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Stable gravastars - an alternative to black holes?

Matt Visser, David L. Wiltshire

TL;DR

The paper addresses the stability of gravastar models by constructing a three-layer Schwarzschild exterior, thin shell, and de Sitter interior system, and recasting the shell dynamics as a zero-energy particle problem with a potential V(a).It derives a master equation and an invertible potential framework that links the shell equation of state to the dynamical stability, enabling explicit expressions for the shell density and tension in terms of V(a) and bulk masses, and specializes these to a gravastar geometry with exterior mass M and interior density parameter k.The work demonstrates that there exist physically reasonable equations of state that yield stable, spherically symmetric pulsations for certain parameter ranges (not universally guaranteed), and it explores several special cases, including V(a)≡0, stiff-shell configurations, and anti-de Sitter interiors, with detailed stability and energy-condition analyses.Overall, the results show that dynamically stable gravastar configurations are possible within this simplified framework, while also highlighting limitations and suggesting that moving the transition layer away from the would-be horizon may be a fruitful direction for more realistic models.

Abstract

The "gravastar" picture developed by Mazur and Mottola is one of a very small number of serious challenges to our usual conception of a "black hole". In the gravastar picture there is effectively a phase transition at/ near where the event horizon would have been expected to form, and the interior of what would have been the black hole is replaced by a segment of de Sitter space. While Mazur and Mottola were able to argue for the thermodynamic stability of their configuration, the question of dynamic stability against spherically symmetric perturbations of the matter or gravity fields remains somewhat obscure. In this article we construct a model that shares the key features of the Mazur-Mottola scenario, and which is sufficiently simple for a full dynamical analysis. We find that there are some physically reasonable equations of state for the transition layer that lead to stability.

Stable gravastars - an alternative to black holes?

TL;DR

The paper addresses the stability of gravastar models by constructing a three-layer Schwarzschild exterior, thin shell, and de Sitter interior system, and recasting the shell dynamics as a zero-energy particle problem with a potential V(a).It derives a master equation and an invertible potential framework that links the shell equation of state to the dynamical stability, enabling explicit expressions for the shell density and tension in terms of V(a) and bulk masses, and specializes these to a gravastar geometry with exterior mass M and interior density parameter k.The work demonstrates that there exist physically reasonable equations of state that yield stable, spherically symmetric pulsations for certain parameter ranges (not universally guaranteed), and it explores several special cases, including V(a)≡0, stiff-shell configurations, and anti-de Sitter interiors, with detailed stability and energy-condition analyses.Overall, the results show that dynamically stable gravastar configurations are possible within this simplified framework, while also highlighting limitations and suggesting that moving the transition layer away from the would-be horizon may be a fruitful direction for more realistic models.

Abstract

The "gravastar" picture developed by Mazur and Mottola is one of a very small number of serious challenges to our usual conception of a "black hole". In the gravastar picture there is effectively a phase transition at/ near where the event horizon would have been expected to form, and the interior of what would have been the black hole is replaced by a segment of de Sitter space. While Mazur and Mottola were able to argue for the thermodynamic stability of their configuration, the question of dynamic stability against spherically symmetric perturbations of the matter or gravity fields remains somewhat obscure. In this article we construct a model that shares the key features of the Mazur-Mottola scenario, and which is sufficiently simple for a full dynamical analysis. We find that there are some physically reasonable equations of state for the transition layer that lead to stability.

Paper Structure

This paper contains 16 sections, 70 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The physical model
  3. The mathematical model
  4. Static shell
  5. Dynamic shell
  6. Conservation laws
  7. The master equation
  8. Derivation
  9. Inverting the potential
  10. Specialization of gravastar geometry
  11. The $V(a)\equiv 0$ case
  12. Special gravastar geometries
  13. $V\equiv 0$ equation of state --- Special limits
  14. Stiff-shell gravastars
  15. Anti-de Sitter gravastars
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Surface energy density, $\sigma$ (in units $M^{-1}$), as a function of radius, $a$ (in units $M$). ($kM^2=1/18$; $V(a)\equiv0$.)
  • Figure 2: Surface tension, $\vartheta$ (in units $M^{-1}$ ), as a function of radius, $a$ (in units $M$). ($kM^2=1/18$; $V(a)\equiv0$.)
  • Figure 3: Equation of state: Surface energy density as a function of surface tension. ($kM^2=1/18$; $V(a)\equiv0$.)
  • Figure 4: Equation of state: Enlargement of the central region of figure \ref{['eos1']} --- surface energy density as a function of surface tension. ($kM^2=1/18$; $V(a)\equiv0$.)
  • Figure 5: Equation of state: Enlargement of the central region for an example in which the dominant energy condition is satisfied. Surface energy density as a function of surface tension for the case $kM^2=1/72$; $V(a)\equiv0$. Parameter values for which the dominant energy condition is violated are shown by a thin line, and parameter values for which the dominant energy condition is satisfied, viz., $2.124319\,M<a<3\,M$, are shown by a thick line.