Hindawi Publishing Corporation Journal of Gravity Volume 2013, Article ID 659605, 8 pages http://dx.doi.org/10.1155/2013/659605 Research Article Collapse of a Relativistic Self-Gravitating Star with Radial Heat Flux: Impact of Anisotropic Stresses Ranjan Sharma and Shyam Das Department of Physics, P.D. Women’s College, Jalpaiguri, West Bengal 735101, India Correspondence should be addressed to Ranjan Sharma; rsharma@iucaa.ernet.in Received 28 February 2013; Accepted 22 April 2013 Academic Editor: Sergei Odintsov Copyright © 2013 R. Sharma and S. Das. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We develop a simple model for a self-gravitating spherically symmetric relativistic star which begins to collapse from an initially static confguration by dissipating energy in the form of radial heat fow. We utilize the model to show how local anisotropy afects the collapse rate and thermal behavior of gravitationally evolving systems. 1. Introduction In cosmology and astrophysics, there exist many outstanding issues relating to a dynamical system collapsing under the infuence of its own gravity. In view of Cosmic Censorship Conjecture, the general relativistic prediction is that such a collapse must terminate into a space-time singularity covered under its event horizon though there are several counter examples where it has been shown that a naked singularity is more likely to be formed (see [1] and references therein). In astrophysics, the end stage of a massive collapsing star has long been very much speculative in nature [1, 2]. From classical gravity perspective, to get a proper understanding of the nature of collapse and physical behavior of a collapsing system, construction of a realistic model of the collapsing system is necessary. Tis, however, turns out to be a difcult task because of the highly nonlinear nature of the governing feld equations. To reduce the complexity, various simplifying methods are ofen adopted and the pioneering work of Oppenheimer and Snyder [3] was a frst step in this direction when collapse of a highly idealized spherically symmetric dust cloud was studied. Since then, various attempts have been made to develop realistic models of gravitationally collapsing systems to understand the nature and properties of collapsing objects. It got a tremendous impetus when Vaidya [4] presented a solution describing the exterior gravitational feld of a stellar body with outgoing radiation and Santos [5] formulated the junction conditions joining the interior space time of the collapsing object to the Vaidya exterior metric [4]. Tese developments have enabled many investigators to construct realistic models of gravitationally evolving systems and also to analyze critically relevance of various factors such as shear, density inhomogeneity, local anisotropy, electromagnetic feld, viscosity, and so forth, on the physical behaviour of collapsing bodies [6–52]. In the absence of any established theory governing gravitational collapse, such investigations have been found to be very use- ful to get a proper understanding about systems undergoing gravitational collapse. Te aim of the present work is to develop a simple model of a collapsing star and investigate the impact of pressure anisotropy on the overall behaviour of the collapsing body. Anisotropic stresses may occur in astrophysical objects for various reasons which include phase transition, density inhomogeneity, shear, and electromagnetic feld [10, 53, 54]. In [53], it has been shown that infuences of shear, elec- tromagnetic feld, and so forth on self-bound systems can be absorbed if the system is considered to be anisotropic, in general. Local anisotropy has been a well-motivated factor in the studies of astrophysical objects and its role on the gross features of static stellar confgurations have been investigated by many authors (see, e.g., [10, 11, 55–59] and references therein). For dynamical systems, though pressure anisotropy is, in general, incorporated in the construction,