English

Schwarzschild-de Sitter black hole in canonical quantization

General Relativity and Quantum Cosmology 2018-12-31 v1 High Energy Physics - Theory

Abstract

We solve Wheeler-De Witt (WDW) metric probability wave equation on the apparent horizon hypersurface of the Schwarzschild de Sitter (SdS) black hole. To do so we choose radial dependent mass function M(r)M(r) for its internal regions in the presence of a dynamical massless quantum matter scalar field ψ(r)\psi(r) and calculate canonical supper hamiltonian constraint on tt-constant hypersurface near the horizon r=M(r)r=M(r). In this case M(r)M(r) become geometrical degrees of freedom while ψ(r)\psi(r) is matter degrees of freedom of the apparent horizon. However our solution is obtained versus the quantum harmonic oscillator which defined against the well known hermit polynomials. In the latter case we obtain quantized mass of the SdS quantum black hole as ΛM(n)=(2n+1122)13\sqrt{\Lambda}M(n)=\big(\frac{2n+1}{12\sqrt{2}}\big)^{\frac{1}{3}} in which Λ\Lambda is the cosmological constant and n=0,1,2,n=0,1,2,\cdots are quantum numbers of the hermit polynomials. This shows that a quantized SdS in its ground state has a nonzero value for the mass M(0)=0.38914/ΛM(0)=0.38914/\sqrt{\Lambda}. Thus one can infer that the latter result satisfies Penrose hypotheses for cosmic censorship where a causal singularity may be covered by a horizon surface.

Keywords

Cite

@article{arxiv.1805.01283,
  title  = {Schwarzschild-de Sitter black hole in canonical quantization},
  author = {Hossein Ghaffarnejad},
  journal= {arXiv preprint arXiv:1805.01283},
  year   = {2018}
}

Comments

7 pages, 3 figure, accepted as ORAL presentation at the `7th International Conference on Mathematical Modeling in Physical Sciences`,August 27-31, 2018, Moscow, Russia

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