Shell Of Matter Research Articles

The cosmic ray signature of dark matter caustics

Gravitational collapse of dark matter, merger of dark matter haloes and tidal disruption of satellites are among processes which lead to the formation of fine and dense dark matter shells, also known as dark matter caustics. The putative weakly interacting species which may form the dark matter are expected to strongly annihilate in these dense regions of the Milky Way halo and generate in particular antiprotons and positrons. We derive the flux of these rare antimatter particles at the Earth and show that it depends significantly on the cut-off radius of the dark matter distribution at the Galactic centre. Boost factors of ∼30 are found with respect to a smooth Navarro, Frenk & White (NFW) profile for high-energy antiprotons and low-energy positrons if this cut-off radius is taken to be 300 pc – a somewhat extreme value though. This yields a detectable antiproton signal around hundreds of Gev in models where the annihilation cross-section today is enhanced by non-perturbative effects as in the generic case of a heavy wino. However, dark matter caustics cannot provide a better explanation for the HEAT excess reported above ∼10 GeV than a smooth NFW or isothermal cored distribution.

Mass spectrum and statistical entropy of the BTZ black hole from canonical quantum gravity

In a recent publication we developed a canonical quantization program describing the gravitational collapse of a spherical dust cloud in $2+1$ dimensions with a negative cosmological constant $\ensuremath{-}\ensuremath{\Lambda}\ensuremath{\equiv}\ensuremath{-}{l}^{\ensuremath{-}2}l0$. In this paper we address the quantization of the Banados-Teitelboim-Zanelli (BTZ) black hole. We show that the mass function describing the black hole is made of two pieces, a constant nonvanishing boundary contribution and a discrete spectrum of the form ${\ensuremath{\mu}}_{n}=\frac{\ensuremath{\hbar}}{l}(n+\frac{1}{2})$. The discrete spectrum is obtained by applying the Wheeler-DeWitt equation with a particular choice of factor ordering and interpreted as giving the energy levels of the collapsed matter shells that form the black hole. Treating a black hole microstate as a particular distribution of shells among the levels, we determine the canonical entropy of the BTZ black hole. Comparison with the Bekenstein-Hawking entropy shows that the boundary energy is related to the central charge of the Virasoro algebra that generates the asymptotic symmetry group of the three-dimensional anti-de Sitter space ${\mathrm{AdS}}_{3}$. This gives a connection between the Wheeler-DeWitt approach and the conformal field theory approach.

Pulsational pair instability as an explanation for the most luminous supernovae

The extremely luminous supernova SN 2006gy (ref. 1) challenges the traditional view that the collapse of a stellar core is the only mechanism by which a massive star makes a supernova, because it seems too luminous by more than a factor of ten. Here we report that the brightest supernovae in the modern Universe arise from collisions between shells of matter ejected by massive stars that undergo an interior instability arising from the production of electron-positron pairs. This 'pair instability' leads to explosive burning that is insufficient to unbind the star, but ejects many solar masses of the envelope. After the first explosion, the remaining core contracts and searches for a stable burning state. When the next explosion occurs, several solar masses of material are again ejected, which collide with the earlier ejecta. This collision can radiate 10(50) erg of light, about a factor of ten more than an ordinary supernova. Our model is in good agreement with the observed light curve for SN 2006gy and also shows that some massive stars can produce more than one supernova-like outburst.

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.

Frankenstein's glue: transition functions for approximate solutions

Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress–energy tensor depends on derivatives of these functions.

