Gravitational collapse with tachyon field and barotropic fluid
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Gravitational collapse with tachyon field and barotropic fluid Yaser Tavakoli · João Marto · Amir Hadi Ziaie · Paulo Vargas Moniz
Received: 18 June 2012 / Accepted: 10 January 2013 © Springer Science+Business Media New York 2013
Abstract A particular class of space-time, with a tachyon field, φ, and a barotropic fluid constituting the matter content, is considered herein as a model for gravitational collapse. For simplicity, the tachyon potential is assumed to be of inverse square form i.e., V (φ) ∼ φ −2 . Our purpose, by making use of the specific kinematical features of the tachyon, which are rather different from a standard scalar field, is to establish the several types of asymptotic behavior that our matter content induces. Employing a dynamical system analysis, complemented by a thorough numerical study, we find classical solutions corresponding to a naked singularity or a black hole formation. In particular, there is a subset where the fluid and tachyon participate in an interesting tracking behaviour, depending sensitively on the initial conditions for the energy densities of the tachyon field and barotropic fluid. Two other classes of solutions are present, corresponding respectively, to either a tachyon or a barotropic fluid regime. Which of these emerges as dominant, will depend on the choice of the barotropic parameter, γ . Furthermore, these collapsing scenarios both have as final state the formation of a black hole.
Y. Tavakoli · J. Marto (B) · P. V. Moniz Departamento de Física, Universidade da Beira Interior, 6200 Covilhã, Portugal e-mail: [email protected] Y. Tavakoli e-mail: [email protected] A. H. Ziaie Department of Physics, Shahid Beheshti University, G. C., Evin, 19839 Tehran, Iran e-mail: [email protected] P. V. Moniz CENTRA, IST, Av. Rovisco Pais, 1, Lisbon, Portugal e-mail: [email protected]
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Keywords
Gravitational collapse · Singularities · Tachyon field
1 Introduction The study of the final state of the gravitational collapse of initially regular distributions of matter is one of the open problems in classical general relativity, having attracted remarkable attention in past decades. When a sufficiently massive star exhausts all the thermonuclear sources of its energy, it would undergo a collapsing scenario due to its own gravity, without reaching a final state in terms of a neutron star or white dwarf. Under a variety of circumstances, singularities will inevitably emerge (geodesic incompleteness in space-time), matter densities and space-time curvatures diverging. Albeit the singularity theorems [1,2] state that there exist space-time singularities in a generic gravitational collapse, they provide no information on the nature of singularities: the problem of whether these regions are hidden by a space-time event horizon or can actually be observed, remains unsolved. The cosmic censorship conjecture (CCC), as hypothesized by Penrose [3], conveys that the singularities appearing at the collapse final outcome must be hidden within an event horizon and thus no distant
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