arXiv subjects

A. Di Prisco

Publications and source records attributed to A. Di Prisco.

At least 55 records · Page 3Linked to original sources

arXiv2011

Tilted Lemaitre-Tolman-Bondi Spacetimes: Hydrodynamic and Thermodynamic Properties

We consider Lemaitre-Tolman-Bondi spacetimes from the point of view of a tilted observer, i.e. one with respect to which the fluid is radially moving. The imperfect fluid and the congruence described by its four-velocity, as seen by the tilted observer is studied in detail. It is shown that from the point of view of such tilted observer the fluid evolves non-reversibly (i.e. with non-vanishing rate of entropy production). The non-geodesic character of the tilted congruence is related to the non-vanishing of the divergence of the 4-vector entropy flow. We determine the factor related to the existence of energy-density inhomogeneities and describe its evolution, these results are compared with those obtained for the non-tilted observer. Finally, we exhibit a peculiar situation where the non-tilted congruence might be unstable.

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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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arXiv2010

On the stability of the shear-free condition

The evolution equation for the shear is reobtained for a spherically symmetric anisotropic, viscous dissipative fluid distribution, which allows us to investigate conditions for the stability of the shear-free condition. The specific case of geodesic fluids is considered in detail, showing that the shear-free condition, in this particular case, may be unstable, the departure from the shear-free condition being controlled by the expansion scalar and a single scalar function defined in terms of the anisotropy of the pressure, the shear viscosity and the Weyl tensor or, alternatively, in terms of the anisotropy of the pressure, the dissipative variables and the energy density inhomogeneity.

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arXiv2009

Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor

The full set of equations governing the structure and the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses, is written down in terms of five scalar quantities obtained from the orthogonal splitting of the Riemann tensor, in the context of general relativity. It is shown that these scalars are directly related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux and the active gravitational mass. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through these scalars. Some solutions are exhibited to illustrate this point.

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arXiv2009

Dynamics of viscous dissipative gravitational collapse: A full causal approach

The Misner and Sharp approach to the study of gravitational collapse is extended to the viscous dissipative case in, both, the streaming out and the diffusion approximations. The dynamical equation is then coupled to causal transport equations for the heat flux, the shear and the bulk viscosity, in the context of Israel--Stewart theory, without excluding the thermodynamics viscous/heat coupling coefficients. The result is compared with previous works where these later coefficients were neglected and viscosity variables were not assumed to satisfy causal transport equations. Prospective applications of this result to some astrophysical scenarios are discussed.

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arXiv2008

All static spherically symmetric anisotropic solutions of Einstein's equations

An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions, is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the knowledge of two functions (instead of one) to generate all possible solutions. To illustrate the method some known cases are recovered.

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arXiv2007

Nonadiabatic charged spherical gravitational collapse

We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of different terms in the dynamical equation are analyzed in detail. The dynamical equation is coupled to a causal transport equation in the context of Israel-Stewart theory. The decrease of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamic state, is reobtained, with the viscosity terms included. In accordance with the equivalence principle, the same decrease factor is obtained for the gravitational force term. The effect of the electric charge on the relation between the Weyl tensor and the inhomogeneity of energy density is discussed.

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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

Some analytical models of radiating collapsing spheres

We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.

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arXiv2005

Thermo--inertial bouncing of a relativistic collapsing sphere: A numerical model

We present a numerical model of a collapsing radiating sphere, whose boundary surface undergoes bouncing due to a decreasing of its inertial mass density (and, as expected from the equivalence principle, also of the ``gravitational'' force term) produced by the ``inertial'' term of the transport equation. This model exhibits for the first time the consequences of such an effect, and shows that under physically reasonable conditions this decreasing of the gravitational term in the dynamic equation may be large enough as to revert the collapse and produce a bouncing of the boundary surface of the sphere.

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arXiv2004

Spherically symmetric dissipative anisotropic fluids: A general study

The full set of equations governing the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behaviour of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure and the density inhomogeneity. In particular we provide the general, necessary and sufficient, condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow of time. Some solutions are also exhibited to illustrate the discussion.

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arXiv2003

On the active gravitational mass of a non-spherical source leaving hydrostatic equilibrium

We obtain an expression for the active gravitational mass (Tolman) of a source of the $γ$ metric, just after its departure from hydrostatic equilibrium, on a time scale of the order of (or smaller than) the hydrostatic time scale. It is shown that for very compact sources, even arbitrarily small departures from sphericity, produce significant decreasing (increasing) in the values of active gravitational mass of collapsing (expanding) spheres, with respect to its value in equilibrium, enhancing thereby the stability of the system.

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arXiv2002

Relativistic gravitational collapse in non-comoving coordinates: The post-quasistatic approximation

A general, iterative, method for the description of evolving self-gravitating relativistic spheres is presented. Modeling is achieved by the introduction of an ansatz, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post--quasistatic approximation. As examples of application of the method we discuss three models, in the adiabatic case.

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arXiv2002

The Thomas precession and the transformation to rotating frames

The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the transformation used. For smaller values of $v/c$ these differences might be measured by extending the time of observation.

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arXiv2001

On the dual interpretation of zero-curvature Friedmann-Robertson-Walker models

Two possible interpretations of FRW cosmologies (perfect fluid or dissipative fluid)are considered as consecutive phases of the system. Necessary conditions are found, for the transition from perfect fluid to dissipative regime to occur, bringing out the conspicuous role played by a particular state of the system (the ''critical point '').

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arXiv2001

Conformally flat anisotropic spheres in general relativity

The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but non-vanishing Weyl tensor, thereby bringing out the different role played by the Weyl tensor, the local anisotropy of pressure and the inhomogeneity of the energy density in the collapse of relativistic spheres.

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