Absorption of charged particles in a Reissner-Nordström black-hole: entropy evolution from relativistic quantum geometry

Abstract

Using Relativistic Quantum Geometry we show that the entropy can decrease in very small BHs, under certain circumstances, but always increases in very massive Black-Holes.

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Notes

  1. 1.

    We shall denote with a ; covariant derivatives on a Riemann manifold and with a | covariant derivatives on a Weyl manifold.

  2. 2.

    In what follows we shall denote with a \(\Delta \) variations on the Riemann manifold, and with a \(\delta \) variations on a Weylian manifold.

  3. 3.

    We can define the operator

    $$ \check{x}^{\alpha }(t,\vec{x}) = \frac{1}{(2\pi )^{3/2}} \int d^{3} k \check{e}^{\alpha } \bigl[ b_{k} \check{x}_{k}(t,\vec{x}) + b ^{\dagger }_{k} \check{x}^{*}_{k}(t,\vec{x}) \bigr] , $$

    such that \(b^{\dagger }_{k}\) and \(b_{k}\) are the creation and destruction operators of space-time, such that \(\langle B \vert [ b _{k},b^{\dagger }_{k'} ] \vert B \rangle = \delta^{(3)}(\vec{k}- \vec{k'})\) and \(\check{e}^{\alpha }=\epsilon^{\alpha }_{ \beta \gamma \delta } \check{e}^{\beta } \check{e}^{\gamma }\check{e} ^{\delta }\).

  4. 4.

    In our case the background quantum state can be represented in a ordinary Fock space in contrast with LQG, where operators is qualitatively different from the standard quantization of gauge fields.

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Acknowledgements

The authors acknowledge UNMdP and CONICET for financial support.

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Correspondence to Mauricio Bellini.

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Arcodía, M.R.A., Ridao, L.S. & Bellini, M. Absorption of charged particles in a Reissner-Nordström black-hole: entropy evolution from relativistic quantum geometry. Astrophys Space Sci 361, 296 (2016). https://doi.org/10.1007/s10509-016-2891-0

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Keywords

  • Black-holes
  • Relativistic quantum geometry