Trapping Horizons in the Sultana-Dyer Space-Time

The Sultana-Dyer space-time is suggested as a model describing a black hole embedded in an expanding universe. Recently, in \cite{0705.4012}, its global structure is analyzed and the trapping horizons are shown. In the paper, by directly calculating the expansions of the radial null vector fields normal to the space-like two-spheres foliating the trapping horizons, we find that the trapping horizon outside the event horizon in the Sultana-Dyer space-time is a past trapping horizon. Further, we find that the past trapping horizon is an outer, instantaneously degenerate or inner trapping horizon accordingly when the radial coordinate is less than, equal to or greater than some value.Comment: no figures, 5 pages; PCAS and key words are adde

Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit

We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $\Omega(x_A, x_B)$ and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the astronomical unit, reported by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of $d{\rm AU}/dt$, i.e., $15 \pm 4$ ~[m/century]. Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion.Comment: 13 pages, 2 figures, accepted for publication in General Relativity and Gravitatio

High-Speed Cylindrical Collapse of Two Perfect Fluids

In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by $c_s, d_s$. It is shown that the high-speed approximation scheme breaks down by non-zero pressures $p_1, p_2$ when $c_s, d_s$ are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainity on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa [1] for the perfect fluid.Comment: 11 pages, 1 figure, accepted for publication in Gen. Rel. Gra

Physical interpretation of gauge invariant perturbations of spherically symmetric space-times

By calculating the Newman-Penrose Weyl tensor components of a perturbed spherically symmetric space-time with respect to invariantly defined classes of null tetrads, we give a physical interpretation, in terms of gravitational radiation, of odd parity gauge invariant metric perturbations. We point out how these gauge invariants may be used in setting boundary and/or initial conditions in perturbation theory.Comment: 6 pages. To appear in PR

Gravitational Collapse of Null Radiation and a String fluid

We consider the end state of collapsing null radiation with a string fluid. It is shown that, if diffusive transport is assumed for the string, that a naked singularity can form (at least locally). The model has the advantage of not being asymptotically flat. We also analyse the case of a radiation-string two-fluid and show that a locally naked singularity can result in the collapse of such matter. We contrast this model with that of strange quark matter.Comment: RevTeX 4.0 (8 pages - no figures). submitted to Phys Rev D. Some changes to abstract, introduction and conclusion - references update

Cosmological expansion and local systems: a Lema\^{i}tre-Tolman-Bondi model

We propose a Lema\^{i}tre-Tolman-Bondi system mimicking a two-body system to address the problem of the cosmological expansion versus local dynamics. This system is strongly bound but participates in the cosmic expansion and is exactly comoving with the cosmic substratum

Higher dimensional radiation collapse and cosmic censorship

We study the occurrence of naked singularities in the spherically symmetric collapse of radiation shells in a higher dimensional spacetime. The necessary conditions for the formation of a naked singularity or a black hole are obtained. The naked singularities are found to be strong in the Tipler's sense and thus violating cosmic censorship conjecture.Comment: 4 pages, ReVTeX, Phys Rev D Vol 62 107502 (2000

Why do naked singularities form in gravitational collapse?

We investigate what are the key physical features that cause the development of a naked singularity, rather than a black hole, as the end-state of spherical gravitational collapse. We show that sufficiently strong shearing effects near the singularity delay the formation of the apparent horizon. This exposes the singularity to an external observer, in contrast to a black hole, which is hidden behind an event horizon due to the early formation of an apparent horizon.Comment: revised for clarity, new figure included; version accepted by Phys. Rev. D (RC

Classical and quantum properties of a 2-sphere singularity

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.Comment: 10 pages, 1 figure, minor corrections, final versio

Dynamics of Non-adiabatic Charged Cylindrical Gravitational Collapse

This paper is devoted to study the dynamics of gravitational collapse in the Misner and Sharp formalism. We take non-viscous heat conducting charged anisotropic fluid as a collapsing matter with cylindrical symmetry. The dynamical equations are derived and coupled with the transport equation for heat flux obtained from the M$\ddot{u}$ller-Israel-Stewart causal thermodynamic theory. We discuss the role of anisotropy, electric charge and radial heat flux over the dynamics of the collapse with the help of coupled equation.Comment: 15 pages, accepted for publication in Astrophys. Space Sc