6,320 research outputs found
Gravitational collapse of generalised Vaidya spacetime
We study the gravitational collapse of a generalised Vaidya spacetime in the
context of the Cosmic Censorship hypothesis. We develop a general mathematical
framework to study the conditions on the mass function so that future directed
non-spacelike geodesics can terminate at the singularity in the past. Thus our
result generalises earlier works on gravitational collapse of the combinations
of Type-I and Type-II matter fields. Our analysis shows transparently that
there exist classes of generalised Vaidya mass functions for which the collapse
terminates with a locally naked central singularity. We calculate the strength
of the these singularities to show that they are strong curvature singularities
and there can be no extension of spacetime through them.Comment: 8 pages, 2 figures, Changes in the text, Matches the accepted version
in Physical Review
Is cosmic censorship restored in higher dimensions?
In this paper we extend the analysis of gravitational collapse of generalised
Vaidya spacetimes to higher dimensions, in the context of the Cosmic Censorship
Conjecture. We present the sufficient conditions on the generalised Vaidya mass
function, that will generate a locally naked singular end state. Our analysis
here generalises all the earlier works on collapsing higher dimensional
generalised Vaidya spacetimes. With specific examples, we show the existence of
classes of mass functions that lead to a naked singularity in four dimensions,
which gets covered on transition to higher dimensions. Hence for these classes
of mass function Cosmic Censorship gets restored in higher dimensions and the
transition to higher dimensions restricts the set of initial data that results
in a naked singularity.Comment: 7 pages, revtex4; Title changed, Matches the PRD versio
Cloud of strings for radiating black holes in Lovelock gravity
We present exact spherically symmetric null dust solutions in the third order
Lovelock gravity with a string cloud background in arbitrary dimensions,.
This represents radiating black holes and generalizes the well known Vaidya
solution to Lovelock gravity with a string cloud in the background. We also
discuss the energy conditions and horizon structures, and explicitly bring out
the effect of the string clouds on the horizon structure of black hole
solutions for the higher dimensional general relativity and
Einstein-Gauss-Bonnet theories. It turns out that the presence of the coupling
constant of the Gauss-Bonnet terms and/or background string clouds completely
changes the structure of the horizon and this may lead to a naked singularity.
We recover known spherically symmetric radiating models as well as static black
holes in the appropriate limits.Comment: 9 pages, To appear in Phys. Rev.
Tri-connectivity Augmentation in Trees
For a connected graph, a {\em minimum vertex separator} is a minimum set of
vertices whose removal creates at least two connected components. The vertex
connectivity of the graph refers to the size of the minimum vertex separator
and a graph is -vertex connected if its vertex connectivity is , . Given a -vertex connected graph , the combinatorial problem {\em
vertex connectivity augmentation} asks for a minimum number of edges whose
augmentation to makes the resulting graph -vertex connected. In this
paper, we initiate the study of -vertex connectivity augmentation whose
objective is to find a -vertex connected graph by augmenting a minimum
number of edges to a -vertex connected graph, . We shall
investigate this question for the special case when is a tree and . In
particular, we present a polynomial-time algorithm to find a minimum set of
edges whose augmentation to a tree makes it 3-vertex connected. Using lower
bound arguments, we show that any tri-vertex connectivity augmentation of trees
requires at least edges, where and
denote the number of degree one vertices and degree two vertices,
respectively. Further, we establish that our algorithm indeed augments this
number, thus yielding an optimum algorithm.Comment: 10 pages, 2 figures, 3 algorithms, Presented in ICGTA 201
Geometrical properties of trapped surfaces and apparent horizons
In this paper, we perform a detailed investigation on the various geometrical
properties of trapped surfaces and the boundaries of trapped region in general
relativity. This treatment extends earlier work on LRS II spacetimes to a
general 4 dimensional spacetime manifold. Using a semi-tetrad covariant
formalism, that provides a set of geometrical and matter variables, we
transparently demonstrate the evolution of the trapped region and also extend
Hawking's topology theorem to a wider class of spacetimes. In addition, we
