arXiv subjects

Thomas Zannias

Publications and source records attributed to Thomas Zannias.

17 recordsLinked to original sources

arXiv2022

Local thermodynamical equilibrium and relativistic dissipation

We introduce a class of relativistic fluid states satisfying the relativistic local thermodynamical equilibrium postulate (abbreviated as relativistic (LTE) postulate). States satisfying this postulate, are states "near equilibrium" (a term defined precisely in the course of the paper) and permit us to attach a fictitious "local thermodynamical equilibrium" state that fits event by event the actual fluid state. They single out an admissible class of rest frames relative to which thermodynamical variables like the energy density, thermodynamical pressure, stresses, particle number density (or densities) measured by observers at rest relative to these frames are becoming frame independent provided second (or higher) order deviations from the fictitious state of "local thermodynamical equilibrium" are ignored. We have verified this property for a large class of theories of relativistic dissipation that include the Hiscock-Lindblom class of first order theories, the Eckart and Landau-Lifshitz theories, the Israel-Stewart transient thermodynamics, the Liu-Müller-Ruggeri theory, fluids of divergence type and the latest developed (BDNK) theory. Moreover, the phenomenological equations describing first order deviations from the fictitious "local thermodynamical equilibrium" state satisfy equations that remain form invariant under change of frame within the class of admissible frames. We proved this property for the Hiscock-Lindblom class of first order theories the Eckart and Landau-Lifshitz theories, the Israel-Stewart transient thermodynamics and the Liu-Müller-Ruggeri theory of relativistic dissipation the (BDNK) theory and we expect that the same property to hold for the class of relativistic fluids of divergence type.

gr-qc↗

arXiv2021

On Extended Thermodynamics: From Classical to the Relativistic Regime

The recent monumental detection of gravitational waves by LIGO, the subsequent detection by the LIGO/VIRGO observatories of a binary neutron star merger seen in the gravitational wave signal $GW170817$,the first photo of the event horizon of the supermassive black hole at the center of the $M87$ galaxy released by the EHT telescope and the ongoing experiments on Relativistic Heavy Ion Collisions at the BNL and at the CERN, demonstrate that we are witnessing the second golden era of observational relativistic gravity. These new observational breakthroughs, although in the long run would influence our views regarding this Kosmos, in the short run, they suggest that relativistic dissipative fluids (or magnetofluids) and relativistic continuous media play an important role on astrophysical-and also subnuclear-scales. This realization brings into the frontiers of current research theories of irreversible thermodynamics of relativistic continuous media. Motivated by these considerations, in this paper, we summarize the progress that has been made in the last few decades in the field of non equilibrium thermodynamics of relativistic continuous media. For coherence and completeness purposes, we begin with a brief description of the balance laws for classical (Newtonian) continuous media and introduce the classical irreversible thermodynamics (CIT) and the role of the local-equilibrium postulate within this theory. Tangentially, we touch the program of rational thermodynamics (RT), the Clausius-Duhem inequality, the theory of constitutive relations and the emergence of the entropy principle and its role in the description of continuous media.

gr-qc↗

arXiv2018

On causality violation on a Kerr-de Sitter spacetime

The causal properties of the family of Kerr-de Sitter spacetimes are analyzed and compared to those of the Kerr family. At first we show that a Kerr-de Sitter spacetime can be viewed as an assembly of Carter's blocks i.e. four dimensional spacetime regions contained within Killing horizons or a Killing horizon and the asymptotic de Sitter region. From this perspective and leaving aside topological identifications, the causal properties of a Kerr de Sitter spacetime are determined by the causal properties of the individual Carter's blocks viewed as spacetimes in their own right. We show that any Carter's block is stably causal except for the blocks that contain the ring singularity. The latter are vicious sets: any two events within such block can be connected by a future (respectively past) directed timelike curve. This behavior is identical to the causal behavior of the Boyer-Lindquist blocks that contains the Kerr ring singularity which are also vicious sets. On the other hand, while for the case of a naked Kerr singularity the entire spacetime is a vicious set and thus closed timelike curves pass through any event including events lying in the asymptotic region, for the case of a Kerr-de Sitter spacetime the cosmological horizons imply that the asymptotic de Sitter region is causally well behaved. In that regard a positive cosmological constant appears to improve the causal behavior of the underlying spacetime.

gr-qc↗

arXiv2018

On the Integrability of the Geodesic Flow on a Friedmann-Robertson-Walker Spacetime

We study the geodesic flow on the cotangent bundle of a Friedman-Robertson-Walker spacetime (M, g). On this bundle, the HamiltonJacobi equation is completely separable and this separability leads us to construct four linearly independent integrals in involution i.e. Poisson commuting amongst themselves and pointwise linearly independent. These integrals involve the six linearly independent Killing fields of the background metric g. As a consequence, the geodesic flow on an FRW background is completely integrable in the Liouville-Arnold sense. For the case of a spatially closed universe we construct families of invariant by the flow sub manifolds.

