxwell-type part of the 3-dimensional quasi-Maxwell form of the {\it vacuum} Einstein field equations in terms of differential forms,…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
We solve the Einstein vacuum-equations for the case of static and axisymmetric solutions in a system of coordinates different from the Weyl standard one. We prove that there exists a class of solutions with the appropriate asymptotical…
Using the Euclidon method, a stationary solution of Einstein's vacuum equations was obtained, describing N rotating axially symmetric masses, which in the absence of rotation describes N arbitrary axially symmetric static masses, for…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
Einstein's field equations are solved exactly for static charged dust distributions. These solutions generalize the Majumdar Papapetrou metrics. Maxwell's equations lead to the equality of charge and mass densities of the dust distribution.…
We construct a class of exact solutions of the noncommutative vacuum Einstein field equations, which are noncommutative analogues of the plane-fronted gravitational waves in classical gravity.
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
It is shown that the class of asymptotically flat solutions to the axisymmetric and stationary vacuum Einstein equations with reflection symmetry of the metric is uniquely characterized by a simple relation for the Ernst potential on the…
We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational…
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match…
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…