Quark-nova remnants

We explore the formation and evolution of debris ejected around quark stars in the Quark Nova scenario, and the application to Soft Gamma-ray Repeaters (SGRs) and Anomolous X-ray Pulsars (AXPs). If an isolated neutron star explodes as a Quark Nova, an Iron-rich shell of degenerate matter forms out of the fall-back (crust) material. Our model can account for many of the observed features of SGRs and AXPs such as: (i) the two types of bursts (giant and regular); (ii) the spin-up and spin-down episodes during and following the bursts with associated persistant increases in $\dot{P}$; (iii) the energetics of the boxing day burst, SGR1806$+$20; (iv) the presence of an Iron line as observed in SGR1900$+$14; (v) the correlation between the far-Infrared and the X-ray fluxes during the bursting episode and the quiescent phase; (vi) the hard X-ray component observed in SGRs during the giant bursts, and (vii) the discrepancy between the ages of SGRs/AXPs and their supernova remnants. We also find a natural evolutionary relationship between SGRs and AXPs in our model which predicts that only the youngest SGRs/AXPs are most likely to exhibit strong bursting. Many features of X-ray Dim Isolated Neutron stars (XDINs) are also accounted for in our model such as, (i) the two-component blackbody spectra; (ii) the absorption lines around 300 eV; and (iii) the excess optical emission.

On the Buchdahl Inequality for Spherically Symmetric Static Shells

A classical result by Buchdahl [6] shows that for static solutions of the spherically symmetric Einstein equations, the ADM mass M and the area radius R of the boundary of the body, obey the inequality 2M/R ≤ 8/9. The proof of this inequality rests on the hypotheses that the energy density is non-increasing outwards and that the pressure is isotropic. In this work neither of Buchdahl’s hypotheses are assumed. We consider non-isotropic spherically symmetric shells, supported in [R 0, R 1], R 0 > 0, of matter models for which the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1. We show a Buchdahl type inequality for shells which are thin; given an \(\epsilon < 1/4\) there is a κ > 0 such that 2M/R 1 ≤ 1 − κ when \(R_1/R_0 \leq 1 + \epsilon\). It is also shown that for a sequence of solutions such that R 1/R 0 → 1, the limit supremum of 2M/R 1 of the sequence is bounded by ((2Ω + 1)2 − 1)/(2Ω + 1)2. In particular if Ω = 1, which is the case for Vlasov matter, the bound is 8/9. The latter result is motivated by numerical simulations [3] which indicate that for non-isotropic shells of Vlasov matter 2M/R 1 ≤ 8/9, and moreover, that the value 8/9 is approached for shells with R 1/R 0 → 1. In [1] a sequence of shells of Vlasov matter is constructed with the properties that R 1/R 0 → 1, and that 2M/R 1 equals 8/9 in the limit. We emphasize that in the present paper no field equations for the matter are used, whereas in [1] the Vlasov equation is important.

On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System

In a previous work \cite{An1} matter models such that the energy density $\rho\geq 0,$ and the radial- and tangential pressures $p\geq 0$ and $q,$ satisfy $p+q\leq\Omega\rho, \Omega\geq 1,$ were considered in the context of Buchdahl's inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, $[R_0,R_1], R_0>0,$ satisfies $R_1/R_0<1/4.$ Moreover, given a sequence of solutions such that $R_1/R_0\to 1,$ then the limit supremum of $2M/R_1$ was shown to be bounded by $((2\Omega+1)^2-1)/(2\Omega+1)^2.$ In this paper we show that the hypothesis that $R_1/R_0\to 1,$ can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of $2M/R_1$ is bounded, but that the limit is $((2\Omega+1)^2-1)/(2\Omega+1)^2=8/9,$ since $\Omega=1$ for Vlasov matter. Thus, static shells of Vlasov matter can have $2M/R_1$ arbitrary close to $8/9,$ which is interesting in view of \cite{AR2}, where numerical evidence is presented that 8/9 is an upper bound of $2M/R_1$ of any static solution of the spherically symmetric Einstein-Vlasov system.