gr-qc↗

arXiv2017

On the behavior of causal geodesics on a Kerr-de Sitter spacetime

We analyze the behavior of causal geodesics on a Kerr-de Sitter spacetime with particular emphasis on their completeness property. We set up an initial value problem (IVP) whose solutions lead to a global understanding of causal geodesics on these spacetime. Causal geodesics that avoid the rotation axis are complete except the ones that hit the ring-like curvature singularity and those that encounter the ring singularity are necessary equatorial ones. We also show the existence of geodesics that cross or lie on the rotation axis. The equations governing the latter family show the repulsive nature of the ring singularity. The results of this work show, that as far as properties of causal geodesics are concerned, Kerr-de Sitter spacetimes behave in a similar manner as the family of Kerr spacetimes.

gr-qc↗

arXiv2015

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

We suggest that the redshift of photons traveling from past to future null infinity through a collapsing object could provide an observational signature capable of differentiating between the formation of a globally naked singularity and the formation of an event horizon. Supporting evidence for this idea is drawn from the analysis of photons with zero angular momentum through the center of a collapsing spherical dust cloud. We show that the frequency shift as a function of proper time with respect to stationary observers has distinct features depending on whether the object collapses to a black hole or a naked singularity.

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arXiv2015

Shadow of a naked singularity

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 observer's 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.

gr-qc↗

arXiv2015

On the global structure of Kerr-de Sitter spacetimes

Taking advantage of the natural length scale set by the cosmological constant $Λ>0$, conditions on the parameters $(Λ, M, a^{2})$ have been found, so that a Kerr-de Sitter specetime either describes a black hole with well separated horizons, or describes degenerate configurations where two or more horizons coincide. As long as the rotation parameter $a^{2}$ is subject to the constraint $a^{2}Λ\ll 1$, while the mass parameter $M$ is subject to: $ a^{2}[1+O(a^{2}Λ)^{2})] \frac {1}{9Λ}[1+2a^{2}Λ+O(a^{2}Λ)^{2})]$ or $M^{2}< a^{2}[1+O(a^{2}Λ)^{2})]$, the Kerr-de Sitter spacetime describes a ring-like singularity enclosed by two cosmological horizons. A Kerr-de Sitter spacetime may also describe configurations where the inner, the outer and one of the cosmological horizons coincide. However, we found that this coalescence occurs provided $M^{2}Λ\sim 1$ and due to the observed smallness of $Λ$, these configurations are probably irrelevant in astrophysical settings. Extreme black holes, i.e. black holes where the inner horizon coincides with the outer black hole horizon are also admitted. We have found that in the limit $M^{2}Λ\ll 1$ and $a^{2}Λ\ll 1$, extreme black holes occur, provided $a^{2}=M^{2}(1+O(ΛM^{2}))$. Finally a coalescence between the outer and the cosmological horizon, although in principle possible, is likely to be unimportant at the astrophysical level, since this requires $M^{2}Λ\sim 1$.

gr-qc↗

arXiv2015

On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse

Motivated by recent work on the structure of the singularity in inhomogeneous Tolman-Bondi collapse models, we investigate the behaviour of null geodesics in the particular case where the collapse is self-similar. The presence of the homothetic Killing vector field implies that the geodesic equation can be described by an integrable Hamiltonian system, and exploiting this fact we provide a full qualitative picture for its phase flow.

gr-qc↗

arXiv2014

The evolution of a spatially homogeneous and isotropic universe filled with a collisionless gas

We review the evolution of a spatially homogeneous and isotropic universe described by a Friedmann-Robertson-Walker spacetime filled with a collisionless, neutral, simple, massive gas. The gas is described by a one-particle distribution function which satisfies the Liouville equation and is assumed to be homogeneous and isotropic. Making use of the isometries of the spacetime, we define precisely the homogeneity and isotropicity property of the distribution function, and based on this definition we give a concise derivation of the most general family of such distribution functions. For this family, we construct the particle current density and the stress-energy tensor and consider the coupled Einstein-Liouville system of equations. We find that as long as the distribution function is collisionless, homogenous and isotropic, the evolution of a Friedmann-Robertson-Walker universe exhibits a singular origin. Its future development depends upon the curvature of the spatial sections: spatially flat or hyperboloid universes expand forever and this expansion dilutes the energy density and pressure of the gas, while a universe with compact spherical sections reaches a maximal expansion, after which it reverses its motion and recollapses to a final crunch singularity where the energy density and isotropic pressure diverge. Finally, we analyze the evolution of the universe filled with the collisionless gas once a cosmological constant is included.

gr-qc↗

arXiv2014

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

This article 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. 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 fibre 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. 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.

