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On the effective metric of a Planck star

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Abstract

Spacetime metrics describing ‘non-singular’ black holes are commonly studied in the literature as effective modification to the Schwarzschild solution that mimic quantum gravity effects removing the central singularity. Here we point out that to be physically plausible, such metrics should also incorporate the 1-loop quantum corrections to the Newton potential and a non-trivial time delay between an observer at infinity and an observer in the regular center. We present a modification of the well-known Hayward metric that features these two properties. We discuss bounds on the maximal time delay imposed by conditions on the curvature, and the consequences for the weak energy condition, in general violated by the large transversal pressures introduced by the time delay.

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Notes

  1. It is worth mentioning that the metric proposed by Bardeen in [5] does reproduce the required behaviour of the newtonian potential. On the other hand, as well as all the line elements proposed, it suffers for the time delay problem.

  2. In the numerical plots, we use the value \(\beta =41/10\pi \).

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Acknowledgments

We kindly acknowledge support from the A*MIDEX project ANR-11-IDEX-0001-02, as well as the Samy Maroun Center For Space, Time and the Quantum.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Pisa, “Enrico Fermi”, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy

    Tommaso De Lorenzo

  2. SISSA, Via Bonomea 265, 34136, Trieste, Italy

    Costantino Pacilio

  3. CNRS, CPT, UMR 7332, Aix Marseille Université, 13288, Marseille, France

    Tommaso De Lorenzo, Costantino Pacilio, Carlo Rovelli & Simone Speziale

  4. CNRS, CPT, UMR 7332, Université de Toulon, 83957, La Garde, France

    Tommaso De Lorenzo, Costantino Pacilio, Carlo Rovelli & Simone Speziale

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  1. Tommaso De Lorenzo
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  2. Costantino Pacilio
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  4. Simone Speziale
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Correspondence to Simone Speziale.

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De Lorenzo, T., Pacilio, C., Rovelli, C. et al. On the effective metric of a Planck star. Gen Relativ Gravit 47, 41 (2015). https://doi.org/10.1007/s10714-015-1882-8

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