Related papers: Global evolution in spherical symmetry for self-gr…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
The Klein-Gordon equation for a scalar field sourced by a static spherically symmetric background is an interesting second-order differential equation with applications in particle physics, astrophysics, and elsewhere. Here we present…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
We report on a numerical investigation of black hole evolution in an Einstein dilaton Gauss-Bonnet (EdGB) gravity theory where the Gauss-Bonnet coupling and scalar (dilaton) field potential are symmetric under a global change in sign of the…
We consider the stability of the toroidal AdS-Schwarzshild black holes as solutions of the Einstein--Klein-Gordon system, with Dirichlet or Neumann boundary conditions for the scalar field. Restricting to perturbations that respect the…
In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to…
In case of a spherically symmetric non-linear scalar field (SF) in flat space, besides singularity at the center, spherical singularities can occur for non-zero values of radial variable $r>0$. We show that in the General Relativity the…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…
We study four-dimensional Einstein-Maxwell fields for which any higher-order corrections to the field equations effectively reduces to just a rescaling of the gravitational and the cosmological constant. These configurations are thus…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…
For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the…
Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite…
I study a class of global, causal geodesically complete solutions to the spherically symmetric Einstein scalar field (SSESF) system . Extending results of Luk-Oh (Quantitative Decay Rates for Dispersive Solutions to the Einstein-Scalar…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
We study the nonlinear stability of the Cauchy horizon in the interior of extremal Reissner-Nordstr\"om black holes under spherical symmetry. We consider the Einstein-Maxwell-Klein-Gordon system such that the charge of the scalar field is…
In this paper, we prove the existence of global in time small data solutions of semilinear Klein-Gordon equations in space-time with a static Schwarzschild radius in the expanding universe.
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…