gr-qc↗

arXiv2013

Tangent bundle formulation of a charged gas

We discuss the relativistic kinetic theory for a simple, collisionless, charged gas propagating on an arbitrary curved spacetime geometry. Our general relativistic treatment is formulated on the tangent bundle of the spacetime manifold and takes advantage of its rich geometric structure. In particular, we point out the existence of a natural metric on the tangent bundle and illustrate its role for the development of the relativistic kinetic theory. This metric, combined with the electromagnetic field of the spacetime, yields an appropriate symplectic form on the tangent bundle. The Liouville vector field arises as the Hamiltonian vector field of a natural Hamiltonian. The latter also defines natural energy surfaces, called mass shells, which turn out to be smooth Lorentzian submanifolds. A simple, collisionless, charged gas is described by a distribution function which is defined on the mass shell and satisfies the Liouville equation. Suitable fibre integrals of the distribution function define observable fields on the spacetime manifold, such as the current density and stress-energy tensor. Finally, the geometric setting of this work allows us to discuss the relationship between the symmetries of the electromagnetic field, those of the spacetime metric, and the symmetries of the distribution function. Taking advantage of these symmetries, we construct the most general solution of the Liouville equation an a Kerr-Newman black hole background.

gr-qc↗

arXiv2013

Relativistic Kinetic Theory: An Introduction

We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare one-form on this bundle, from which the symplectic form and a volume form are constructed. Then, we define an appropriate Hamiltonian on the bundle which, together with the symplectic form yields the Liouville vector field. The corresponding flow, when projected onto the base manifold, generates geodesic motion. Whenever the flow is restricted to energy surfaces corresponding to a negative value of the Hamiltonian, its projection describes a family of future-directed timelike geodesics. A collisionless gas is described by a distribution function on such an energy surface, satisfying the Liouville equation. Fibre integrals of the distribution function determine the particle current density and the stress-energy tensor. We show that the stress-energy tensor satisfies the familiar energy conditions and that both the current and stress-energy tensor are divergence-free. Our discussion also includes the generalization to charged gases, a summary of the Einstein-Maxwell-Vlasov system in any dimensions, as well as a brief introduction to the general relativistic Boltzmann equation for a simple gas.

gr-qc↗

arXiv2012

The propagation of particles and fields in wormhole geometries

We discuss several properties of static, spherically symmetric wormholes with particular emphasis on the behavior of causal geodesics and the propagation of linear fields. We show there always exist null geodesics which are trapped in a region close to the throat. Depending upon the detailed structure of the wormhole geometry, these trapped geodesics can be stable, unlike the case of the Schwarzschild black hole. We also show that test scalar fields propagating on such wormholes are stable. However, when a mixture of ghost and Klein-Gordon scalar fields is used as a source of the Einstein equations we prove that the resulting static, spherically symmetric wormhole configurations are linearly unstable.

gr-qc↗

arXiv2010

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

Recently, spherically symmetric, static wormholes supported by exotic dust and a radial magnetic field have been derived and argued to be stable with respect to linear radial fluctuations. In this report we point out that these wormholes are unstable due to the formation of shell-crossing singularities when the nonlinearities of the theory are taken into account.

gr-qc↗

arXiv1997

The Extended Power Law as Intrinsic Signature For a Black Hole

We analyze the exact general relativistic exact integro-differential equation of radiative transfer describing the interaction of low energy photons with a Maxwellian distribution of hot electrons in gravitational field of a Schwarzschild black hole. We prove that due to Comptonization an initial arbitrary spectrum of low energy photons unavoidably results in spectra characterized by an extended power-law feature. We examine the spectral index by using both analytical and numerical methods for a variety of physical parameters as such the plasma temperature and the mass accretion rate. The presence of the event horizon as well as the behaviour of the null geodesics in its vicinity largely determine the dependence of the spectral index on the flow parameters. We come to the conclusion that the bulk motion of a converging flow is more efficient in upscattering photons than thermal Comptonization provided that the electron temperature in the flow is of order of a few keV or less. In this case, the spectrum observed at infinity consists of a soft component produced by those input photons that escape after a few scatterings without any significant energy change and of hard component (described by a power law) produced by the photons that underwent significant upscattering. The luminosity of the power-law component is relatively small compared to that of the soft component. For accretion into black hole the spectral energy index of the power-law is always higher than one for plasma temperature of order of a few keV. This result suggests that the bulk motion Comptonization might be responsible for the power-law spectra seen in the black-hole X-ray sources.

astro-ph↗

arXiv1993

On the mechanism of trapped surface formation

By a combination of analytical and numerical methods, the density profile of a momentarily at rest spherical star is varied, and the corresponding response in the area of the spherical shells is monitored. It is shown that the inner apparent horizon (if it exists) must lie within or at most on the star's surface, while no such restriction is found for the outer apparent horizon. However, an apparent horizon lying in the vacuum region will always have non vanishing area, as long as the ADM mass of the system is non zero. Furthermore for density profiles not decreasing inwards, it appears that all spherical trapped surfaces lie on a thick spherical shell. Finally for a uniform density star a simple criterion is found, relating density and proper radius that guarantees the presence or absence of trapped regions.

gr-qc↗