Quasinormal modes of regular black holes with non-linear electrodynamical sources

Abstract

We compute the spectrum of quasinormal frequencies of regular black holes obtained in the presence of Non-Linear Electrodynamics. In particular, we perturb the black hole with a minimally coupled massive scalar field, and we study the corresponding perturbations adopting the 6th order WKB approximation. We analyze in detail the impact on the spectrum of the charge of the black hole, the quantum number of angular momentum and the overtone number. All modes are found to be stable. Finally, a comparison with other charged black holes is made, and an analytical expression for the quasinormal spectrum in the eikonal limit is provided. PACS. XX.XX.XX No PACS code given 1 IntroductionAlthough black holes (BHs) and gravitational waves (GWs) are predicted to exist within the framework of Einstein's General Relativity (GR) [1], until a few years ago there was only indirect evidence for the existence of both of them. Galactic centres are supposed to host supermassive BHs [2-4], while gravitational waves had been indirectly seen in orbital decay of binary systems due to emission of gravitational radiation [5]. The historical LIGO direct detection of GWs [6-8] has provided the strongest evidence so far that BHs do exist in Nature and that they merge, and it has opened a completely new window to the Universe. Despite the fact that BHs are the simplest objects in the Universe, characterized entirely by a handful of parameters, such as mass, spin and charges, they are fascinating objects bringing together many different areas, from gravitation to thermodynamics to quantum mechanics, and they are of paramount importance to gravitation, since they have the potential of revealing (at least) some of the hidden secrets of quantum gravity.A special attention is devoted to non-linear electrodynamics (NLE), which has a long history and it has been studied over the years in several different contexts. Maxwell's classical theory is based on a system of linear equations, but when quantum effects are taken into account, the effective equations become non-linear. The first models go back to the 30's when Euler and Heisenberg obtained QED corrections [9], while Born and Infeld obtained a finite self-energy of point-like charges [10]. Furthermore, a non-trivial extension of Maxwell's theory leads to the by now well-known Einstein-power-Maxwell (EpM) theory described by a Lagrangian density of the form L(F ) = F k , where F is the usual Maxwell invariant, to be defined below, and k is an arbitrary rational number. This class of theories maintain the nice properties of conformal invariance in any number of space time dimensionality D provided that k = D/4. Black hole solutions in (1+2)-dimensional and higher-dimensional EpM theories have been obtained in [11] and [12] respectively (see also [13,14] for scale-dependent black holes in the presence of EpM NLE). More exotic NLE models, such as logarithmic [15], rational [16], and exponential [17] among others, have been studied in connection to black hole physics.Furthermore, the well-known Reissn...

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Greybody factor and quasinormal modes of Regular Black Holes

“…Even more, such frequencies depend on i) the geometry and ii) the type of perturbations [25]. Along the years, the study of QNM becomes more essential than ever, and certain seminal works have been performed up to now, for instance see [26][27][28] and more recent works [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

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