Genericity aspects in gravitational collapse to black holes and naked singularities

We investigate here the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. We first study here in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.Comment: 24 pages, 6 figures, some changes in text and figures to match the version accepted for publication by IJMP

Cosmic censorship and spherical gravitational collapse with tangential pressure

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive pressure there is a finite region near the center which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be covered by a horizon. For negative pressure the entire object collapses inwards, but any singularities that could arise are not naked. Thus the nature of the evolution is very different from that of dust, even when the ratio of pressure to density is infinitesimally small.Comment: 16 pages, Latex file, two figures, uses epsf.st

A hadronic scenario for HESS J1818-154

Aims: G15.4+0.1 is a faint supernova remnant (SNR) that has recently been associated with the gamma-ray source HESS J1818-154. We investigate a hadronic scenario for the production of the gamma-ray emission. Methods: Molecular 13CO (J=1-0) taken from the Galactic Ring Survey (GRS) and neutral hydrogen (HI) data from the Southern Galactic Plane Survey (SGPS) have been used in combination with new 1420 MHz radio continuum observations carried out with the Giant Metrewave Radio Telescope (GMRT). Results: From the new observations and analysis of archival data we provided for the first time a reliable estimate for the distance to the SNR G15.4+0.1 and discovered molecular clouds located at the same distance. On the basis of HI absorption features, we estimate the distance to G15.4+0.1 in 4.8+/-1.0 kpc. The 13CO observations clearly show a molecular cloud about 5 arcmin in size with two bright clumps, labeled A and B, clump A positionally associated with the location of HESS J1818-154 and clump B in coincidence with the brightest northern border of the radio SNR shell. The HI absorption and the 13CO emission study indicates a possible interaction between the molecular material and the remnant. We estimate the masses and densities of the molecular gas as (1.2+/-0.5)X10^3 M_sun and (1.5+/-0.4)X10^3 cm^-3 for clump A and (3.0+/-0.7)X10^3 M_sun and (1.1+/-0.3)X10^3 cm^-3 for clump B. Calculations show that the average density of the molecular clump A is sufficient to produce the detected gamma-ray flux, thus favoring a hadronic origin for the high-energy emission.Comment: Accepted to be published in Astronomy and Astrophysics Letter

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

Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Time dependent spectral modeling of Markarian 421 during a violent outburst in 2010

We present the results of extensive modeling of the spectral energy distributions (SEDs) of the closest blazar (z=0.031) Markarian 421 (Mrk 421) during a giant outburst in February 2010. The source underwent rapid flux variations in both X-rays and very high energy (VHE) gamma-rays as it evolved from a low-flux state on 2010 February 13-15 to a high-flux state on 2010 February 17. During this period, the source exhibited significant spectral hardening from X-rays to VHE gamma-rays while exhibiting a "harder when brighter" behavior in these energy bands. We reproduce the broadband SED using a time-dependent multi-zone leptonic jet model with radiation feedback. We find that an injection of the leptonic particle population with a single power-law energy distribution at shock fronts followed by energy losses in an inhomogeneous emission region is suitable for explaining the evolution of Mrk 421 from low- to high-flux state in February 2010. The spectral states are successfully reproduced by a combination of a few key physical parameters, such as the maximum $\&$ minimum cutoffs and power-law slope of the electron injection energies, magnetic field strength, and bulk Lorentz factor of the emission region. The simulated light curves and spectral evolution of Mrk 421 during this period imply an almost linear correlation between X-ray flux at 1-10 keV energies and VHE gamma-ray flux above 200 GeV, as has been previously exhibited by this source. Through this study, a general trend that has emerged for the role of physical parameters is that, as the flare evolves from a low- to a high-flux state, higher bulk kinetic energy is injected into the system with a harder particle population and a lower magnetic field strength.Comment: 13 pages, 5 figures, accepted for publication in MNRA