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

Abstract

Using the the concept of cracking we explore the influence of 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 behaviour of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of selfgravitating 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 particular point within the distribution, the tangential speed of sound is greater than the radial one.

Analytical study of anisotropic compact star models

“…Cracking was introduced by Herrera [110] as a possibility of breaking of perturbed selfgravitating spheres. Abreu et al [111] found a simple requirement for avoiding this to happen, namely that the region of stability be…”

Cracking on anisotropic neutron stars

“…The physically reasonable interior solutions of a NS should satisfy several energy conditions [10,11,12]. The corresponding energy conditions are described as follows.…”

“…The recent investigation on the properties of anisotropic compact stars are reported for examples in Reference [8,2,3]. In general, physical meaningful anisotropic fluid equation of state (EOS) should follow general physical energy conditions [10,11,12]. So far energy condition analysis for anisotropic fluid is investigated only for the case compact objects which are described by polytropes type of EOS.…”

“…On the other hand, it is know that anisotropic EOS may rise up a kind instability due to density fluctuation so-called cracking. Recent studies of the potential presence of cracking in the stars matter using different approaches for examples can be seen in Reference [11,12,13]. However, the discussion of fulfillment of energy condition and potentially appearing of cracking in anisotropic NS using more realistic and up to date NS EOS are not yet done so far.…”

“…For anisotropic pressure models, we also use the ones of Doneva-Yazadjiev (DY) [2] and Herrera-Barreto (HB) [3]. In cracking analysis, we use the same methods as the one used in Reference [11,13].…”