Thin Shell Of Matter Research Articles

Composite vacuum Brans-Dicke wormholes

We construct a new static spherically symmetric configuration composed of interior and exterior Brans-Dicke vacua matched at a thin matter shell. Both vacua correspond to the same Brans-Dicke coupling parameter $\omega$, however they are described by the Brans class I solution with different sets of parameters of integration. In particular, the exterior vacuum solution has $C_{ext}(\omega)\equiv 0$. In this case the Brans class I solution for any $\omega$ reduces to the Schwarzschild one being consistent with restrictions on the post-Newtonian parameters following from recent Cassini data. The interior region possesses a strong gravitational field, and so the interior vacuum solution has $C_{int}(\omega)=-1/(\omega+2)$. In this case the Brans class I solution describes a wormhole spacetime provided $\omega$ lies in the narrow interval $-2-\frac{\sqrt{3}}{3}<\omega<-2$. The interior and exterior regions are matched at a thin shell made from an ordinary perfect fluid with positive energy density and pressure obeying the barotropic equation of state $p=k\sigma$ with $0\le k\le1$. The resulting configuration represents a composite wormhole, i.e. the thin matter shell with the Schwarzschild-like exterior region and the interior region containing the wormhole throat.

STATIC SPHERICALLY SYMMETRIC SCALAR FIELD SPACETIMES WITH C0 MATCHING

All the classes of static massless scalar field models currently available in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields coupled to gravity, which does not have any strong curvature singularity. This class of models contain a thin shell of singular matter, which has a physical interpretation. The central curvature singularity is, however, avoided which is common to all static massless scalar field spacetime models known so far. Our result thus points out that the full class of solutions in this case may contain non-singular models, which is an intriguing possibility.

Numerical study of the adiabatic index effect for the Vishniac instability in supernova remnants

The Vishniac instability is supposed to explain the fragmentation of the thin shell of shocked matter in the radiative phase of supernova remnants. However its implication and its consequence on the morphological evolution of stellar systems is not fully demonstrated. The present paper tackles this subject by numerical simulations and focus on the role of the adiabatic index in the instability growth. The HYDRO-MUSCL 2D hydrodynamics code has been used to simulate the evolution of a supernova remnant thin shell and the triggering of the Vishniac instability in this thin shell. We have studied the temporal behavior of the perturbation. The first result of the numerical study is the existence of the Vishniac instability in the simulations. This result is proved by the overstability process observed in the simulations as predicted by the theoretical analysis. The second important result is the damping of the perturbation at late evolution and for all the set of parameters. Indeed the accretion of matter onto the shock damps the instability when theoretical analysis predicts its occurrence.

Black holes, compact objects and solar system tests in non-relativistic general covariant theory of gravity

We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in terms of the U(1) gauge field A. When solar system tests are considered, severe constraints on A are obtained, which seemingly pick up the Schwarzschild solution uniquely. In contrast to other versions of the Horava-Lifshitz theory, non-singular static stars made of a perfect fluid without heat flow can be constructed, due to the coupling of the fluid with the gauge field. These include the solutions with a constant pressure. We also study the general junction conditions across the surface of a star. In general, the conditions allow the existence of a thin matter shell on the surface. When applying these conditions to the perfect fluid solutions with the vacuum ones as describing their external spacetimes, we find explicitly the matching conditions in terms of the parameters appearing in the solutions. Such matching is possible even without the presence of a thin matter shell.

Black holes and stars in the Horava-Lifshitz theory with the projectability condition

We systematically study spherically symmetric static spacetimes filled with a fluid in the Horava-Lifshitz theory of gravity with the projectability condition, but without the detailed balance. We establish that when the spacetime is spatially Ricci flat the unique vacuum solution is the de Sitter Schwarzshcild solution, while when the spacetime has a nonzero constant curvature, there exist two different vacuum solutions; one is an (Einstein) static universe, and the other is a new spacetime. This latter spacetime is maximally symmetric and not flat. We find all the perfect fluid solutions for such spacetimes, in addition to a class of anisotropic fluid solutions of the spatially Ricci flat spacetimes. To construct spacetimes that represent stars, we investigate junction conditions across the surfaces of stars and obtain the general matching conditions with or without the presence of infinitely thin shells. It is remarkable that, in contrast to general relativity, the radial pressure of a star does not necessarily vanish on its surface even without the presence of a thin shell, due to the presence of high order derivative terms. Applying the junction conditions to our explicit solutions, we show that it is possible to match smoothly these solutions (all with nonzero radial pressures) to vacuum spacetimes without the presence of thin matter shells on the surfaces of stars.

Can accretion disk properties distinguish gravastars from black holes?

