arXiv subjects

A. Di Prisco

Publications and source records attributed to A. Di Prisco.

At least 37 records · Page 2Linked to original sources

arXiv2018

Definition of complexity for dynamical spherically symmetric dissipative self-gravitating fluid distributions

The recently proposed definition of complexity for static and spherically symmetric self--gravitating systems [1], is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the structure of the fluid distribution, but also the condition of minimal complexity of the pattern of evolution. As we shall see these two issues are deeply intertwined. For the complexity factor of the structure we choose the same as for the static case, whereas for the simplest pattern of evolution we assume the homologous condition. The dissipative and non-dissipative cases are considered separately. In the latter case the fluid distribution, satisfying the vanishing complexity factor condition and evolving homologously, corresponds to a homogeneous (in the energy density), geodesic and shear-free, isotropic (in the pressure) fluid. In the dissipative case the fluid is still geodesic, but shearing, and there exists (in principle) a large class of solutions. Finally we discuss about the stability of the vanishing complexity condition.

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arXiv2018

The transition of a gravitationally radiating, dissipative fluid, to equilibrium

We describe the transition of a graviationally radiating, axially and reflection symmetric dissipative fluid, to a non--radiating state. It is shown that very shortly after the end of the radiating regime, at a time scale of the order the thermal relaxation time, the thermal adjustment time and the hydrostatic time (whichever is larger), the system reaches the equilibrium state. This result is at variance with all the studies carried out in the past, on gravitational radiation outside the source, which strongly suggest that after a radiating period, the conditions for a return to a static case, look rather forbidding. As we shall see, the reason for such a discrepancy resides in the fact that some elementary, but essential, physical properties of the source, have been overlooked in these latter studies.

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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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arXiv2018

Self-similarity in static axially symmetric relativistic fluids

We carry on a general study on axially symmetric, static fluids admitting a conformal Killing vector (CKV). The physical relevance of this kind of symmetry is emphasized. Next, we investigate all possible consequences derived from the imposition of such a symmetry. Special attention is paid to the problem of symmetry inheritance. Several families of solutions endowed with a CKV are exhibited.

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arXiv2016

The spacetime outside a source of gravitational radiation: The axially symmetric null fluid

We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric spacetimes. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the $1+3$ formalism.

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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

Physical infeasibility of geodesic dissipative dust as a source of gravitational radiation

Using a framework based on the 1+3 formalism, we show that a source represented by a geodesic, dissipative, rotational dust, endowed with axial and reflection symmetry, violates regularity conditions at the center of the fluid distribution, unless the dissipative flux vanishes. In this latter case the vorticity also must vanish, and the resulting spacetime is Friedman--Robertson--Walker (FRW). Therefore it does not produce gravitational radiation.

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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

Conformally flat polytropes for anisotropic matter

We analyze in detail conformally flat spherically symmetric fluid distributions, satisfying a polytropic equation of state. Among the two possible families of relativistic polytropes, only one contains models which satisfy all the required physical conditions. The ensuing configurations are necessarily anisotropic and show interesting physical properties. Prospective applications of the presented models to the study of super-Chandrasekhar white dwarfs, are discussed.

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arXiv2014

Shear-free axially symmetric dissipative fluids

We study the general properties of axially symmetric dissipative configurations under the shear-free condition. The link between the magnetic part of the Weyl tensor and the vorticity, as well as the role of the dissipative fluxes, are clearly exhibited. As a particular case we examine the geodesic fluid. In this latter case, the magnetic part of the Weyl tensor always vanishes, suggesting that no gravitational radiation is produced during the evolution. Also (for the geodesic case), in the absence of dissipation, the system evolves towards a FRW spacetime if the expansion scalar is positive.

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arXiv2014

Dissipative collapse of axially symmetric, general relativistic, sources: A general framework and some applications

We carry out a general study on the collapse of axially (and reflection) symmetric sources in the context of general relativity. All basic equations and concepts required to perform such a general study are deployed. These equations are written down for a general anisotropic dissipative fluid. The proposed approach allows for analytical studies as well as for numerical applications. A causal transport equation derived from the Israel-Stewart theory is applied, to discuss some thermodynamic aspects of the problem. A set of scalar functions (the structure scalars) derived from the orthogonal splitting of the Riemann tensor are calculated and their role in the dynamics of the source is clearly exhibited. The characterization of the gravitational radiation emitted by the source is discussed.

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arXiv2013

Nature of the vorticity in the Gödel spacetime

The physical meaning of the vorticity of the matter content in Gödel spacetime is analyzed in some detail. As we shall see, unlike the situation in general stationnary axially symmetric spacetimes (Lewis--Papapetrou), the vorticity in Gödel spacetime is not associated to a circular flow of superenergy on the plane orthogonal to the vorticity vector. This fact might be at the origin of the strange behaviour of gyroscopes in such spacetime. The analysis emerging from the tilted version of Gödel spacetime supports further this point of view. In order to tell apart the two situations (with and without circular flow of superenergy) we introduce two different definitions of vorticity, related to the presence (absence) of such a flow.

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arXiv2013

Axially symmetric static sources: A general framework and some analytical solutions

We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed with axial symmetry. The structure scalars are calculated and the inhomogeneity factors are identified. Finally some exact analytical solutions were found. One of these solutions describes an incompressible spheroid with isotropic pressure and becomes the well known interior Schwarzschild solution in the spherically symmetric limit, however it cannot be matched smoothly to any Weyl exterior metric. Another family of solutions was found that corresponds to an anisotropic fluid distribution and can in principle be matched to a Weyl exterior.

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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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arXiv2012

Reversible Dissipative Processes, Conformal Motions and Landau Damping

The existence of a dissipative flux vector is known to be compatible with reversible processes, provided a timelike conformal Killing vector (CKV) $χ^α=\frac{V^α}{T}$ (where $V^α$ and $T$ denote the four-velocity and temperature respectively) is admitted by the space-time. Here we show that if a constitutive transport equation, either within the context of standard irreversible thermodynamics or the causal Israel--Stewart theory, is adopted, then such a compatibility also requires vanishing dissipative fluxes. Therefore, in this later case the vanishing of entropy production generated by the existence of such CKV is not actually associated to an imperfect fluid, but to a non-dissipative one. We discuss also about Landau damping.

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arXiv2011

Expansion-Free Cavity Evolution: Some exact Analytical Models

We consider spherically symmetric distributions of anisotropic fluids with a central vacuum cavity, evolving under the condition of vanishing expansion scalar. Some analytical solutions are found satisfying Darmois junction conditions on both delimiting boundary surfaces, while some others require the presence of thin shells on either (or both) boundary surfaces. The solutions here obtained model the evolution of the vacuum cavity and the surrounding fluid distribution, emerging after a central explosion. This study complements a previously published work where modeling of the evolution of such kind of systems was achieved through a different kinematical condition.

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arXiv2011

On the Role of Electric Charge and Cosmological Constant in Structure Scalars

The physical meaning of structure scalars is analyzed for charged dissipative spherical fluids and for neutral dust in the presence of cosmological constant. The role played by such factors in the structure scalars is clearly brought out and physical consequences are discussed. Particular attention needs to be paid to the changes introduced by the above mentioned factors in the inhomogeneity factor and the evolution of the expansion scalar and the shear tensor.

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