Thomas Zannias

The uniqueness of the Bekenstein black hole

The general static, spherically symmetric, asymptotically flat solution of the Einstein equations coupled to a conformal scalar field is determined; it depends on three free parameters. One of the parameters is eliminated by the requirement that the solution admits a smooth horizon and no naked curvature singularities, leading to the black hole solution discovered by Bekenstein. Although the scalar field is unbounded on the horizon, this should not be considered as a physical pathology.

Magnetic field decay in neutron stars: Analysis of general relativistic effects

An analysis of the role of general relativistic effects on the decay of neutron stars magnetic field is presented. At first, a generalized induction equation on an arbitrary static background geometry has been derived and, secondly, by a combination of analytical and numerical techniques, a comparison of the time scales for the decay of an initial dipole magnetic field in flat and curved spacetime is discussed. For the case of very simple neutron star models, rotation not accounted for and in the absence of cooling effects, we find that the inclusion of general relativistic effects result, on the average, in an enlargement of the decay time of the field in comparison to the flat spacetime case. Via numerical techniques we show that, the enlargement factor depends upon the dimensionless compactness ratio

The geometry of the tangent bundle and the relativistic kinetic theory of gases

{\epsilon}={2GM \over c^{2}R}

Shadow of a naked singularity

, and for

Global structure of Kerr–de Sitter spacetimes

{\epsilon}

Nonlinear instability of wormholes supported by exotic dust and a magnetic field

in the range

Kantowski–Sachs metrics with source: A massless scalar field

(0.3~,~0.5)

Tangent bundle formulation of a charged gas

, corresponding to compactness ratio of realistic neutron star models, this factor is between 1.2 to 1.3. The present analysis shows that general relativistic effects on the magnetic field decay ought to be examined more carefully than hitherto. A brief discussion of our findings on the impact of neutron stars physics is also presented.

Relativistic Kinetic Theory: An Introduction

This paper discusses the relativistic kinetic theory for a simple collisionless gas from a geometric perspective. We start by reviewing the rich geometrical structure of the tangent bundle TM of a given spacetime manifold, including the splitting of the tangent spaces of TM into horizontal and vertical subspaces and the natural metric and symplectic structure it induces on TM. Based on these structures we introduce the Liouville vector field L and a suitable Hamiltonian function H on TM. The Liouville vector field turns out to be the Hamiltonian vector field associated to H. On the other hand, H also defines the mass shells as Lorentzian submanifolds of the tangent bundle. When restricted to these mass shells, the projection of the integral curves of L on the base manifold describes a family of future directed timelike geodesics. A simple collisionless gas is described by a distribution function on a particular mass shell, satisfying the Liouville equation. Together with the Liouville vector field the distribution function can be thought of as defining a fictitious incompressible fluid on the mass shells, with associated conserved current density. Flux integrals of this current density provide the averaged properties of the gas, while suitable fiber integrals of the distribution function define divergence-free tensor fields on the spacetime manifold such as the current density and stress?energy tensor. Finally, we discuss the relationship between symmetries of the spacetime manifold and symmetries of the distribution function. Taking advantage of the natural metric and symplectic structure on TM, we show that groups of isometries G of the spacetime manifold lift naturally to groups of isometries and symplectic flows on the tangent bundle. Motivated by these properties, we define a distribution function to be G-invariant whenever it is invariant under the lifted isometries. As a first application of our formalism we derive the most general spherically symmetric distribution function on any spherically symmetric spacetime and write the Einstein?Liouville equations as effective field equations on the two-dimensional radial manifold. As a second application we derive the most general collisionless distribution function on a Kerr black hole spacetime background.

Observational distinction between black holes and naked singularities: the role of the redshift function

We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on the sky of the asymptotic observer. We find that the resulting redshift and properties of the shadow depend crucially on whether the final outcome of the complete gravitational collapse is a black hole or a naked singularity. In the black hole case, the shadow is due to the high redshift acquired by the photons as they approach the event horizon, implying that their energy is gradually redshifted toward zero within a few crossing times associated with the event horizon radius. In contrast to this, a naked singularity not only absorbs photons originating from the source, but it also emits infinitely redshifted photons with and without angular momenta. This emission introduces an abrupt cutoff in the frequency shift of the photons detected in directions close to the radial one, and it is responsible for the shadow masking the source in the naked singularity case. Furthermore, even though the shadow forms and begins to grow immediately after the observer crosses the Cauchy horizon, it takes many more crossing times than in the black hole case for the source to be occulted from the observers eyes. We discuss possible implications of our results for testing the weak cosmic censorship hypothesis. Even though at late times the image of the source perceived by the observer looks the same in both cases, the dynamical formation of the shadow and the redshift images has distinct features and time scales in the black hole versus the naked singularity case. For stellar collapse, these time scales seem to be too short to be resolved with existing technology. However, our results may be relevant for the collapse of seeds leading to supermassive black holes.