Gravastars, hypothetic astrophysical objects, consisting of a dark energy condensate surrounded by a strongly correlated thin shell of anisotropic matter, have been proposed as an alternative to the standard black hole picture of general relativity. Observationally distinguishing between astrophysical black holes and gravastars is a major challenge for this latter theoretical model. This is due to the fact that in static gravastars large stability regions (of the transition layer of these configurations) exist that are sufficiently close to the expected position of the event horizon, so that it would be difficult to distinguish the exterior geometry of gravastars from an astrophysical black hole. However, in the context of stationary and axially symmetrical geometries, a possibility of distinguishing gravastars from black holes is through the comparative study of thin accretion disks around rotating gravastars and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around slowly rotating gravastars, with all the metric tensor components estimated up to the second order in the angular velocity. Due to the differences in the exterior geometry, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures. In addition to this, it is also shown that the conversion efficiency of the accreting mass into radiation is always smaller than the conversion efficiency for black holes, i.e. gravastars provide a less efficient mechanism for converting mass to radiation than black holes. Thus, these observational signatures provide the possibility of clearly distinguishing rotating gravastars from Kerr-type black holes.

Reduced Hamiltonian for intersecting shells

The gauge usually adopted for extracting the reduced Hamiltonian of a thin spherical shell of matter in general relativity, becomes singular when dealing with two or more intersecting shells. We introduce here a more general class of gauges which is apt for dealing with intersecting shells. As an application we give the Hamiltonian treatment of two intersecting shells, both massive and massless. Such a formulation is applied to the computation of the semiclassical tunneling probability of two shells. The probability for the emission of two shells is simply the product of the separate probabilities thus showing no correlation in the emission probabilities in this model.

Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes

We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energy-momentum tensor [Phys. Rev. D 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of electromagnetic matter. We show the system reduces to the Reissner-Nordstrom spacetime in general, spherically symmetric coordinates in the vacuum limit. Furthermore, we show reduction to the charged Vaidya spacetime in non-null coordinates when certain equations of states are chosen. A model of gravitational collapse is discussed whereby a charged fluid resides within a boundary of finite radial extent on the initial hypersurface, and is allowed to radiate charged particles. Our formalism allows for the discussion of all regions in this model without the need for complicated matching schemes at the interfaces between successive regions. As further examples we consider the collapse of a thin shell of charged matter onto a Reissner-Nordstrom black hole. Finally, we reduce the entire system of equations to the static case such that we have the equations for hydrostatic equilibrium of a charged fluid.

Where are all the gravastars? Limits upon the gravastar model from accreting black holes

The gravastar model, which postulates a strongly correlated thin shell of anisotropic matter surrounding a region of anti-de Sitter space, has been proposed as an alternative to black holes. We discuss constraints that present-day observations of well-known black hole candidates place on this model. We focus upon two black hole candidates known to have extraordinarily low luminosities: the supermassive black hole in the galactic centre, Sagittarius A*, and the stellar-mass black hole, XTE J1118 + 480. We find that the length scale for modifications of the type discussed in Chapline et al (2003 Int. J. Mod. Phys. 18 3587–90) must be sub-Planckian.

Relativistic dynamics of spherical timelike shells

The dynamics of general relativistic timelike spherically symmetric thin shells of matter is considered, putting special emphasis on the physical interpretation of the models and, therefore, on the dependence of the dynamical behavior upon then the choice of the equation of state. From this point of view the general formalism is reviewed both in the Israel’s and in the canonical (Lagrangian and Hamiltonian) approach. Known exact solutions corresponding to closed equations of state are reviewed as well, and a new, wide class of nonlinear barotropic solutions is introduced and discussed in detail.

Comment on “Absence of trapped surfaces and singularities in cylindrical collapse”

Recently, the gravitational collapse of an infinite cylindrical thin shell of matter in an otherwise empty spacetime with two hypersurface orthogonal Killing vectors was studied by Gon\c{c}alves [Phys. Rev. {\bf D65}, 084045 (2002).]. By using three "alternative" criteria for trapped surfaces, the author claimed to have shown that {\em they can never form either outside or on the shell, regardingless of the matter content for the shell, except at asymptotical future null infinite}. Following Penrose's original idea, we first define trapped surfaces in cylindrical spacetimes in terms of the expansions of null directions orthogonal to the surfaces, and then show that the first criterion used by Gon\c{c}alves is incorrect. We also show that his analysis of non-existence of trapped surfaces in vacuum is incomplete. To confirm our claim, we present an example that is a solution to the vacuum Einstein field equations and satisfies all the regular conditions imposed by Gon\c{c}alves. After extending the solution to the whole spacetime, we show explicitly that trapped surfaces exist in the extended region.

