Related papers: Initial data sets for the Schwarzschild spacetime
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The…
The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for…
We construct large classes of vacuum general relativistic initial data sets, possibly with a cosmological constant Lambda, containing ends of cylindrical type.
The spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates (i.e. polar slicing and areal radial coordinate) is considered. An improved continuation criterion for global existence of classical solutions is given. Two other…
We describe a proof of M.T. Anderson's result on the rigidity of complete stationary initial data for the Einstein vacuum equations in spacetime dimension 3 + 1, under an extra assumption on the norm of the stationary Killing vector field.…
Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to $-1$, apparently one could still expect an effectively static geometry, in the…
Using only a thought experiment and Einstein's correspondence principal, a model is derived that correctly predicts the Schwarzschild time dilation expression in limiting cases. The method requires almost no prerequisite knowledge from the…
The initial shear field, characterized by a primordial perturbation potential, plays a crucial role in the formation of large scale structures. Hence, considerable analytic work has been based on the joint distribution of its eigenvalues,…
Initial data corresponding to spacetimes containing black holes are considered in the time symmetric case. The solutions are obtained by matching across the apparent horizon different, conformally flat, spatial metrics. The exterior metric…
We derive the statistical entropy of the Schwarzschild black hole by considering the asymptotic symmetry algebra near the $\cal{I^{-}}$ boundary of the spacetime at past null infinity. Using a two-dimensional description and the Weyl…
We study the canonical formalism of a spherically symmetric space-time. In the context of the 3+1 decomposition with respect to the radial coordinate $r$, we set up an effective Lagrangian in which a couple of metric functions play the role…
For a static and spherically symmetric spacetime, we investigate the class of exact solutions that arise when two fundamental geometric constraints are imposed simultaneously: the Karmarkar's condition and the vanishing of the Weyl tensor.…
Precise initial conditions (ICs) are crucial for accurate computation in cosmological perturbation theory. We derive the consistent ICs for Horndeski theory in the Effective Field Theory (EFT) approach, assuming constant EFT functions at…
Given a spherical spacelike three-geometry, there exists a very simple algebraic condition which tells us whether, and in which, Schwarzschild solution this geometry can be smoothly embedded. One can use this result to show that any given…
We consider the semiclassical Schr\"odinger-Poisson system with a special initial data of WKB type such that the solution of the limiting hydrodynamical equation becomes time-global in dimensions at least three. We give an example of such…
The success of the moving puncture method for the numerical simulation of black hole systems can be partially explained by the properties of stationary solutions of the 1+log coordinate condition. We compute stationary 1+log slices of the…
The standard procedure to generate initial conditions (IC) in numerical simulations is to use the Zel'dovich approximation (ZA). Although the ZA correctly reproduces the linear growing modes of density and velocity perturbations, non-linear…
We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these…
We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a…
We construct compact initial data of constant mean curvature $\widetilde{K}$ for Einstein's 4d vacuum equations with $\widehat{\Lambda} = \Lambda - (\widetilde{K}^2/3)$ positive, where $\Lambda$ is the cosmological constant, via the…