Related papers: Spherically symmetric dynamical horizons
Several dynamical symmetries of the Dirac Hamiltonian are reviewed in a systematic manner and the conditions under which such symmetries hold. These include relativistic spin and orbital angular momentum symmetries, SO(4)\times…
It is shown that all spherical symmetric potentials are capable of producing dynamical symmetries in classical one-body motions, thanks to the inevitable existence of symmetry axes associated with turning points for corresponding…
We examine the solution of the constraints in spherically symmetric general relativity when spacetime has a flat spatial hypersurface. We demonstrate explicitly that given one flat slice, a foliation by flat slices can be consistently…
A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma,…
Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing…
We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…
Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical…
The orthonormal set of Spherical Harmonics provides a natural way of expanding whole sky redshift and peculiar velocity surveys.
We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces.…
This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further…
The supersymmetry of near-horizon geometries in heterotic supergravity is considered. A necessary and sufficient condition for a solution to preserve more than the minimal N=2 supersymmetry is obtained. A supersymmetric near-horizon…
In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison…
In MHD symmetric systems the equilibrium physical quantities are dependent on two variables only. In this cases it is possible to find a magnetic surface function that has the same symmetry. Under the assumption that the metric determinant…
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…
The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…
A general analysis for characterizing and classifying `isolated horizons' is presented in terms of null tetrads and spin coefficients. The freely specifiable spin coefficients corresponding to isolated horizons are identified and specific…
We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field…
Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established,…
In this paper, we introduce a new method for study on backward stochastic differential equations with stopping time as time horizon. And using this, we show that some results on backward stochastic differential equations with constant time…
Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…