Relativistic shells: Dynamics, horizons, and shell crossing

We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived and subsequently specialized to the vacuum case. We first examine the relative motion of two dust shells by focusing on the dynamics of the exterior shell, whereby the problem is reduced to that of a single shell with different active Schwarzschild masses on each side. We then examine the dynamics of shells with nonvanishing tangential pressure p, and show that there are no stable---stationary, or otherwise---solutions for configurations with a strictly linear barotropic equation of state, $p=\ensuremath{\alpha}\ensuremath{\sigma},$ where $\ensuremath{\sigma}$ is the proper surface energy density and $\ensuremath{\alpha}\ensuremath{\in}(\ensuremath{-}1,1).$ For arbitrary equations of state, we show that, provided the weak energy condition holds, the strong energy condition is necessary and sufficient for stability. We examine in detail the formation of trapped surfaces, and show explicitly that a thin boundary layer causes the apparent horizon to evolve discontinuously. Finally, we derive an analytical (necessary and sufficient) condition for neighboring shells to cross, and compare the discrete shell model with the well-known continuous Lema\^{\i}tre-Tolman-Bondi dust case.

Absence of trapped surfaces and singularities in cylindrical collapse

The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces in the vacuum portion of spacetime causally available to geodesic timelike observers. At asymptotic future null infinity, however, congruences of outgoing radial null geodesics become marginally trapped, due to the convergence induced by the shear caused by the interaction of a transverse wave component with the geodesics. The matter shell itself is shown to be always free of trapped surfaces, for this class of geometries. Finally, two simplified matter models are analytically examined. For one model, the weak energy condition is shown to be a necessary condition for collapse to halt; for the second case, it is a sufficient condition for collapse to be able to halt.

Nearly everywhere flat spaces

We discuss some spacetimes, which are flat everywhere except for a thin shell of matter or a string of matter, in the framework of the Israel formalism. First we study spherically symmetric universes with a single sheet of matter. Then we show that the construction of a cosmic string as a limit of various thin shell distributions of matter leads to identical results.

Rigidly Rotating Dust in General Relativity

A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.

Black hole formation in AdS and thermalization on the boundary

We investigate black hole formation by a spherically collapsing thin shell of matter in AdS space. This process has been suggested to have a holographic interpretation as thermalization of the CFT on the boundary of the AdS space. The AdS/CFT duality relates the shell in the bulk to an off-equilibrium state of the boundary theory which evolves towards a thermal equilibrium when the shell collapses to a black hole. We use 2-point functions to obtain information about the spectrum of excitations in the off-equilibrium state, and discuss how it characterizes the approach towards thermal equilibrium. The full holographic interpretation of the gravitational collapse would require a kinetic theory of the CFT at strong coupling. We speculate that the kinetic equations should be interpreted as a holographic dual of the equation of motion of the collapsing shell.

Puncture of gravitating domain walls

We investigate the semi-classical instability of vacuum domain walls to processes where the domain walls decay by the formation of closed string loop boundaries on their worldvolumes. Intuitively, a wall which is initially spherical may `pop', so that a hole corresponding to a string boundary component on the wall, may form. We find instantons, and calculate the rates, for such processes. We show that after puncture, the hole grows exponentially at the same rate that the wall expands. It follows that the wall is never completely thermalized by a single expanding hole; at arbitrarily late times there is still a large, thin shell of matter which may drive an exponential expansion of the universe. We also study the situation where the wall is subjected to multiple punctures. We find that in order to completely annihilate the wall by this process, at least four string loops must be nucleated. We argue that this process may be relevant in certain brane-world scenarios, where the universe itself is a domain wall.

Gravitational collapse of perfect fluid

The spherical gravitational collapse of a compact packet consisting of perfect fluid is studied. The spacetime outside the packet is described by the out-going Vaidya radiation fluid. It is found that when the collapse has continuous self-similarity the formation of black holes always starts with zero mass, and when the collapse has no self-similarity, the formation of black holes always starts with a finite non-zero mass. The packet is usually accompanied by a thin matter shell. The effects of the shell on the collapse are also studied.

Gravitational collapse of a shell of quantized matter

The semiclassical collapse, including lowest-order back-reaction, of a thin shell of self-gravitating quantized matter is illustrated. The conditions for which self-gravitating matter forms a thin shell are first discussed and an effective Lagrangian for such matter is obtained. The matter-gravity system is then quantized, the semiclassical limit for gravitation is taken and the method of adiabatic invariants is applied to the resulting time-dependent matter Hamiltonian. The governing equations are integrated numerically, for suitable initial conditions, in order to illustrate the effect of back-reaction, due to the creation of matter, in slowing down the collapse near the horizon.

Erratum: Causality violation and the weak energy condition

A simple self gravitating system --- a thin spherical shell of charged pressureless matter --- is naively quantized as a test case of quantum gravitational collapse. The model is interpreted in terms of an inner product on the positive energy states. An S-matrix is constructed describing scattering between negatively and positively infinite radius.