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Quantum dust cores of rotating black holes

Tommaso Bambagiotti, Roberto Casadio

Abstract

A quantum description of dust cores for black hole geometries can be obtained by quantising the geodesic motion of dust particles and finding the corresponding many-body ground state. We here generalise previous works in spherical symmetry to rotating geometries and show the effect of angular momentum on the size of the core and effective interior geometry.

Quantum dust cores of rotating black holes

Abstract

A quantum description of dust cores for black hole geometries can be obtained by quantising the geodesic motion of dust particles and finding the corresponding many-body ground state. We here generalise previous works in spherical symmetry to rotating geometries and show the effect of angular momentum on the size of the core and effective interior geometry.
Paper Structure (15 sections, 89 equations, 2 figures)

This paper contains 15 sections, 89 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Rotating geodesics
  3. Action and equations of motion
  4. Axial motion
  5. Equatorial motion
  6. Ground state and perturbative spectrum
  7. Non-rotating case
  8. Slow-rotation corrections
  9. Core size
  10. Near extremal rotation
  11. Quantum rotating core
  12. Angular momentum and horizon quantisation
  13. Effective interior geometry
  14. Conclusions and outlook
  15. Effective mass functions

Figures (2)

  • Figure 1: Core radii vs horizon radii for the whole range of classical Kerr black holes $A^2\le G_{\rm N}^2\,M^2$ (left panel); right panel shows the region of near extremal rotation magnified.
  • Figure 2: Function $\Delta$ in Eq. \ref{['e:delta']} for $m_{\rm int}$ (left panel) and $m_{\rm par}$ (right panel) for different values of $\delta=A/G_{\rm N}\, M$, with $M=150 \, m_{\rm p}$. The dotted lines correspond to the maximum values $\delta_{\rm i} \simeq 0.867$ (left panel) and $\delta_{\rm p} \simeq 0.953$ (right panel).