arXiv subjects

J. Carot

Publications and source records attributed to J. Carot.

At least 19 recordsLinked to original sources

arXiv2023

Quasi--hyperbolically symmetric $γ$-metric

We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi--hyperbolically symmetric $γ$-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric $γ$-metric, and the hyperbolically symmetric black hole. As in this latter case, it is found that test particles experience a repulsive force within the horizon (naked singularity), which prevents them to reach the center. However in the present case this behavior is affected by the parameter $γ$ which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the $θ-r$ subspace. Possible relevance of these results in the explanation of extragalactic jets, is brought out.

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arXiv2020

Elastic thick shells in General Relativity

It is shown that exact spherically symmetric solutions to Einstein's Field Equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a well defined constitutive function, and are such that elastic perturbations propagate causally. Two toy-models are then built up in which a thick elastic, spherically symmetric shell with the above properties, separates two Robertson-Walker regions corresponding to different values of the curvature $k$. The junction conditions (continuity of the first and second fundamental forms) are shown to be exactly satisfied across the corresponding matching spherical surfaces.

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arXiv2019

Complexity of the Bondi metric

A recently introduced concept of complexity for relativistic fluids is extended to the vacuum solutions represented by the Bondi metric. A complexity hierarchy is established, ranging from the Minkowski spacetime (the simplest one) to gravitationally radiating systems (the more complex). Particularly interesting is the possibility to differentiate between natural non--radiative (NNRS) and non--natural non--radiative (NNNRS) systems, the latter appearing to be simpler than the former. The relationship between vorticity and the degree of complexity is stressed.

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arXiv2018

Tilted shear-free axially symmetric fluids

We carry on a systematic study of the physical properties of axially symmetric fluid distributions, which appear to be geodesic, shear--free, irrotational, non--dissipative and purely electric, for the comoving congruence of observers, from the point of view of the tilted congruence. The vanishing of the magnetic part of the Weyl tensor for the comoving congruence of observers, suggests that no gravitational radiation is produced during the evolution of the system. Instead, the magnetic part of the Weyl tensor as measured by tilted observers is non vanishing (as well as the shear, the four--acceleration, the vorticity and the dissipation), giving rise to a flux of gravitational radiation that can be characterized through the super--Poynting vector. This result strengthens further the relevance of the role of observers in the description of a physical system. An explanation of this dual interpretation in terms of the information theory, is provided.

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arXiv2016

Earliest stages of the non-equilibrium in axially symmetric, self-gravitating, dissipative fluids

We report a study on axially and reflection symmetric dissipative fluids, just after its departure from hydrostatic and thermal equilibrium, at the smallest time scale at which the first signs of dynamic evolution appear. Such a time scale is smaller than the thermal relaxation time, the thermal adjustment time and the hydrostatic time. It is obtained that the onset of non--equilibrium will critically depend on a single function directly related to the time derivative of the vorticity. Among all fluid variables (at the time scale under consideration), only the tetrad component of the anisotropic tensor in the subspace orthogonal to the four--velocity and the Killing vector of axial symmetry, shows signs of dynamic evolution. Also, the first step toward a dissipative regime begins with a non--vanishing time derivative of the heat flux component along the meridional direction. The magnetic part of the Weyl tensor vanishes (not so its time derivative), indicating that the emission of gravitational radiation will occur at later times. Finally, the decreasing of the effective inertial mass density, associated to thermal effects, is clearly illustrated.

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arXiv2015

Axially symmetric dissipative fluids in the quasi--static approximation

Using a framework based on the $1+3$ formalism we carry out a study on axially and reflection symmetric dissipative fluids, in the quasi--static regime. We first derive a set of invariantly defined "velocities", which allow for an inambiguous definition of the quasi--static approximation. Next we rewrite all the relevant equations in this aproximation and extract all the possible, physically relevant, consequences ensuing the adoption of such an approximation. In particular we show how the vorticity, the shear and the dissipative flux, may lead to situations where different kind of "velocities" change of sign within the fluid distribution with respect to theirs sign on the boundary surface. It is shown that states of gravitational radiation are not {\it a priori} incompatible with the quasistatic--regime. However, any such state must last for an infinite period of time, thereby diminishing its physical relevance.

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arXiv2015

Shearing and geodesic axially symmetric perfect fluids that do not produce gravitational radiation

Using a framework based on the 1+3 formalism we carry out a study on axially and reflection symmetric perfect and geodesic fluids, looking for possible models of sources radiating gravitational waves. Therefore, the fluid should be necessarily shearing, for otherwise the magnetic part of the Weyl tensor vanishes, leading to a vanishing of the super-Poynting vector. However, for the family of perfect, geodesic fluids considered here, it appears that all possible cases reduce to conformally flat, shear--free, vorticity-free, fluids, i.e Friedmann-Roberston-Walker. The super-Poynting vector vanishes and therefore no gravitational radiation is expected to be produced. The physical meaning of the obtained result is discussed.

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arXiv2014

Cylindrically symmetric static solutions of the Einstein field equations for elastic matter

The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical solutions satisfying the dominant energy conditions. Furthermore, we show that the solutions can be matched at a finite radius to suitable $Λ$-vacuum exteriors given by the Linet-Tian spacetime.

