We develop a simple model for a self-gravitating spherically symmetric relativistic star which begins to collapse from an initially static configuration by dissipating energy in the form of radial heat flow. We utilize the model to show how local anisotropy affects 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 influence 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. This, however, turns out to be a difficult task because of the highly nonlinear nature of the governing field equations. To reduce the complexity, various simplifying methods are often adopted and the pioneering work of Oppenheimer and Snyder [3] was a first 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 field 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]. These 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 field, 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 useful to get a proper understanding about systems undergoing gravitational collapse. The aim of the present work is to develop a simple model of a
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