Charged Cylindrical Collapse of Anisotropic Fluid

Following the scheme developed by Misner and Sharp, we discuss the dynamics of gravitational collapse. For this purpose, an interior cylindrically symmetric spacetime is matched to an exterior charged static cylindrically symmetric spacetime using the Darmois matching conditions. Dynamical equations are obtained with matter dissipating in the form of shear viscosity. The effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we show that homogeneity in energy density and conformal flatness of spacetime are necessary and sufficient for each other.Comment: 19 pages, accepted for publication in Gen. Relativ. Gra

Ideal Stars and General Relativity

We study a system of differential equations that governs the distribution of matter in the theory of General Relativity. The new element in this paper is the use of a dynamical action principle that includes all the degrees of freedom, matter as well as metric. The matter lagrangian defines a relativistic version of non-viscous, isentropic hydrodynamics. The matter fields are a scalar density and a velocity potential; the conventional, four-vector velocity field is replaced by the gradient of the potential and its scale is fixed by one of the eulerian equations of motion, an innovation that significantly affects the imposition of boundary conditions. If the density is integrable at infinity, then the metric approaches the Schwarzschild metric at large distances. There are stars without boundary and with finite total mass; the metric shows rapid variation in the neighbourhood of the Schwarzschild radius and there is a very small core where a singularity indicates that the gas laws break down. For stars with boundary there emerges a new, critical relation between the radius and the gravitational mass, a consequence of the stronger boundary conditions. Tentative applications are suggested, to certain Red Giants, and to neutron stars, but the investigation reported here was limited to polytropic equations of state. Comparison with the results of Oppenheimer and Volkoff on neutron cores shows a close agreement of numerical results. However, in the model the boundary of the star is fixed uniquely by the required matching of the interior metric to the external Schwarzschild metric, which is not the case in the traditional approach.Comment: 26 pages, 7 figure

Interior of a Schwarzschild black hole revisited

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.Comment: 15 pages, 7 figures, Revtex4. V2: Version to appear in Foundations of Physic

The phase free, longitudinal, magnetic component of vacuum electromagnetism

A charge $q$ moving in a reference laboratory system with constant velocity {\bf V} in the $X$-axis produces in the $Z$-axis a longitudinal, phase free, vacuum magnetic field which is identified as the radiated ${\bf B}^{(3)}$ field of Evans, Vigier and others.Comment: ReVTeX file, 7pp., no figure

Dynamics of Viscous Dissipative Plane Symmetric Gravitational Collapse

We present dynamical description of gravitational collapse in view of Misner and Sharp's formalism. Matter under consideration is a complicated fluid consistent with plane symmetry which we assume to undergo dissipation in the form of heat flow, radiation, shear and bulk viscosity. Junction conditions are studied for a general spacetime in the interior and Vaidya spacetime in the exterior regions. Dynamical equations are obtained and coupled with causal transport equations derived in context of M$\ddot{u}$ller Israel Stewart theory. The role of dissipative quantities over collapse is investigated.Comment: 17 pages, accepted for publication in Gen. Relativ. Gra

Neutron stars in generalized f(R) gravity

Quartic gravity theory is considered with the Einstein-Hilbert Lagrangean $R+aR^{2}+bR_{\mu \nu}R^{\mu \nu},$ $R_{\mu \nu}$ being Ricci\'s tensor and R the curvature scalar. The parameters $a$ and $b$ are taken of order 1 km$^{2}.$ Arguments are given which suggest that the effective theory so obtained may be a plausible approximation of a viable theory. A numerical integration is performed of the field equations for a free neutron gas. As in the standard Oppenheimer-Volkoff calculation the star mass increases with increasing central density until about 1 solar mass and then decreases. However a dramatic difference exists in the behaviour of the baryon number, which increases monotonically. The calculation suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.Comment: Keywords: stars, neutron stars; gravity; modified gravity Accepted in Astrophysics and Space Scienc

Neutron Stars in a Varying Speed of Light Theory

We study neutron stars in a varying speed of light (VSL) theory of gravity in which the local speed of light depends upon the value of a scalar field $\phi$. We find that the masses and radii of the stars are strongly dependent on the strength of the coupling between $\phi$ and the matter field and that for certain choices of coupling parameters, the maximum neutron star mass can be arbitrarily small. We also discuss the phenomenon of cosmological evolution of VSL stars (analogous to the gravitational evolution in scalar-tensor theories) and we derive a relation showing how the fractional change in the energy of a star is related to the change in the cosmological value of the scalar field.Comment: 15 pages, 2 figures. Added solutions with a more realistic equation of state. To be published in PR

Thermodynamics with long-range interactions: from Ising models to black-holes

New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to calculate the degree of non-extensivity for such a system. We find that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. The system still possesses a parameter akin to a global temperature, which is constant throughout the substance. There is also a useful quantity which acts like a {\it local temperatures} and it varies throughout the substance. These quantities are closely related to counterparts found in general relativity. A lattice model with long-range spin-spin coupling is studied. This is compared with systems such as those encountered in general relativity, and gravitating systems with Newtonian-type interactions. A long-range lattice model is presented which can be seen as a black-hole analog. One finds that the analog's temperature and entropy have many properties which are found in black-holes. Finally, the entropy scaling behavior of a gravitating perfect fluid of constant density is calculated. For weak interactions, the entropy scales like the volume of the system. As the interactions become stronger, the entropy becomes higher near the surface of the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22 pages, 2 figure

Minimum black hole mass from colliding Gaussian packets

We study the formation of a black hole in the collision of two Gaussian packets. Rather than following their dynamical evolution in details, we assume a horizon forms when the mass function for the two packets becomes larger than half the flat areal radius, as it would occur in a spherically symmetric geometry. This simple approximation allows us to determine the existence of a minimum black hole mass solely related to the width of the packets. We then comment on the possible physical implications, both in classical and quantum physics, and models with extra spatial dimensions.Comment: 11 pages, 4 figure

Non-adiabatic collapse of a quasi-spherical radiating star

A model is proposed of a collapsing quasi-spherical radiating star with matter content as shear-free isotropic fluid undergoing radial heat-flow with outgoing radiation. To describe the radiation of the system, we have considered both plane symmetric and spherical Vaidya solutions. Physical conditions and thermodynamical relations are studied using local conservation of momentum and surface red-shift. We have found that for existence of radiation on the boundary, pressure on the boundary is not necessary.Comment: 8 Latex pages, No figures, Revtex styl