Quasi-spherical gravitational collapse and the role of initial data, anisotropy and inhomogeneity

In this paper, the role of anisotropy and inhomogeneity has been studied in quasi-spherical gravitational collapse. Also the role of initial data has been investigated in characterizing the final state of collapse. Finally, a linear transformation on the initial data set has been presented and its impact has been discussed.Comment: RevTex, 7 Latex pages, No figure

Role of initial data in spherical collapse

We bring out here the role of initial data in causing the black hole and naked singularity phases as the final end state of a continual gravitational collapse. The collapse of a type I general matter field is considered, which includes most of the known physical forms of matter. It is shown that given the distribution of the density and pressure profiles at the initial surface from which the collapse evolves, there is a freedom in choosing rest of the free functions, such as the velocities of the collapsing shells, so that the end state could be either a black hole or a naked singularity depending on this choice. It is thus seen that it is the initial data that determines the end state of spherical collapse in terms of these outcomes, and we get a good picture of how these phases come about.Comment: 5 pages, Revtex4, Revised version, To appear in Physical Review

A characterization of the central shell-focusing singularity in spherical gravitational collapse

We give a characterization of the central shell-focusing curvature singularity that can form in the spherical gravitational collapse of a bounded matter distribution obeying the dominant energy condition. This characterization is based on the limiting behaviour of the mass function in the neighbourhood of the singularity. Depending on the rate of growth of the mass as a function of the area radius R, the singularity may be either covered or naked. The singularity is naked if this growth rate is slower than R, covered if it is faster than R, and either naked or covered if the growth rate is same as R.Comment: 12 pages, Latex, significantly revised version, including change of title. Revised version to appear in Classical and Quantum Gravit

On the genericity of spacetime singularities

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.Comment: 19 pages, To be published in the Raychaudhuri Volume, eds. Naresh Dadhich, Pankaj Joshi and Probir Ro

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

On the global visibility of singularity in quasi-spherical collapse

We analyze here the issue of local versus the global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions as to when a singularity will be only locally naked, rather than being globally visible, thus preseving the weak censorship hypothesis. The conditions for formation of a black hole or naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is the singularity in Szekeres spacetimes can be ``directionally naked''.Comment: Latex file, 32 pages, 12 postscript figures. To appear in the Journal of General Relativity and Gravitatio

The Final Fate of Spherical Inhomogeneous Dust Collapse

We examine the role of the initial density and velocity distribution in the gravitational collapse of a spherical inhomogeneous dust cloud. Such a collapse is described by the Tolman-Bondi metric which has two free functions: the `mass-function' and the `energy function', which are determined by the initial density and velocity profile of the cloud. The collapse can end in a black-hole or a naked singularity, depending on the initial parameters characterizing these profiles. In the marginally bound case, we find that the collapse ends in a naked singularity if the leading non-vanishing derivative of the density at the center is either the first one or the second one. If the first two derivatives are zero, and the third derivative non-zero, the singularity could either be naked or covered, depending on a quantity determined by the third derivative and the central density. If the first three derivatives are zero, the collapse ends in a black hole. In particular, the classic result of Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole, is recovered as a special case. Analogous results are found when the cloud is not marginally bound, and also for the case of a cloud starting from rest. We also show how the strength of the naked singularity depends on the density and velocity distribution. Our analysis generalizes and simplifies the earlier work of Christodoulou and Newman [4,5] by dropping the assumption of evenness of density functions. It turns out that relaxing this assumption allows for a smooth transition from the naked singularity phase to the black-hole phase, and also allows for the occurrence of strong curvature naked singularities.Comment: 23 pages; Plain Tex; TIFR-TAP preprin

Sub-Nanosecond Time of Flight on Commercial Wi-Fi Cards

Time-of-flight, i.e., the time incurred by a signal to travel from transmitter to receiver, is perhaps the most intuitive way to measure distances using wireless signals. It is used in major positioning systems such as GPS, RADAR, and SONAR. However, attempts at using time-of-flight for indoor localization have failed to deliver acceptable accuracy due to fundamental limitations in measuring time on Wi-Fi and other RF consumer technologies. While the research community has developed alternatives for RF-based indoor localization that do not require time-of-flight, those approaches have their own limitations that hamper their use in practice. In particular, many existing approaches need receivers with large antenna arrays while commercial Wi-Fi nodes have two or three antennas. Other systems require fingerprinting the environment to create signal maps. More fundamentally, none of these methods support indoor positioning between a pair of Wi-Fi devices without~third~party~support. In this paper, we present a set of algorithms that measure the time-of-flight to sub-nanosecond accuracy on commercial Wi-Fi cards. We implement these algorithms and demonstrate a system that achieves accurate device-to-device localization, i.e. enables a pair of Wi-Fi devices to locate each other without any support from the infrastructure, not even the location of the access points.Comment: 14 page