Search results for "Schwarzschild"
showing 10 items of 87 documents
Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell
2020
A method is given to compute the stress-energy tensor for a massless minimally coupled scalar field in a spacetime where a black hole forms from the collapse of a spherically symmetric null shell in four dimensions. Part of the method involves matching the modes for the in vacuum state to a complete set of modes in Schwarzschild spacetime. The other part involves subtracting from the unrenormalized expression for the stress-energy tensor when the field is in the in vacuum state, the corresponding expression when the field is in the Unruh state and adding to this the renormalized stress-energy tensor for the field in the Unruh state. The method is shown to work in the two-dimensional case wh…
Pseudospectrum and Black Hole Quasinormal Mode Instability
2020
We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) the instability of all overtones under small-scale ("ultraviolet") perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospec…
Flat synchronizations in spherically symmetric space-times
2010
It is well known that the Schwarzschild space-time admits a spacelike slicing by flat instants and that the metric is regular at the horizon in the associated adapted coordinates (Painleve-Gullstrand metric form). We consider this type of flat slicings in an arbitrary spherically symmetric space-time. The condition ensuring its existence is analyzed, and then, we prove that, for any spherically symmetric flat slicing, the densities of the Weinberg momenta vanish. Finally, we deduce the Schwarzschild solution in the extended Painleve-Gullstrand-Lemaitre metric form by considering the coordinate decomposition of the vacuum Einstein equations with respect to a flat spacelike slicing.
Locating Objects Away from Earth Surface: Positioning Accuracy
2013
The motion of the Galileo and GPS satellite constellations is simulated in Schwarzschild space-time, whereas photons travel in Minkowski space-time. This is a good enough approach to deal with the main goal of this paper: the study of positioning accuracy in the framework of the so-called relativistic positioning. Our study is based on numerical 4D simulations. In this meeting, the contribution of J.A. Morales-Lladosa contains some basic ideas which have been important to perform our numerical calculations. For four chosen emitters (satellites) of a certain constellation, many receivers located at different distances from Earth surface and in distinct directions are considered. Thus, we ver…
Structure and stability of traversable thin-shell wormholes in Palatini f(R) gravity
2020
We study the structure and stability of traversable wormholes built as (spherically symmetric) thin shells in the context of Palatini f(R) gravity. Using a suitable junction formalism for these theories we find that the effective number of degrees of freedom on the shell is reduced to a single one, which fixes the equation of state to be that of massless stress-energy fields, contrary to the general relativistic and metric f(R) cases. Another major difference is that the surface energy density threading the thin shell, needed in order to sustain the wormhole, can take any sign and may even vanish, depending on the desired features of the corresponding solutions. We illustrate our results by…
Numerical evolutions of spherical Proca stars
2017
Vector boson stars, or $\textit{Proca stars}$, have been recently obtained as fully non-linear numerical solutions of the Einstein-(complex)-Proca system. These are self-gravitating, everywhere non-singular, horizonless Bose-Einstein condensates of a massive vector field, which resemble in many ways, but not all, their scalar cousins, the well-known (scalar) $\textit{boson stars}$. In this paper we report fully-non linear numerical evolutions of Proca stars, focusing on the spherically symmetric case, with the goal of assessing their stability and the end-point of the evolution of the unstable stars. Previous results from linear perturbation theory indicate the separation between stable and…
Spherical symmetric dust collapse in a Vector-Tensor gravity
2018
There is a viable vector-tensor gravity (VTG) theory, whose vector field produces repulsive forces leading to important effects. In the background universe, the effect of these forces is an accelerated expansion identical to that produced by vacuum energy (cosmological constant). Here, we prove that another of these effects arises for great enough collapsing masses which lead to Schwarzschild black holes and singularities in general relativity (GR). For these masses, pressure becomes negligible against gravitational attraction and the complete collapse cannot be stopped in the context of GR; however, in VTG, a strong gravitational repulsion could stop the falling of the shells towards the s…
Quasistationary solutions of scalar fields around accreting black holes
2016
Massive scalar fields can form long-lived configurations around black holes. These configurations, dubbed quasi-bound states, have been studied both in the linear and nonlinear regimes. In this paper we show that quasi-bound states can form in a dynamical scenario in which the mass of the black hole grows significantly due to the capture of infalling matter. We solve the Klein-Gordon equation numerically in spherical symmetry, mimicking the evolution of the spacetime through a sequence of analytic Schwarzschild black hole solutions of increasing mass. It is found that the frequency of oscillation of the quasi-bound states decreases as the mass of the black hole increases. In addition, accre…
An algorithm for computing geometric relative velocities through Fermi and observational coordinates
2013
We present a numerical method for computing the \textit{Fermi} and \textit{observational coordinates} of a distant test particle with respect to an observer. We apply this method for computing some previously introduced concepts of relative velocity: \textit{kinematic}, \textit{Fermi}, \textit{spectroscopic} and \textit{astrometric} relative velocities. We also extend these concepts to non-convex normal neighborhoods and we make some convergence tests, studying some fundamental examples in Schwarzschild and Kerr spacetimes. Finally, we show an alternative method for computing the Fermi and astrometric relative velocities.
Head-on collisions and orbital mergers of Proca stars
2019
Proca stars are self-gravitating Bose-Einstein condensates obtained as numerical stationary solutions of the Einstein-(complex)-Proca system. These solitonic can be both stable and form dynamically from generic initial data by the mechanism of gravitational cooling. In this paper we further explore the dynamical properties of these solitonic objects by performing both head-on collisions and orbital mergers of equal mass Proca stars, using fully non-linear numerical evolutions. For the head-on collisions, we show that the end point and the gravitational waveform from these collisions depends on the compactness of the Proca star. Proca stars with sufficiently small compactness collide leaving…