Embolic aspects of black hole entropy

Dec 8, 2017
8 pages
Published in:
  • Int.J.Geom.Meth.Mod.Phys. 15 (2018) 10, 1850175,
  • APS Physics 15 (2018) 1850175
  • Published: Aug 23, 2018
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Abstract: (WSP)
We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3 + 1)-dimensional spacetimes. We treat the case of horizons having space-like sections Σ which are topological spheres, following Hawking’s and the Topological Censorship theorems. We use the injectivity radius of the induced metric on Σ to encode the linear dimensions of the elementary cells giving rise to such entropy. We use the topological entropy of Σ as the fundamental quantity expressing the complexity of Σ on which its entropy depends. We point out the significance, in this context, of the Berger and Croke isoembolic inequalities.
Note:
  • 11 pages. No figures. LaTeX2e. Final form, to be published in the Int. J. Geom. Methods Mod. Physics
  • Riemannian geometry
  • isoembolic inequalities
  • black holes
  • entropy
  • topological censorship
  • black hole: entropy
  • entropy: topological
  • metric: induced
  • space-time
  • horizon