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From a particularly simple solution of the Ernst equation, we build a solution of the vacuum stationary axisymmetric Einstein equations depending on three parameters. The parameters are associated to the total mass of the source and its…
We develop a correspondence between arbitrary tensors and matrices based on the use of Kronecker products and associated identities. Utilizing the rules of matrix differentiation we derive the vacuum Einstein field equations as a…
We examine gravitational waves in an isolated axi--symmetric reflexion symmetric NGT system. The structure of the vacuum field equations is analyzed and the exact solutions for the field variables in the metric tensor are found in the form…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
Physically admissible choice of the "essential" coordinates identified with components of the metric tensor and co-moving frame of reference reduced to the formulation of the stationary axisymmetric GR problem. Such nontraditional approach…
We examine gravitational waves in an isolated axi--symmetric reflexion symmetric NGT system. The structure of the vacuum field equations is analyzed and the exact solutions for the field variables in the metric tensor are found in the form…
We set up a vacuum theory of gravity with an extra dimension of vanishing proper length. The most general solution to the field equations are presented. This formulation is free of Kaluza-Klein modes and does not allow the propagation of…
We present the results of the computation of a twisting type N solution to vacuum Einstein equations following an iterative approach. Our results show that the higher order terms fail to provide a full exact solution with non-vanishing…
False vacuum decay in field theory may be formulated as a boundary value problem in Euclidean space. In a previous work, we studied its solution in single scalar field theories with quadratic gravity and used it to find obstructions to…
For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
A black hole solution of Einstein's field equations with cylindrical symmetry is found. Using the Hamiltonian formulation one is able to define mass and angular momentum for the cylindrical black hole through the corresponding and…
Standard General Relativity assumes that, in the absence of classical matter sources, spacetime is empty. This chapter considers and analyses the new behaviours of the gravitational field that appear when one substitutes this emptiness by a…
Translation by S. Antoci and A. Loinger of the fundamental memoir, that contains the ORIGINAL form of the solution of Schwarzschild's problem. The solution is regular in the whole space-time, with the only exception of the origin 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…
The cylindrically-symmetric static vacuum equations of Conformal Gravity are solved for the case of additional boost symmetry along the axis. We present the complete family of solutions which describe the exterior gravitational field of…
We study a class of static spherically symmetric vacuum solutions in modified teleparallel gravity solving the field equations for a specific model Ansatz, requiring the torsion scalar $T$ to be constant. We discuss the models falling in…
Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are found. In even dimensions the solution has many similarities with the…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
According to general relativity, black holes are incomplete, which prevents developing a complete physical description of their dynamical formation and evolution once quantum effects are taken into account. Theories beyond general…