Related papers: On the link between the Maxwell and linearised Ein…
I present a new method to generate rotating solutions of the Einstein--Maxwell equations from static solutions, and briefly discuss its general properties.
We study the instability of Schwarzschild black holes and the appearance of scalarized solutions in Einstein-scalar-Gauss-Bonnet gravity performing a time-domain analysis in a perturbative scheme. First we consider a quadratic coupling…
The Kaluza-Klein formalism of the Einstein's theory, based on the (2,2)-fibration of a generic 4-dimensional spacetime, describes general relativity as a Yang-Mills gauge theory on the 2-dimensional base manifold, where the local gauge…
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
In this paper the macroscopic Einstein and Maxwell equations for system, in which the electromagnetic interactions are dominating (for instance, the cosmological plasma before the moment of recombination), are derived. Ensemble averaging of…
We construct a one-parameter family of static and spherically symmetric solutions to the Einstein-Vlasov system bifurcating from the Schwarzschild spacetime. The constructed solutions have the property that the spatial support of the matter…
In this paper, we consider the Maxwell-Klein-Gordon and Maxwell-Chern-Simons-Higgs systems in the temporal gauge. By using the fact that when the spatial gauge potentials are in the Coulomb gauge, their $\dot{H}^1$ norms can be controlled…
We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized…
We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By…
We present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity. The advantage of this formalism relies in the fact that it does not require a…
We study shear-free spherically symmetric relativistic gravitating fluids with heat flow and electric charge. The solution to the Einstein-Maxwell system is governed by the generalised pressure isotropy condition which contains a…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal…
The equations governing the perturbations of the Schwarzschild metric satisfy the Regge-Wheeler-Zerilli-Moncrief system. Applying the technique introduced in [2], we prove an integrated local energy decay estimate for both the Regge-Wheeler…
We consider the equations of linearised gravity on the Schwarzschild spacetime in a double null gauge. Applying suitably commuted versions of the conservation laws derived in earlier work of the second author we establish control on the…
We study the physical consequences of two diffferent but closely related perturbation schemes applied to the Einstein-Maxwell equations. In one case the starting space-time is flat while in the other case it is Schwarzschild. In both cases…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
I derive an exact, static, axially symmetric solution of the Einstein-Maxwell equations representing two massless magnetic dipoles, and compare it with the corresponding solution of Einstein's equations for two massless spinning particles…
We develop a small-data Maxwell--Higgs theory on Schwarzschild and slowly rotating Kerr black-hole exteriors for gauge-invariant nonnegative self-interactions near the trivial vacuum. The Schwarzschild part gives a complete global,…