Gravitational collapse with tachyon field and barotropic fluid

TL;DR

This paper investigates gravitational collapse involving a tachyon field and barotropic fluid, revealing conditions leading to black hole or naked singularity formation through dynamical system analysis and numerical methods.

Contribution

It introduces a novel model combining tachyon fields with barotropic fluids in gravitational collapse and analyzes their asymptotic behaviors and final states.

Findings

Collapse can result in black holes or naked singularities.

Tachyon and fluid can exhibit tracking behavior depending on initial conditions.

Final state is typically a black hole, influenced by the barotropic parameter b3.

Abstract

A particular class of space-time, with a tachyon field, \phi, 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(\phi) \sim \phi^{-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, \gamma. Furthermore, these collapsing scenarios both have as final state the formation of a black hole.