Singularity deep inside the spherical charged black hole core

We study analytically the spacelike singularity inside a spherically-symmetric, charged black hole coupled to a self-gravitating spherical massless scalar field. We assume spatial homogeneity, and find a generic solution in terms of a formal series expansion. This solution is tested against fully-nonlinear and inhomogeneous numerical simulations. We find full compliance between our analytical solution and the pointwise behavior of the singularity in the numerical simulations. This is a strong scalar-curvature monotonic spacelike singularity, which connects to a weak null singularity at asymptotically-late advanced time.Comment: 6 pages, to be published in Phys. Rev.

Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation

Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure

Orbital evolution of a particle around a black hole: II. Comparison of contributions of spin-orbit coupling and the self force

We consider the evolution of the orbit of a spinning compact object in a quasi-circular, planar orbit around a Schwarzschild black hole in the extreme mass ratio limit. We compare the contributions to the orbital evolution of both spin-orbit coupling and the local self force. Making assumptions on the behavior of the forces, we suggest that the decay of the orbit is dominated by radiation reaction, and that the conservative effect is typically dominated by the spin force. We propose that a reasonable approximation for the gravitational waveform can be obtained by ignoring the local self force, for adjusted values of the parameters of the system. We argue that this approximation will only introduce small errors in the astronomical determination of these parameters.Comment: 11 pages, 7 figure

Self force on static charges in Schwarzschild spacetime

We study the self forces acting on static scalar and electric test charges in the spacetime of a Schwarzschild black hole. The analysis is based on a direct, local calculation of the self forces via mode decomposition, and on two independent regularization procedures: A spatially-extended particle model method, and on a mode-sum regularization prescription. In all cases we find excellent agreement with the known exact results.Comment: 21 pages, 9 Encapsulated PostScript figures, submitted to Class. Quantum Gra

The Central Singularity in Spherical Collapse

The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide variety of circumstances. These conditions allow conclusions to be drawn about the nature of the singularity without having to integrate the geodesic equations. In particular, any geodesic with a non-zero amount of angular momentum which impinges on the singularity terminates in a strong curvature singularity.Comment: 17 pages; revised and corrected with improved result

Scalar field collapse in three-dimensional AdS spacetime

We describe results of a numerical calculation of circularly symmetric scalar field collapse in three spacetime dimensions with negative cosmological constant. The procedure uses a double null formulation of the Einstein-scalar equations. We see evidence of black hole formation on first implosion of a scalar pulse if the initial pulse amplitude $A$ is greater than a critical value $A_*$. Sufficiently near criticality the apparent horizon radius $r_{AH}$ grows with pulse amplitude according to the formula $r_{AH} \sim (A-A_*)^{0.81}$.Comment: 10 pages, 1 figure; references added, to appear in CQG(L

The Speciality Index as invariant indicator in the BKL Mixmaster Dynamics

The speciality index, which has been mainly used in Numerical Relativity for studying gravitational waves phenomena as an indicator of the special or non-special Petrov type character of a spacetime, is applied here in the context of Mixmaster cosmology, using the Belinski-Khalatnikov-Lifshitz map. Possible applications for the associated chaotic dynamics are discussed

Towards wave extraction in numerical relativity: the quasi-Kinnersley frame

The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times non-perturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time.Comment: 13 pages, 3 figure

Reissner Nordstr\"{o}m Background Metric in Dynamical Co-ordinates: Exceptional Behaviour of Hadamard States

We cast the Reissner Nordstrom solution in a particular co-ordinate system which shows dynamical evolution from initial data. The initial data for the $E<M$ case is regular. This procedure enables us to treat the metric as a collapse to a singularity. It also implies that one may assume Wald axioms to be valid globally in the Cauchy development, especially when Hadamard states are chosen. We can thus compare the semiclassical behaviour with spherical dust case, looking upon the metric as well as state specific information as evolution from initial data. We first recover the divergence on the Cauchy horizon obtained earlier. We point out that the semiclassical domain extends right upto the Cauchy horizon. This is different from the spherical dust case where the quantum gravity domain sets in before. We also find that the backreaction is not negligible near the central singularity, unlike the dust case. Apart from these differences, the Reissner Nordstrom solution has a similarity with dust in that it is stable over a considerable period of time. The features appearing dust collapse mentioned above were suggested to be generally applicable within spherical symmetry. Reissner Nordstrom background (along with the quantum state) generated from initial data, is shown not to reproduce them

The driver’s visual perception research to analyze pedestrian safety at twilight

Road traffic movement at nightfall (twilight) is characterizing by a reduction of light time of the day and the rapid nightfall onset, thus the driver's eyes have less time to adapt to rapid sudden changes in illumination. The visual perception and the reaction time of the driver in conditions when pedestrians appear in nightfall conditions on the street and road network in a city is considered in the paper. Researched was conducted in uncontrolled pedestrian crossings in nightfall conditions on Ukrainian roads. Regularities of the vehicle’s driver and pedestrians’ interaction in nightfall conditions are obtained. Road traffic accidents occurrence probabilities at the twilight time considering the driver’s reaction time and the car’s movement parameters was analyzed. As a result, a model for estimating the variation the reaction time of the driver when a pedestrian appears in the nightfall (twilight) conditions was calibrated