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Gravitational repulsive effects in 3D regular black holes

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Abstract

In this work, we consider the effects of repulsive gravity in an invariant way for four static 3D regular black holes, using the eigenvalues of the Riemann curvature tensor, the Ricci scalar, and the strong energy conditions. The eigenvalues of the solutions are non-vanishing asymptotically (in asymptotically AdS) and increase as the source of gravity is approached, providing a radius at which the passage from attractive to repulsive gravity might occur. We compute the onsets and the regions of repulsive gravity and conclude that the regular behavior of the solutions at the origin of coordinates can be interpreted as due to the presence of repulsive gravity, which also turns out to be related with the violation of the strong energy condition. We showed that in all of the solutions for the allowed region of parameters, gravity changes its sign, but the repulsive regions only for the non-logarithmic solution are affected by the mass that generates the regular black hole. The repulsive regions for the logarithmic solutions are dependent on electric charge and the AdS\(_{3}\) length. The implications and physical consequences of these results are discussed in detail.

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Notes

  1. Interestingly, despite extensive investigations, no scenarios of gravitational collapse have conclusively confirmed the validity of the cosmic censorship hypothesis, which posits that singularities are always concealed from observation. Consequently, there remains the possibility that, under specific circumstances, naked singularities may emerge during the course of mass distribution collapsing gravitationally [13].

  2. Including local degrees of freedom makes the theory closer to its four-dimensional counterpart; this can be achieved by deforming the theory, giving a mass to the graviton [39, 41].

  3. In 3D flat spacetime, the only solution with the horizon is flat space cosmology [50, 51]. The other solutions are the kink-like solution with the gravitational field which is described by a conical space with its deficit angle corresponding to the mass of the particle. [40, 42].

  4. In this direction, one can find electrically charged black holes, dilatonic black holes, black holes arising in string theory, black holes in topologically massive gravity, and warped-AdS black holes [42,43,44,45,46,47,48,49].

  5. It should be noted that the logarithmic solutions can also be solutions of 3D gravity theories at the chiral point.

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Acknowledgements

The work of OL is partially financed by the Ministry of Education and Science of the Republic of Kazakhstan, Grant: IRN AP19680128. The work of HQ was partially supported by UNAM-DGAPA-PAPIIT, Grant No. 114520, and CONACYT-Mexico, Grant No. A1-S-31269.

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Authors and Affiliations

  1. Università di Camerino, Via Madonna delle Carceri 9, 62032, Camerino, Italy

    Orlando Luongo

  2. SUNY Polytechnic Institute, Utica, NY, 13502, USA

    Orlando Luongo

  3. INAF - Osservatorio Astronomico di Brera, Milano, Italy

    Orlando Luongo

  4. Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, 06123, Perugia, Italy

    Orlando Luongo

  5. Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040, Almaty, Kazakhstan

    Orlando Luongo

  6. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico, Mexico

    Hernando Quevedo

  7. Dipartimento di Fisica and Icra, Università di Roma “La Sapienza”, Roma, Italy

    Hernando Quevedo

  8. School of Physics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran

    S. N. Sajadi

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  1. Orlando Luongo
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OL: Conceptualization, Writing an original draft, review and editing HQ: Conceptualization, Validation, review and editing SNS: Software, Writing an original draft, review and editing

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Correspondence to S. N. Sajadi.

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Luongo, O., Quevedo, H. & Sajadi, S.N. Gravitational repulsive effects in 3D regular black holes. Gen Relativ Gravit 56, 17 (2024). https://doi.org/10.1007/s10714-024-03207-x

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