Related papers: Solving the Einstein field equations
Perturbative techniques are important for modified theories of gravity since they allow to calculate deviations from General Relativity without recurring to exact solutions, which can be difficult to find. When applied to models such as…
A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum Einstein equation is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis,…
We derive a local curvature estimate for four-dimensional stationary solutions to the inheriting Einstein-Maxwell-Klein-Gordon equations. In particular, it implies that any such stationary geodesically complete solution with vanishing…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
It is shown that the Einstein gravity + Higgs scalar field have cosmological regular solutions with deceleration/acceleration phases and with bouncing off from a singularity. The behavior of the solution near to a flex point is in detail…
We study self-consistent static solutions for an Einstein universe in a graph-based induced gravity. In the generalization of the deconstruction model based on the graph, the eigenvalues of the graph Laplacian and the adjacent matrix gives…
Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field,…
We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commutating Killing vectors. This method consists in writing the axisymmetric stationry Einstein…
In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.
We present the solution space of the field equations in the Einstein-aether theory for the case of a vacuum Bianchi Type V space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by…
We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the…
In this paper we present Plane symmetric, Cylindrically Symmetric and Spherically Symmetric Black hole or Vacuum solutions of Einstein Field Equations(EFEs). Some of these solutions are new which we have not seen in the literature. This…
Solutions of Einstein vacuum equations, for a static pseudospherically symmetric system, are presented. They describe a naked singularity and a singular solution with many resemblances to the Schwartzschild solution but with two major…
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the…
We study UV-finite theory of induced gravity. We use scalar fields, Dirac fields and vector fields as matter fields whose one-loop effects induce the gravitational action. To obtain the mass spectrum which satisfies the UV-finiteness…
Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss…