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Charged scalar fields around Einstein-power-Maxwell black holes

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Abstract

We study the propagation of massless charged scalar fields, and compute the corresponding quasinormal modes of the Einstein-power-Maxwell spacetime in (1+3) dimensions. By employing two different numerical schemes, we characterize the behavior of the modes throughout the whole parameter space of the model. Our results indicate the existence of two distinct families of modes. A family directly related to the photon-sphere of the black hole and another family, which comes into play for near-extremal black hole charges. Our numerics show that close to extremality, the fundamental near-extremal modes become longer-lived compared to the corresponding fundamental photon-sphere modes and are approximated by the formula \(\omega _{\text {NE}}\approx e \Phi (r_h)-i\kappa _h\), where e is the charge of the scalar field and \(\Phi (r_h)\), \(\kappa _h\) are the electric potential and surface gravity of the black hole event horizon. Finally, it is shown that the near-extremal family becomes purely imaginary in the \(e\rightarrow 0\) limit.

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Acknowledgements

The author is grateful to the anonymous reviewers for comments and suggestions that improved the quality of the manuscript. G. P. thanks the Fundação para a Ciência e Tecnologia (FCT), Portugal, for the financial support to the Center for Astrophysics and Gravitation-CENTRA, Instituto Superior Técnico, Universidade de Lisboa, through the Grant No. UID/FIS/00099/2013. Part of the computations were performed at the cluster “Baltasar-Sete-Sóis”, and supported by the MaGRaTh–646597 ERC Consolidator Grant. The author thankfully acknowledges the computer resources, technical expertise and assistance provided by Sérgio Almeida and Manuel Torrinha at CENTRA/IST. Finally, the author wishes to thank K. Destounis for a collaboration during the early stages of this work.

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  1. Centro de Astrofísica e Gravitação-CENTRA, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Avenida Rovisco Pais 1, 1049-001, Lisbon, Portugal

    Grigoris Panotopoulos

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Panotopoulos, G. Charged scalar fields around Einstein-power-Maxwell black holes. Gen Relativ Gravit 51, 76 (2019). https://doi.org/10.1007/s10714-019-2560-z

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