Red and blue shift in spherical and axisymmetric spacetimes and astrophysical constraints

We compute the red and blue shifts for astrophysical and cosmological sources. In particular, we consider low, intermediate and high gravitational energy domains. Thereby, we handle the binary system Earth-Mars as low energy landscape whereas white dwarfs and neutron stars as higher energy sources. To this end, we take into account a spherical Schwarzschild-de Sitter spacetime and an axially symmetric Zipoy-Voorhees metric to model all the aforementioned systems. Feasible outcomes come from modeling neutron stars and white dwarfs with the Zipoy-Voorhees metric, where quadrupole effects are relevant, and framing solar system objects using a Schwarzschild-de Sitter spacetime. In the first case, large delta parameters seem to be favorite, leading to acceptable bounds mainly for neutron stars. In the second case, we demonstrate incompatible red and blue shifts with respect to lunar and satellite laser ranging expectations, once the cosmological constant is taken to Planck satellite's best fit. To heal this issue, we suggest coarse-grained experimental setups and propose Phobos for working out satellite laser ranging in order to get more suitable red and blue shift intervals, possibly more compatible than current experimental bounds. Implications to cosmological tensions are also debated

A Time-Like Naked Singularity

We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture.Comment: 4 pages, Revtex4, To appear in Physical Review

On the invariant causal characterization of singularities in spherically symmetric spacetimes

The causal character of singularities is often studied in relation to the existence of naked singularities and the subsequent possible violation of the cosmic censorship conjecture. Generally one constructs a model in the framework of General Relativity described in some specific coordinates and finds an ad hoc procedure to analyze the character of the singularity. In this article we show that the causal character of the zero-areal-radius (R=0) singularity in spherically symmetric models is related with some specific invariants. In this way, if some assumptions are satisfied, one can ascertain the causal character of the singularity algorithmically through the computation of these invariants and, therefore, independently of the coordinates used in the model.Comment: A misprint corrected in Theor. 4.1 /Cor. 4.

On trapped surface formation in gravitational collapse II

Further to our consideration on trapped surfaces in gravitational collapse, where pressures were allowed to be negative while satisfying weak energy condition to avoid trapped surface formation, we discuss here several other attempts of similar nature in this direction. Certain astrophysical aspects are pointed out towards examining the physical realization of such a possibility in realistic gravitational collapse

Accretion Disk Luminosity for Black Holes Surrounded by Dark Matter with Anisotropic Pressure

We investigate the luminosity of the accretion disk of a static black hole surrounded by dark matter with anisotropic pressure. We calculate all basic orbital parameters of test particles in the accretion disk, such as angular velocity, angular momentum, energy, and radius of the innermost circular stable orbit as functions of the dark matter density, radial pressure, and anisotropic parameter, which establishes the relationship between the radial and tangential pressures. We show that the presence of dark matter with anisotropic pressure makes a noticeable difference in the geometry around a Schwarzschild black hole, affecting the radiative flux, differential luminosity, and spectral luminosity of the accretion disk

New mathematical framework for spherical gravitational collapse

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of singular null geodesics to existence of regular curves which are super-solutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed.Comment: 8 pages, LaTeX2

Spherical Dust Collapse in Higher Dimensions

We consider here the question if it is possible to recover cosmic censorship when a transition is made to higher dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear that in a generic higher dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes, on the nature of the initial data from which the collapse develops, is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.Comment: Revtex4, Title changed, To appear in Physical Review