On the effective metric of a Planck star

  • Tommaso De Lorenzo
  • Costantino Pacilio
  • Carlo Rovelli
  • Simone SpezialeEmail author
Editor's Choice (Research Article)


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.


Quantum gravity Black hole physics Spacetime singularities Apparent horizons 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Tommaso De Lorenzo
    • 1
    • 3
    • 4
  • Costantino Pacilio
    • 2
    • 3
    • 4
  • Carlo Rovelli
    • 3
    • 4
  • Simone Speziale
    • 3
    • 4
    Email author
  1. 1.Dipartimento di FisicaUniversità di PisaPisaItaly
  2. 2.SISSATriesteItaly
  3. 3.CNRS, CPT, UMR 7332Aix Marseille UniversitéMarseilleFrance
  4. 4.CNRS, CPT, UMR 7332Université de ToulonLa GardeFrance

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