Stability and horizon formation during dissipative collapse
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Stability and horizon formation during dissipative collapse Nolene F. Naidu1 · Robert S. Bogadi1 · Anand Kaisavelu2 · Megan Govender1 Received: 8 May 2020 / Accepted: 12 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We investigate the role played by density inhomogeneities and dissipation on the final outcome of collapse of a self-gravitating sphere. By imposing a perturbative scheme on the thermodynamical variables and gravitational potentials we track the evolution of the collapse process starting off with an initially static perfect fluid sphere which is shear-free. The collapsing core dissipates energy in the form of a radial heat flux with the exterior spacetime being filled with a superposition of null energy and an anisotropic string distribution. The ensuing dynamical process slowly evolves into a shear-like regime with contributions from the heat flux and density fluctuations. We show that the anisotropy due to the presence of the strings drives the stellar fluid towards instability with this effect being enhanced by the density inhomogeneity. An interesting and novel consequence of this collapse is the earlier formation of the horizon. Keywords Radiative collapse · Anisotropic stresses · Density inhomogeneities
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Stellar interior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Nolene F. Naidu [email protected] Robert S. Bogadi [email protected] Anand Kaisavelu [email protected] Megan Govender [email protected]
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Department of Mathematics, Faculty of Applied Sciences, Durban University of Technology, Durban 4000, South Africa
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Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa 0123456789().: V,-vol
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Exterior spacetime and matching conditions Perturbative scheme . . . . . . . . . . . . . Explicit form of the temporal function . . . . Dynamical model . . . . . . . . . . . . . . Radiating collapse . . . . . . . . . . . . . . 7.1 Luminosity . . . . . . . . . . . . . . . 7.2 Horizon formation . . . . . . . . . . . . 7.2.1 Case 1: T˙ = 0 . . . . . . . . . . . 7.2.2 Case 2: grΣ = 0 . . . . . . . . . 8 Stability analysis . . . . . . . . . . . . . . . 9 Physical analysis and conclusion . . . . . . References . . . . . . . . . . . . . . . . . . . .
N. F. Naidu et al. . . . . . . . . . . . .
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