Charged scalar fields around Einstein-power-Maxwell black holes
TL;DR: In this article, the propagation of massless charged scalar fields and corresponding quasinormal modes of the Einstein-power-Maxwell spacetime in (1+3) dimensions were studied.
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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01 Jan 2005
TL;DR: The speziellen Relativitatstheorie liegt folgendes Postulat zugrunde, welchem auch durch die Galilei-Newtonsche Mechanik Genuge geleistet wird: Wird ein Koordinatensystem K so gewahlt, das in bezug auf dasselbe die physikalischen Gesetze in ihrer einfachsten Form gelten, so gelten dieselben Gesetzes auch in Bez
Abstract: Der speziellen Relativitatstheorie liegt folgendes Postulat zugrunde, welchem auch durch die Galilei-Newtonsche Mechanik Genuge geleistet wird: Wird ein Koordinatensystem K so gewahlt, das in bezug auf dasselbe die physikalischen Gesetze in ihrer einfachsten Form gelten, so gelten dieselben Gesetze auch in Bezug auf jedes andere Koordinatensystem K′, das relativ zu K in gleichformiger Translationsbewegung begriffen ist. Dieses Postulat nennen wir „spezielles Relativitatsprinzip“. Durch das Wort „speziell“ soll angedeutet werden, das das Prinzip auf den Fall beschrankt ist, das K′ eine gleichformige Translationsbewegung gegen K ausfuhrt, das sich aber die Gleichwertigkeit von K′ und K nicht auf den Fall ungleichformiger Bewegung von K′ gegen K erstreckt.
183 citations
TL;DR: In this paper, the scale dependence applied to black holes in the presence of non-linear electrodynamics was studied and a vanishing cosmological constant in (3+1) dimensions was obtained.
19 citations
24 Mar 2020
TL;DR: In this article, the quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory are computed for the eikonal limit.
Abstract: We compute the quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory. The impact on the spectrum of the electric charge of the black holes, of the angular degree, of the overtone number, and of the mass of the test scalar field is investigated in detail. The quasinormal spectra in the eikonal limit are computed as well for several different space-time dimensionalities.
15 citations
TL;DR: The quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory are computed for several different space-time dimensionalities.
Abstract: We compute the quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory. The impact on the spectrum of the electric charge of the black holes, of the angular degree, of the overtone number, and of the mass of the test scalar field is investigated in detail. The quasinormal spectra in the eikonal limit are computed as well for several different space-time dimensionalities.
14 citations
TL;DR: In this article, the authors studied the propagation of charged scalar fields in the background of $2+1$-dimensional Coulomb-like AdS black holes, and showed that such propagation is unstable under Dirichlet boundary conditions.
Abstract: We study the propagation of charged scalar fields in the background of $2+1$-dimensional Coulomb-like AdS black holes, and we show that such propagation is unstable under Dirichlet boundary conditions. However, all the unstable modes are superradiant and all the stable modes are nonsuperradiant, according with the superradiant condition. Mainly, we show that when the scalar field is charged the quasinormal frecuencies (QNFs) are always complex, contrary to the uncharged case, where for small values of the black hole charge the complex QNFs are dominant, while that for bigger values of the black hole charge the purely imaginary QNFs are dominant.
11 citations
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01 Jan 1983TL;DR: In a course of lectures on the underlying mathematical structures of classical gravitation theory given in 1978, Brandon Carter as discussed by the authors began with the statement ‘If I had been asked five years ago to prepare a course for recent developments in classical gravity theory, I would not have hesitated on the classical theory of black holes as a central topic of discussion. But I am grateful to them for their courtesy in assigning to me this privilege.
Abstract: In a course of lectures on the ‘underlying mathematical structures of classical gravitation theory’ given in 1978, Brandon Carter began with the statement ‘If I had been asked five years ago to prepare a course of lectures on recent developments in classical gravitation theory, I would not have hesitated on the classical theory of black holes as a central topic of discussion. However, the most important developments in gravitational theory during the last three or four years have not been in the classical domain at all…’ Carter is undoubtedly right in his assessment that the mathematical theory of black holes has not been in the mainstream of research in relativity since 1973. I therefore find it difficult to understand why the organizers of this meeting should have chosen precisely this topic for the opening talk of this meeting. But I am grateful to them for their courtesy in assigning to me this privilege.
4,165 citations
01 Jan 1916
2,229 citations
TL;DR: In this article, it was shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and therefore remain stable if subjected to a small nonspherical perturbation.
Abstract: It is shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and will therefore remain stable if subjected to a small nonspherical perturbation.
2,105 citations
TL;DR: In this paper, the authors compared Dirac's theory of the positron to those proposed by Born and showed that the field strength of large fields differs strongly from those of small fields.
Abstract: [arXiv:physics/0605038]: According to Dirac’s theory of the positron, an electromagnetic field tends to create pairs of particles which leads to a change of Maxwell’s equations in the vacuum. These changes are calculated in the special case that no real electrons or positrons are present and the field varies little over a Compton wavelength. The resulting effective Lagrangian of the field reads: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) + conj.}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) - conj. } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. $\cal{E}$, $\cal{B}$ field strengths. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle 137} \frac{\displaystyle e}{\displaystyle(e^2/m c^2)^2}$ critical field strengths. The expansion terms in small fields (compared to $\cal{E}$) describe light-light scattering. The simplest term is already known from perturbation theory. For large fields, the equations derived here differ strongly from Maxwell’s equations. Our equations will be compared to those proposed by Born. Original German abstract [Z.Phys. 98(1936)714]: Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abanderung der Maxwellschen Gleichungen des Vakuums. Diese Abanderungen werden fur den speziellen Fall berechnet, in dem keine wirklichen Elektronen und Positronen vorhanden sind, und in dem sich das Feld auf Strecken der Compton-Wellenlange nur wenig andert. Es ergibt sich fur das Feld eine Lagrange-Funktion: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) + konj}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) - konj } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. ($\cal{E}$, $\cal{B}$ Kraft auf das Elektron. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle ,,137``} \frac{\displaystyle e}{\displaystyle (e^2/m c^2)^2}$ „Kritische Feldstarke“.) Ihre Entwicklungsglieder fur (gegen $\vert\cal{E}_k\vert$) kleine Felder beschreiben Prozesse der Streuung von Licht an Licht, deren einfachstes bereits aus einer Storungsrechnung bekannt ist. Fur grose Felder sind die hier abgeleiteten Feldgleichungen von den Maxwellschen sehr verschieden. Sie werden mit den von Born vorgeschlagenen verglichen.
2,059 citations