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Motion of test particles in quasi anti-de Sitter regular black holes

Dario Corona, Roberto Giambò, Orlando Luongo

Abstract

We explore the characteristics of two novel regular spacetimes that exhibit a non-zero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman-Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the two metrics asymptotically tend to negative values, resembling quintessence. In addition, we study test particle motions, illustrating the main discrepancies among our models and more conventional metrics exhibiting non-vanishing anti-de Sitter phase.

Motion of test particles in quasi anti-de Sitter regular black holes

Abstract

We explore the characteristics of two novel regular spacetimes that exhibit a non-zero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman-Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the two metrics asymptotically tend to negative values, resembling quintessence. In addition, we study test particle motions, illustrating the main discrepancies among our models and more conventional metrics exhibiting non-vanishing anti-de Sitter phase.
Paper Structure (9 sections, 36 equations, 2 figures)

This paper contains 9 sections, 36 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Geometric warm up
  3. Spherical symmetry with asymptotic quintessence
  4. Comparing our solution with anti-de Sitter spacetime
  5. Introducing vacuum energy for the axisymmetric case
  6. Geodesic test particle motion
  7. Spherical symmetry
  8. Axial symmetry
  9. Final outlooks

Figures (2)

  • Figure 1: Motion in the plane $\theta=\pi/2$ of timelike geodesics with $E=4, L=2$. Here $\Lambda$ is set to -1 and $k=0.7$, not far away from $2/3$ that is the value yielding exactly the anti-de Sitter spacetime, see Eq. \ref{['eq:k-dS']}. The blue closed curve is an anti-de Sitter timelike geodesic, and the orange one is a geodesic for the metric discussed above.
  • Figure 2: Same as in Fig. \ref{['geo_sph']} with respect to the asymmetric metrics obtained via the GNJ algorithm discussed in Ref. aaaAzreg-Ainou:2014aqa. The rotation parameter $a$ here is conventionally set to 0.1.