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Dilaton gravity, (quasi-) black holes, and scalar charge

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Abstract

Electrically charged dust is considered in the framework of Einstein–Maxwell–dilaton gravity with a Lagrangian containing the interaction term \(P(\chi )F_{\mu \nu }F^{\mu \nu }\), where \(P(\chi )\) is an arbitrary function of the dilaton scalar field \(\chi \), which can be normal or phantom. Without assumption of spatial symmetry, we show that static configurations exist for arbitrary functions \(g_{00} = \exp (2\gamma (x^{i}))\) (\(i=1,2,3\)) and \(\chi =\chi (\gamma )\). If \(\chi = \mathrm{const}\), the classical Majumdar–Papapetrou (MP) system is restored. We discuss solutions that represent black holes (BHs) and quasi-black holes (QBHs), deduce some general results and confirm them by examples. In particular, we analyze configurations with spherical and cylindrical symmetries. It turns out that cylindrical BHs and QBHs cannot exist without negative energy density somewhere in space. However, in general, BHs and QBHs can be phantom-free, that is, can exist with everywhere nonnegative energy densities of matter, scalar and electromagnetic fields.

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Notes

  1. This paper, entitled “Scalar-tensor theory and scalar charge”, was published 40 years ago. The title of the present paper is chosen deliberately to mark this date.

  2. Stringlike configurations with an angular defect would also be admissible, but they are impossible with the metric (85).

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Acknowledgments

We thank CNPq (Brazil) and FAPES (Brazil) for partial financial support.

Author information

Authors and Affiliations

  1. Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Street, Moscow, 119361, Russia

    K. A. Bronnikov

  2. Institute of Gravitation and Cosmology, PFUR, 6 Miklukho-Maklaya Street, Moscow, 117198, Russia

    K. A. Bronnikov

  3. I. Kant Baltic Federal University, Al. Nevsky St. 14, Kaliningrad, 236041, Russia

    K. A. Bronnikov

  4. Departamento de Física, Universidade Federal do Espírito Santo, Av. Fernando Ferrari 514, Campus de Goiabeiras, Vitória, ES, CEP 29075-910, Brazil

    J. C. Fabris & R. Silveira

  5. Department of Physics and Technology, Kharkov V.N. Karazin National University, 4 Svoboda Square, Kharkov, 61077, Ukraine

    O. B. Zaslavskii

  6. Institute of Mathematics and Mechanics, Kazan Federal University, 18 Kremlyovskaya Street, Kazan, 420008, Russia

    O. B. Zaslavskii

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  1. K. A. Bronnikov
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  2. J. C. Fabris
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  3. R. Silveira
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  4. O. B. Zaslavskii
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Correspondence to O. B. Zaslavskii.

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Bronnikov, K.A., Fabris, J.C., Silveira, R. et al. Dilaton gravity, (quasi-) black holes, and scalar charge. Gen Relativ Gravit 46, 1775 (2014). https://doi.org/10.1007/s10714-014-1775-2

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