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Asymptotic analysis of the "simulated horizon" segment of the Collins spiral

Stephen L. Adler

Abstract

The Tolman-Oppenheimer-Volkoff (TOV) equations for a massless fluid take the form of a pair of coupled autonomous first order differential equations, which can be employed in a model for a ``dynamical gravastar'' black hole mimicker. The mimicker has no true horizon, but rather a ``simulated horizon'', outside which the geometry resembles a Schwarzschild black hole, but inside which the $g_{00}$ component of the metric is always positive and becomes exponentially small. Collins has reinterpreted the relevant TOV equations in terms of a two-dimensional flow with a spiral form, and Zöllner and Kämpfer have mapped the simulated horizon to a specific segment of the Collins spiral. We give here results of an asymptotic analysis, relating initial values at the small radius end of this spiral segment to the black hole mimicker mass and other parameters that emerge at the large radius kink in the TOV solution, which corresponds to the simulated horizon.

Asymptotic analysis of the "simulated horizon" segment of the Collins spiral

Abstract

The Tolman-Oppenheimer-Volkoff (TOV) equations for a massless fluid take the form of a pair of coupled autonomous first order differential equations, which can be employed in a model for a ``dynamical gravastar'' black hole mimicker. The mimicker has no true horizon, but rather a ``simulated horizon'', outside which the geometry resembles a Schwarzschild black hole, but inside which the component of the metric is always positive and becomes exponentially small. Collins has reinterpreted the relevant TOV equations in terms of a two-dimensional flow with a spiral form, and Zöllner and Kämpfer have mapped the simulated horizon to a specific segment of the Collins spiral. We give here results of an asymptotic analysis, relating initial values at the small radius end of this spiral segment to the black hole mimicker mass and other parameters that emerge at the large radius kink in the TOV solution, which corresponds to the simulated horizon.

Paper Structure

This paper contains 14 sections, 23 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. TOV solution represented as a Collins spiral
  3. The black hole mimicker "simulated horizon"
  4. The mimicker model reinterpreted as a "core-corona" model, with the "simulated horizon" mapped into a segment of the Collins spiral
  5. Relativistic fluid (corona region) TOV equations rewritten as an autonomous system in terms of scale invariant variables
  6. An illustratiion of the solutions
  7. Combining the linear plots of Fig. 1 and Fig. 2 into a Collins spiral
  8. Asymptotic Analysis
  9. Left hand and kink peak parameters
  10. Mapping between parameter sets
  11. Heuristic derivation of the scaling relations
  12. Further regularities
  13. Physical application
  14. Acknowledgement

Figures (3)

  • Figure 1: Plot of $\alpha$, from just below the kink at $t\simeq 13.2164$ to exponentially large radius values.
  • Figure 2: Plot of $\delta$, from just below the kink at $t\simeq 13.2164$ to exponentially large radius values.
  • Figure 3: Plot of the Collins spiral, obtained by combining the plots of Fig. 1 and Fig. 2 as a planar parametric plot.