H. Hernández

Sound speeds, cracking and the stability of self-gravitating anisotropic compact objects

Using the concept of cracking we explore the influence that density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity. This concept, conceived to describe the behavior of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of self-gravitating compact objects. We show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions. In fact, it is found that these regions could occur when, at a particular point within the distribution, the tangential speed of sound is greater than the radial one.

Nonlocal equation of state in anisotropic static fluid spheres in general relativity

We show that it is possible to obtain, at least certain regions within spherically symmetric static matter configurations, credible anisotropic fluids satisfying a nonlocal equation of state. This particular type of equation of state provides, at a given point, the radial pressure not only as a function of the density at that point, but its functional throughout the enclosed distribution. To establish the physical plausibility of the proposed family of solutions satisfying a nonlocal equation of state, we study the constraints imposed by the junction, energy, and some intuitive physical conditions. We show that these static fluids having this particular equation of state are naturally anisotropic in the sense that they satisfy, identically, the anisotropic Tolmanx96Oppenheimerx96Volkov equation. We also show that it is possible to obtain physically plausible static anisotropic spherically symmetric matter configurations starting from known density profiles, and also for configurations where tangential press...

NON-LOCAL EQUATION OF STATE IN GENERAL RELATIVISTIC RADIATING SPHERES

We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a non-local equation of state. This equation describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. We have found that these types of dynamic bounded matter configurations, with constant compactness or gravitational potentials at the surface, admit a conformal Killing vector field and fulfil the energy conditions for anisotropic imperfect fluids. We present several analytical and numerical models satisfying these equations of state which collapse as reasonable radiating anisotropic spheres in general relativity.

Cracking of Self-Gravitating Compact Objects with Local and Non Local Equations of State

We discuss the effect that small fluctuations of density and local anisotropy (principal unequal stresses) may have on the occurrence of cracking in spherical compact objects having a non local and local politropic equations of state. A non local equation of state provides, at a given point, the radial pressure not only as function of the density at that point, but its functional throughout the enclosed distribution. It is shown that departures from the equilibrium may lead to the appearance of cracking and it seams to be related not only to fluctuations on the local anisotropy but also to the density. We have found that these fluctuations should have the same sign and the effect of the perturbations in density qualitatively different to the variations in anisotropy.

Plausible families of compact objects with a nonlocal equation of state

We present the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. We explore how their physical vari...

Radiation hydrodynamics and Radiating Spheres in General Relativity

We comment on a method proposed to study the evolution of General Relativistic Radiating Spheres in both radiation limits, i.e. free streaming out and diffusion, extending it to handle any general radiating spherically symmetric distribution of matter. It is also shown that several dynamic models may emerge from a sole static equation of state. Previous erroneous calculations concerning this method are also commented.

On the eccentricity behaviour of radiating slowly rotating bodies in general relativity

We study different models of radiating slowly rotating bodies up to the first order in the angular velocity. It is shown that up to this order the evolution of the eccentricity is highly model dependent even for very compact objects.