Related papers: The Common Solution Space of General Relativity
We first present an overview of the Schwarzschild vacuum spacetime within general relativity, with particular emphasis on the role of scalar polynomial invariants and the null frame approach (and the related Cartan invariants), that…
We explore how far one can go in constructing $d$-dimensional static black holes coupled to $p$-form and scalar fields before actually specifying the gravity and electrodynamics theory one wants to solve. At the same time, we study to what…
A formalism for analyzing the complete set of field equations describing Macroscopic Gravity is presented. Using this formalism, a cosmological solution to the Macroscopic Gravity equations is determined. It is found that if a particular…
The Schwarzschild-Melvin spacetime is an exact solution of the Einstein electrovacuum equations describing a black hole immersed in a magnetic field which is asymptotically aligned with the z-axis. It plays an important role in our…
The description of a point mass in general relativity (GR) is given in the framework of the field formulation of GR where all the dynamical fields, including the gravitational field, are considered in a fixed background spacetime. With the…
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively.…
Sachs has derived quaternion field equations that fully exploit the underlying symmetry of the principle of general relativity, one in which the fundamental 10 component metric field is replaced by a 16 component four-vector quaternion.…
We outline the class of globally regular spherically symmetric solutions to the minimally coupled GR equations asymptotically de Sitter in the origin and asymptotically Schwarzschild at infinity. A source term connects smoothly de Sitter…
Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einsteins Field equations for vacuum, yields the Schwarzschild Metric as the unique solution,…
Schwarzschild's 'interior solution' is a space-time metric that satisfies Einstein's gravitational field equations with a source term that Einstein created on the basis of an unjustified identification of the conceptually distinct notions…
A proof is given that the space $\L$ of solutions of the linearized vacuum Einstein's equation around a Schwarzschild black hole is parameterized by two scalar fields which are gauge invariant combinations of perturbed algebraic and…
Generalization of a known theorem to generate static, spherically symmetric black-hole solutions in higher dimensional Lovelock gravity is presented. Particular limits, such as Gauss-Bonnet (GB) and/or Einstein-Hilbert (EH) in any dimension…
The solution of Einstein field equations for static spherically symmetric spacetime metric with anisotropic internal stresses has been obtained. The matter has vanishing complexity and a spacetime metric that satisfies the Karmarkar…
Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the…
In this work, we present a new interpretation of the only static vacuum solution of Einstein's field equations with planar symmetry, the Taub solution. This solution is a member of the $AIII$ class of metrics, along with the type D Kasner…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
The weak field approximation in a model of de Sitter gravity is investigated in the static and spherically symmetric case, under the assumption that the vacuum spacetime without perturbations from matter fields is a torsion-free de Sitter…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes.…
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…