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Repulsive gravity effects in horizon formation

Horizon remnants in naked singularities

Abstract

Repulsive gravity is a well known characteristic of naked singularities. In this work, we explore light surfaces and find new effects of repulsive gravity. We compare Kerr naked singularities with the corresponding black hole counterparts and find certain structures that are identified as horizon remnants. We argue that these features might be significant for the comprehension of processes that lead to the formation or eventually destruction of black hole Killing horizons. These features can be detected by observing photon orbits, particularly close to the rotation axis, which can be used to distinguish naked singularities from black holes.

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Notes

  1. 1.

    https://eventhorizontelescope.org/.

  2. 2.

    An interesting speculative interpretation of the super-spinner solutions explores the duality between elementary particles and BHs, with quantum BH as the link between microphysics and macrophysics [37,38,39,40,41]. In any case, the NSs, which are present in the Kerr, Reissner-Nörstrom, and Kerr-Newman spacetimes, provide a perspective of crucial interest regarding the elementary particles description in general relativity and the definition of the characteristic charge, mass, and spin-mass ratio, radius and particles number of self-gravitating objects[42,43,44,45,46,47,48]. In self-gravitating objects such as boson stars or fermion stars, the repulsive gravity factors may -n of a critical charge and particle number of the object itself [49,50,51,52,53,54].

  3. 3.

    The BH formation after collapse has been associated with trapped surfaces formation, that is, a singularity without trapped surfaces is usually considered as a proof of its naked singularity nature[64,65,66,67,68,69]. Nevertheless, the non-existence of trapped surfaces after or during the gravitational collapse is not a proof of the existence of a NS. It is possible to choose a very particular slicing of spacetime during the formation of a spherically symmetric black hole where no trapped surfaces exist (see also [70, 71]).

  4. 4.

    Equation \(\varDelta \omega _{\pm }=\mathbf {c}\) can be solved for the spins \(a_z^{\pm }\equiv \sqrt{\left[ {r^2 \left[ 2-\mathbf {c}^2 r (r+2)\right] \pm 2 \sqrt{r^3 \left[ r-4 \mathbf {c}^2 (r+2)\right] }}\right] / {\mathbf {c}^2 (r+2)^2}}\), where \(a_z^-=a_z^+=0\) for \(\mathbf {c}= \pm {2 \sqrt{r-2}}/{r^{3/2}}\). Furthermore, it is clear that the values of \(\mathbf {c}\) such that \(a_z^{\pm }=0\), which correspond to the Schwarzschild case, have as extreme case \(r=3M\). That is, \(a_z\) are curves with equal difference in frequency, which is null, as expected, on the horizon in the extended plane- Fig.  (2).

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Acknowledgements

This work was partially supported by UNAM-DGAPA-PAPIIT, Grant No. 114520, Conacyt-Mexico, Grant No. A1-S-31269, and by the Ministry of Education and Science of Kazakhstan, Grant No. BR05236730 and AP05133630.

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Correspondence to Daniela Pugliese.

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Pugliese, D., Quevedo, H. Repulsive gravity effects in horizon formation. Gen Relativ Gravit 53, 89 (2021). https://doi.org/10.1007/s10714-021-02858-4

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Keywords

  • Black holes
  • Naked singularities
  • Killing horizons
  • Light surfaces
  • Photon orbits