Astrophys Space Sci (2015) 357:107 DOI 10.1007/s10509-015-2335-2 ORIGINAL ARTICLE Horizon free eternally collapsing anisotropic radiating star B.C. Tewari 1 · Kali Charan 1 Received: 21 September 2014 / Accepted: 28 March 2015 © Springer Science+Business Media Dordrecht 2015 Abstract We present a class of exact solutions of relativis- tic field equations for a shear-free spherically symmetric anisotropic fluid undergoing radial heat flow. The interior metric fulfilled all the relevant physical and thermodynamic conditions and matched with Vaidya exterior metric over the boundary. Initially mass and radius are infinite and finally they both contract to a point as time approaches zero with- out forming an event horizon at the boundary. Since, for this class of models, the collapse begins at infinite past and con- tinues in the finite present, such models may be considered as examples of “Eternal Collapse”. For this given model, the luminosity is time independent so it radiates with uniform rate throughout the collapse process and the rate of collapse increases in comparison to isotropic case. Keywords Exact solutions · Radiating star · Anisotropic fluid · Gravitational collapse · Naked singularity · Eternally collapsing object 1 Introduction Relativistic astrophysics opens up numerous challenges for researchers to study different aspects of gravitational col- lapse. Therefore, a detailed description of gravitational col- lapse of massive stars and the modelling of the structure of compact objects under various conditions is a problem that attracts a significant attention in relativistic astrophysics. B B.C. Tewari drbctewari@yahoo.co.in K. Charan kcyadav2008@gmail.com 1 Department of Mathematics, Kumaun University, S.S.J. Campus, Almora, India The maiden exact solution of spherical GR collapse was due to Oppenheimer and Snyder (1939) (OS) and which appar- ently suggested that continued GR collapse results in forma- tion of “Black Holes” (BH). In order to obtain exact solu- tion, OS however were compelled to make most unrealistic assumptions such as (i) the fluid has no pressure (dust) even when singularity would be formed, (ii) the fluid has uniform density implying infinite sound speed in violation of GR, and of course (iii) no dissipation, no heat flow. Even if one would relax the assumption by assuming the dust to be inhomogeneous, there could be infinite so- lutions, and, in principle, there could be “naked singular- ities”, i.e., singularities not covered by an Event Horizon (EH). Dust collapse apart, there are many semi-analytical and numerical studies which claim non-formation of BHs. And non-formation of BHs is promptly interpreted as for- mation of “naked singularities”. It may be noted that the idea of a gravitational “singularity” requires that the singu- lar state if formed in a finite comoving proper time (τ = Finite). However except for the dust case, it is impossible to compute τ in a truly analytical manner. Also, by draw- ing inspiration from examples of dust collapse, it is assumed that “trapped surfaces” should form for continued GR col- lapse. Under this crucial assumption, the singularity theo- rems suggest that continued collapse should result in grav- itational singularities, be it covered or naked. And as per the Cosmic Censorship Conjecture of Penrose (1969), Na- ture should avoid “naked singularities”. This idea is often misinterpreted by stating that continued GR collapse must form BHs. Nonetheless, Mitra (2000, 2002, 2006c, 2009b, 2009a) showed that, in order that the worldliness of the col- lapsing fluid remains time like, trapped surfaces must not form at-least for spherical GR collapse. In the absence of trapped surfaces, the “singularity theorems” get invalidated, and accordingly Mitra (2000, 2002, 2006a, 2006b) and Mi-