The spherical collapse model with shell-crossing

In this work, we study the formation and evolution of dark matter haloes by means of the spherical infalling model with shell-crossing. We present a framework to tackle this effect properly based on the numerical follow-up, with time, of that individual shell of matter that contains always the same fraction of mass with respect to the total mass. In this first step, we do not include angular momentum, velocity dispersion or triaxiality. Within this framework -named as the spherical shell tracker - we investigate the dependence of the evolution of the halo with virial mass, with the adopted mass fraction of the shell, and for different cosmologies. We find that our results are very sensitive to a variation of the halo virial mass or the mass fraction of the shell that we consider. However, we obtain a negligible dependence on cosmology. Furthermore, we show that the effect of shell-crossing plays a crucial role in the way that the halo reaches the stabilization in radius and the virial equilibrium. We find that the values currently adopted in the literature for the actual density contrast at the moment of virialization, δ vir , may not be accurate enough. In this context, we stress the problems related to the definition of a virial mass and a virial radius for the halo. The question of whether the results found here may be obtained by tracking the shells with an analytic approximation remains to be explored.

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.

The Role of the Institutions of Higher Education in the Promotion of the Entrepreneurship and the Small Business

Entrepreneurship is listed among the key competencies of the new generations. It is essential trait for the young people in the new, fast changing environment, no matter shell they link their careers with the small business or not. Consequently, the education systems can substantially contribute to the successful promotion of the entrepreneurship and to the larger employment of the new graduates within their own business ventures. According to the Working Program of the European Union (EU) known as Education and Training for the 2010 the entrepreneurship should be studied on the levels of the elementary, the intermediate and the higher education, as well as through the systems of the life long learning. The requirements for the higher education systems are particularly explicit. The entrepreneurship trait should be integrated in all curricula and motivate the students to choose it as a distinct course, too. Various combinations between technical and business expertise and the implementation of the business concepts developed by the students should particularly be encouraged. The objective of this paper is to explore the best practices in the education for entrepreneurship in the EU, the countries of the European Charter for Small Businesses (including Macedonia) and in the USA, and to identify the possibilities for their application in our institutions of the higher education.

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 Gravitational Collapse of a Cylindrical Shell of Dust

The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at this naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and ensures that the dust shell passes through the naked singularity. When the cylindrical shell leaves its symmetry axis away, the naked singularity disappears, and regularity is recovered. We construct numerical solutions with this feature. This result implies that the gravity produced by a thick cylindrical shell of dust is too weak to bind the shell even if it engenders the formation of a curvature singularity which is so strong as to satisfy the limiting focusing condition. For this reason, this naked singularity is very weak in the extended spacetime; the metric tensor is $C^{1-}$ even at the naked singularity, and the extended spacetime is complete for almost all geodesics. This feature is also seen for singular hypersurfaces. Such an extended spacetime can be regarded as phenomenological in the sense that it is valid if the relevant microphysics length scale is sufficiently small compared to the scale of interest.

GRBs, SGRs by UHE leptons showering, blazing and re-brightening by precessing Gamma Jets in-off axis

A list of questions regarding Gamma Ray Bursts (GRBs) and Soft Gamma Repeaters (SGRs) remain unanswered within the Fireball-cone and Magnetar explosive scenarios. A persistent, thin (less than micron-sr solid angle) precessing and spinning gamma jet, with a power output comparable to the progenitor supernova (SN) or XRay pulsar, may explain these issues. The precessing jets may have a few hours characteristic decay time, while their decreasing intensity follow a power law for thousands of years. The orientation of the spinning and precessing beam respect to the line of sight plays a key role : the farthest GRB events in widest cosmic volumes correspond generally to a very narrow and on-axis beam, while for the nearest ones sources are mostly observable off-axis. Consequentely the far ones are the hardest and the most bright and viceversa nearest one are mostly softer and longest ones as in Amati correlation. We expect that nearby off-axis GRBs would be accompanied by a chain of OT and radio bumps as in GRB030329-SN2003 and latest GRB060218-SN2006 events. Delayed blazing jets are observable in the local universe as X-Ray Flahes (XRFs) or short GRBs often as orphan afterglow event, and at closer distances as SGRs and anomalous X-ray Pulsars AXRPs. The gamma jet is originated by ultra-relativistic electron pairs showering via Synchrotron (or Inverse Compton) radiation. The electron pairs escape from the inner SN core thanks to a more penetrating couriers, the relativistic PeV muon pairs, themselves secondaries of inner UHE hadron jets. They are 'transparent' through the SN shells of matter and lights; they decay far away in to electron pairs (and later on) in gamma and neutrinos jets. Then GRBs (and SGRs) are not the most explosive event of the Universe, but just the most beamed ones.

