Related papers: Spherical symmetry as a test case for unconstraine…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as…
We resume former discussions of the conformally invariant wave equation on a Schwarzschild background, with a particular focus on the behaviour of solutions near the 'cylinder', i.e. Friedrich's representation of spacelike infinity. This…
Within a semiclassical framework, we investigate spherically symmetric solutions of the Einstein equations that (i) develop a trapped region within a finite time as measured by distant observers, and (ii) remain sufficiently regular at the…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
Motivated by the newest progress in geometric flows both in mathematics and physics, we apply the geometric evolution equation to study some black-hole problems. Our results show that, under certain conditions, the geometric evolution…
We introduce a set of constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations in spherical symmetry, based on its hyperbolic structure. While the outgoing…
We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear Schr\"odinger equation as a model example, we show that the…
Rare events of large-scale spatially-correlated exponential random fields are studied. The influence of spatial correlations on clustering and non-sphericity is investigated. The size of the performed simulations permits to study…
We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique local solutions and unique global solutions for small initial data. We also generalize Christodoulou's…
With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…
We introduce a two-parameter static, nonspherically-symmetric black hole solution in the Einstein theory of gravity coupled with a massless scalar field. The scalar field depends only on the polar coordinate $\theta$ in the spherical…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
This thesis deals with critical collapse of a massless scalar field coupled to Einstein's equations in spherical symmetry. The system is numerically investigated from both global and local points of view using a characteristic slicing and…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
We investigate the interior of a dynamical black hole as described by the Einstein-Maxwell-charged-Klein-Gordon system of equations with a cosmological constant, under spherical symmetry. In particular, we consider a characteristic initial…
We study axisymmetric solution to the conformally invariant wave equation on a Kerr background by means of numerical and analytical methods. Our main focus is on the behaviour of the solutions near spacelike infinity, which is appropriately…
We prove the global existence and uniqueness of classical solutions with small initial data and with wake-like decaying null infinity for the spherically symmetric Einstein-scalar-field equations with potential, where the scalar potential V…
This paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
Spherically symmetric solutions in F(R) theories in astronomical systems with rising energy density are studied. The range of parameters is established for which the flat space-time approximation for the background metric is valid. For the…