Anisotropic Gravitational Collapse with Linear Equation of State

Ayan Chatterjee, Suresh Jaryal

Department of Physics & Astronomical Science, School of Physical & Material Sciences, Central University of Himachal Pradesh (CUHP), Dharamshala, Kangra (HP), India 176215

*Corresponding Author E-mail: ayan.theory@gmail.com, suresh.fifthd@gmail.com

ABSTRACT:

The study of the Gravitational collapse of anisotropic fluid for type I matter field with spherical symmetric spacetime with linear equation of state is carried out. We show that if the collapse evolves from a regular initial data, there exist a large classes of solutions of Einstein equations, such that the end state of the collapse leads to either a black hole or a naked singularity. Our results reduce to those obtained earlier for a perfect fluid model. The nature of the null curve emanating from the center and hence the singularity, is shown to depend upon the values of anisotropic coefficient parameter together with the mass and the velocity profiles.

KEYWORDS: Gravitational collapse.

1. INTRODUCTION:

The study of gravitational collapse, beginning with the profound work of Oppenheimer, Snyder [1] and Dutt [2] (OSD), has been used to address fundamental issues of classical and quantum gravity. The OSD case was limited to collapse of a dust cloud but provided important clues to the nature and mode of formation of space time singularities out of a massive star. It is clear by now that though the model is simple, the mathematical structure used there may be used to understand more complicated and real life examples of collapse of a massive astrophysical star. In this paper, we shall show that the OSD model may be tweaked and expanded to include more complicated energy-momentum tensors. Further, we shall evaluate the space time metric arising out of collapse of such matter fields.

Before we begin, let us give a brief guide to the literature. As is well known, stars of mass approximately 10 , after ending of fuel, collapses continuously under gravity to form a space time singularity. According to the principle of cosmic censorship (CCH) [3], the singularities of this kind appearing in endless gravitational collapse are always hidden by the event horizon. The space time region inside the so- called event horizon is called the black hole (BH) region [4]. The final fate of endless gravitational collapse of matter cloud depends upon the choice of equation of state (EoS) and initial data. Oppenheimer and Snyder [1], and Dutt [2] studied dust collapse, showed once the collapse starts it eventually reaches to a stage when no light emitted from its surface can escape away to faraway

observers, the epoch when an event horizon forms with the material entering the black hole horizon and eventually ending at the singularity of the space time, hence, black hole as only possible final fate of the pressure less dust collapse [5]. It has been argued that this scenario is not entirely correct and that light may be observed, although for a small proper time interval, by far away observers [7-12]. This then, as these authors argue, bring into question the validity of the CCH. However, the fundamental work of Christodoulou [13] has shown that the CCH, hold true, at least for spherical collapse. Still, it remains to be proved or disproved if a null ray is visible to a local observer [14]. This then would create a Cauchy horizon whose nature and stability is yet to be established formally. Further, there has been a growing interest in understanding the phenomenon of collapse of astrophysical stars with different equation of states and energy-momentum tensors [15, 16]. In this paper, we shall develop and study one more model by including pressure terms in the Einstein equations. Our aim is not to address the complex issues like the CCH but is much simpler. Are these effects, of developing a Cauchy horizon, due to simpler choices of energy- momentum tensors? What is the space time metric for these energy-momentum tensors?

In the next section, we set- up our conventions and the mathematical framework. This is followed by the methods to solve the Einstein equations. We conclude in section III.

3. CONCLUSION:

We have shown that even in presence of more complicated matter models than as considered by OSD, Cauchy horizons may develop in these cases of gravitational collapse. The nature of these singularities, has however, not been developed in this paper and will be addressed elsewhere. Furthermore, it remains to be seen if these horizons are stable under perturbations of matter and spacetime.

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Received on 14.11.2016 Modified on 25.11.2016

DOI: 10.5958/2349-2988.2017.00024.9

Research J. Science and Tech. 2017; 9(1):150-154.