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The non-linear superposition of the stationary euclidon solution with an arbitrary axially symmetric stationary gravitational field on the basis of the method of variation of parameters was constructed. Stationary soliton solution of the…

The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…

Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.

Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle…

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…

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…

A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…

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…

A new method is proposed, that establishes a one to one correspondance between the whole set of static axially symmetric vacuum GR solutions and a specific class of stationary axially symmetric scalar-Einstein solutions having a given mass…

We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations…

We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the…

We find a vacuum stationary twisted solution in four-dimensional Einstein gravity. Its frame dragging angular velocities are antisymmetric with respect to the equatorial plane. It possesses a symmetry of joint inversion of time and parity…

We investigate static axially symmetric black hole solutions in a four-dimensional Einstein-Yang-Mills-SU(2) theory with a negative cosmological constant $\Lambda$. These solutions approach asymptotically the anti-de Sitter spacetime and…

Numerical solutions of the Einstein-Yang-Mills equations with a negative cosmological constant are constructed. These axially symmetric solutions approach asymptotically the anti-de Sitter spacetime and are regular everywhere. They are…

Here I present a stationary cylindrically symmetric asymptotically Einstein static universe solution with the matter consisting of a cosmological and rotating dust term which admits predicted black hole event horizon.

Class of axially symmetric solutions of vacuum Einstein field equations including the Papapetrou solution as particular case has been found. It has been shown that the derived solution describes the external axial symmetric gravitational…

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the…

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…

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…

In this work we intend to discuss the solitonic solutions of Einstein's field equations in vacuum by constructing the solution to N solitons and studying some aspects of it. In conclusion, it will be shown how the Kerr black hole can be…