perform a stability analysis for the apparent horizons in this formalism,
encompassing earlier works on this subject. As examples, we consider the
stability of MOTS of the Schwarzschild geometry and Oppenheimer-Snyder
collapse.Comment: 16 pages, Revtex
Universality of isothermal fluid spheres in Lovelock gravity
We show universality of isothermal fluid spheres in pure Lovelock gravity
where the equation of motion has only one th order term coming from the
corresponding Lovelock polynomial action of degree . Isothermality is
characterized by the equation of state, and the property,
. Then the solution describing isothermal spheres, which
exist only for the pure Lovelock equation, is of the same form for the general
Lovelock degree in all dimenions . We further prove that the
necessary and sufficient condition for the isothermal sphere is that its metric
is conformal to the massless global monopole or the solid angle deficit metric,
and this feature is also universal.Comment: 11 page
Exact barotropic distributions in Einstein-Gauss-Bonnet gravity
New exact solutions to the field equations in the Einstein--Gauss--Bonnet
modified theory of gravity for a 5--dimensional spherically symmetric static
distribution of a perfect fluid is obtained. The Frobenius method is used to
obtain this solution in terms of an infinite series. Exact solutions are
generated in terms of polynomials from the infinite series. The 5--dimensional
Einstein solution is also found by setting the coupling constant to be zero.
All models admit a barotropic equation of state. Linear equations of state are
admitted in particular models with the energy density profile of isothermal
distributions. We examine the physicality of the solution by studying
graphically the isotropic pressure and the energy density. The model is well
behaved in the interior and the weak, strong and dominant energy conditions are
satisfied.Comment: 15 pages, submitted for publicatio
Accretion onto a black hole in a string cloud background
We examine the accretion process onto the black hole with a string cloud
background, where the horizon of the black hole has an enlarged radius , due to the string cloud parameter . The problem of stationary, spherically symmetric accretion of a polytropic
fluid is analysed to obtain an analytic solution for such a perturbation.
Generalised expressions for the accretion rate , critical radius
, and other flow parameters are found. The accretion rate is an
explicit function of the black hole mass , as well as the gas boundary
conditions and the string cloud parameter . We also find the gas
compression ratios and temperature profiles below the accretion radius and at
the event horizon. It is shown that the mass accretion rate, for both the
relativistic and the non-relativistic fluid by a black hole in the string cloud
model, increases with increase in .Comment: 9 pages, To appear in Phys. Rev.
Clouds of strings in third-order Lovelock gravity
Lovelock theory is a natural extension of the Einstein theory of general
relativity to higher dimensions in which the first and second orders
correspond, respectively, to general relativity and Einstein-Gauss-Bonnet
gravity. We present exact black hole solutions of -dimensional
spacetime for first-, second-, and third-order Lovelock gravities in a string
cloud background. Further, we compute the mass, temperature, and entropy of
black hole solutions for the higher-dimensional general relativity and
Einstein-Gauss-Bonnet theories and also perform thermodynamic stability of
black holes. It turns out that the presence of the Gauss-Bonnet term and/or
background string cloud completely changes the black hole thermodynamics.
Interestingly, the entropy of a black hole is unaffected due to a background
string cloud. We rediscover several known spherically symmetric black hole
solutions in the appropriate limits.Comment: 13 pages, 7 figures, Accepted for publication in Physical Review
Compact stars with quadratic equation of state
We provide new exact solutions to the Einstein-Maxwell system of equations
for matter configurations with anisotropy and charge. The spacetime is static
and spherically symmetric. A quadratic equation of state is utilised for the
matter distribution. By specifying a particular form for one of the
gravitational potentials and the electric field intensity we obtain new exact
solutions in isotropic coordinates. In our general class of models, an earlier
model with a linear equation of state is regained. For particular choices of
parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR
J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical
analysis for the star PSR J1903+0327 reveals that our model is reasonable.Comment: 10 pages, submitted for publicatio
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