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arXiv2012

Vorticity and entropy production in tilted Szekeres spacetimes

We analyze the properties of the tilted Szekeres spacetime, i.e. the version of such spacetime as seen by a congruence of observers with respect to which the fluid is moving. The imperfect fluid and the kinematical variables associated to the four-velocity of the fluid assigned by tilted observers are studied in detail. As it happens for the case of the Lemaitre--Tolman--Bondi spacetime, the fluid evolves nonreversibly (with nonvanishing entropy production) and is nongeodesic. However unlike that later case, the tilted observer detects vorticity in the congruence of the fluid world lines. Also, as for the nontilted congruence the magnetic part of the Weyl tensor vanishes, reinforcing the nonradiative character of this kind of spacetime. Possible physical implications of these results are discussed.

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arXiv2010

Lemaitre-Tolman-Bondi dust spacetimes: Symmetry properties and some extensions to the dissipative case

We consider extensions of Lemaitre-Tolman-Bondi (LTB) spacetimes to the dissipative case. For doing that we previously carry out a systematic study on LTB. This study is based on two different aspects of LTB. On the one hand, a symmetry property of LTB will be presented. On the other hand, the description of LTB in terms of some fundamental scalar functions (structure scalars) appearing in the orthogonal splitting of Riemann tensor will be provided. We shall consider as "natural" generalizations of LTB (hereafter referred to as GLTB) either those metrics admitting some similar kind of symmetry as LTB, or those sharing structure scalars with similar dependence on the metric.

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arXiv2009

General spherically symmetric elastic stars in Relativity

The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as theones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the way, a few general results for spacetimes admitting isometries are deduced, and their consequences are fully exploited in the case of spherical symmetry relating them next to the the case in which the material content of the spacetime is some elastic material. This paper extends and generalizes the pioneering work by Magli and Kijowski [1], Magli [2] and [3], and complements, in a sense, that by Karlovini and Samuelsson in their interesting series of papers [4], [5] and [6].

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arXiv2009

The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy

We calculate the instantaneous proper radial acceleration of test particles (as measured by a locally defined Lorentzian observer) in a Weyl spacetime, close to the horizon. As expected from the Israel theorem, there appear some bifurcations with respect to the spherically symmetric case (Schwarzschild), which are explained in terms of the behaviour of the superenergy, bringing out the physical relevance of this quantity in the study of general relativistic systems.

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arXiv2007

Frame dragging and super-energy

We show that the vorticity appearing in stationary vacuum spacetimes is always related to the existence of a flow of super-energy on the plane orthogonal to the vorticity vector. This result, toghether with the previously established link between vorticity and super--energy in radiative (Bondi-Sachs) spacetimes strength further the case for this latter quantity as the cause of frame dragging.

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arXiv2007

Energetics of the Einstein-Rosen spacetime

A study covering some aspects of the Einstein--Rosen metric is presented. The electric and magnetic parts of the Weyl tensor are calculated. It is shown that there are no purely magnetic E--R spacetimes, and also that a purely electric E--R spacetime is necessarily static. The geodesics equations are found and circular ones are analyzed in detail. The super--Poynting and the ``Lagrangian'' Poynting vectors are calculated and their expressions are found for two specific examples. It is shown that for a pulse--type solution, both expressions describe an inward radially directed flow of energy, far behind the wave front. The physical significance of such an effect is discussed.

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arXiv2007

Why does gravitational radiation produce vorticity?

We calculate the vorticity of world--lines of observers at rest in a Bondi--Sachs frame, produced by gravitational radiation, in a general Sachs metric. We claim that such an effect is related to the super--Poynting vector, in a similar way as the existence of the electromagnetic Poynting vector is related to the vorticity in stationary electrovacum spacetimes.

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arXiv2006

Gravitational radiation, vorticity and the electric and magnetic part of Weyl tensor

The electric and the magnetic part of the Weyl tensor, as well as the invariants obtained from them, are calculated for the Bondi vacuum metric. One of the invariants vanishes identically and the other only exhibits contributions from terms of the Weyl tensor containing the static part of the field. It is shown that the necessary and sufficient condition for the spacetime to be purely electric is that such spacetime be static. It is also shown that the vanishing of the electric part implies Minkowski spacetime. Unlike the electric part, the magnetic part does not contain contributions from the static field. Finally a speculation about the link between the vorticity of world lines of observers at rest in a Bondi frame, and gravitational radiation, is presented.

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arXiv2005

Almost-stationary motions and gauge conditions in General Relativity

An almost-stationary gauge condition is proposed with a view to Numerical Relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is derived by a variational principle, by minimizing the deviations from isometry. The corresponding almost-stationary gauge condition allows one to put the field equations in hyperbolic form, both in the free-evolution ADM and in the Z4 formalisms.

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arXiv2005

Hydrodynamics in Class B Warped Spacetimes

We discuss certain general features of type B warped spacetimes which have important consequences on the material content they may admit and its associated dynamics. We show that, for Warped B spacetimes, if shear and anisotropy are nonvanishing, they have to be proportional. We also study some of the physics related to the warping factor and of the underlying decomposable metric. Finally we explore the only possible cases compatible with a type B Warped geometry which satisfy the dominant energy conditions. As an example of the above mentioned consequences we consider a radiating fluid and two non-spherically symmetric metrics which depend upon an arbitrary parameter, such that if the parameter vanishes the spherical symmetry is recovered.

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