New derivation of the variational principle for the dynamics of a gravitating spherical shell

The dynamics of a self-gravitating matter shell in general relativity is discussed in general. The case of a spherical shell composed of an arbitrary ideal fluid is then considered, and its Lagrangian function is derived from first principles. For this purpose, the standard Hilbert action is modified by an appropriate surface term at spatial infinity. The total Hamiltonian of the composed ``$\mathrm{\text{shell}}+\mathrm{\text{gravity}}$'' system is then calculated. Known results for the dust matter are recovered as particular cases. The above ``surface renormalization'' of the Hilbert action may be used for any spatially flat spacetime.

Evolution of thick shells in curved spacetimes

We extend our previous formalism in order to analyse the dynamics of a general shell of matter with an arbitrary finite thickness immersed in a curved spacetime. Within this new formulation, we obtain the equations of motion of a spherically symmetric dust thick shell immersed in vacuum as well as Friedmann–Robertson–Walker spacetimes.

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.

The interstellar medium in the Upper Cepheus-Cassiopeia region

We have studied the kinematics and spatial distribution of the interstellar gas in the sky region 110° ≤l≤ 135°, 10° ≤ b ≤ 20°, using the extensive Leiden-Dwingeloo Survey of H I emission and the Columbia Survey of CO emission. The spectra show two main velocity components, namely feature A that has a mean local standard of rest (LSR) velocity of ∼0 km s -1 and is due to the Lindblad ring of the Gould belt, and feature C that has a mean LSR velocity of ∼ -11 km s -1 and is associated to the local arm or Orion arm. The H i and CO distributions of feature A in the region trace a large complex of gas and dust known as the Cepheus Flare, which lies at a distance of 300 pc. The spectral line profiles of feature A, which are rather broad and often double-peaked, reveal that the Cepheus Flare forms part of a big expanding shell of interstellar matter that encloses an old supernova remnant associated with a void inside the Cepheus Flare. On the other hand, by analysing the distribution and velocity structure of feature C, we have detected a second large expanding shell in the region, located at a distance of 800 pc in the local arm. This shell surrounds the stellar association Cepheus OB4 and was probably generated by stellar winds and supernovae of Cepheus OB4. The radii, expansion velocities and Hi masses of the two shells are approximately 50 pc, 4 km s -1 and 1.3 x 10 4 M ⊙ for the Cepheus Flare shell and 100 pc, 4 km s -1 and 9.9 x 10 4 M ⊙ for the Cepheus OB4 shell. Both shells have similar ages of the order of a few 10 6 yr.

Classical dynamics and stability of collapsing thick shells of matter

We study the collapse towards the gravitational radius of a macroscopic spherical thick shell surrounding an inner massive core. This overall electrically neutral macroshell is composed of many nested δ-like massive microshells which can bear non-zero electric charge, and a possibly non-zero cosmological constant is also included. The dynamics of the shells is described by means of Israel's (Lanczos) junction conditions for singular hypersurfaces and, adopting a Hartree (mean-field) approach, an effective Hamiltonian for the motion of each microshell is derived which allows us to check the stability of the matter composing the macroshell. We end by briefly commenting on the quantum effects which may arise from the extension of our classical treatment to the semiclassical level.

Black hole non-formation in the matrix model

The leading classical low-energy effective actions for two-dimensional string theories have solutions describing the gravitational collapse of shells of matter into a black hole. It is shown that string loop corrections can be made arbitrarily small up to the horizon, but $\alpha'$ corrections cannot. The matrix model is used to show that typical collapsing shells do not form black holes in the full string theory. Rather, they backscatter out to infinity just before the horizon forms. The matrix model is also used to show that the naively expected particle production induced by the collapsing shell vanishes to leading order. This agrees with the string theory computation. From the point of view of the effective low energy field theory this result is surprising and involves a delicate cancellation between various terms.