Dirac Equation on the Kerr–Newman Spacetime and Heun Functions

Dariescu, Ciprian; Stelea, Cristian

doi:10.1155/2021/5512735

Cited by 12 publications

(6 citation statements)

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“…Heun-type equations are known to appear in many applications in gravity, especially as solutions of the wave equations [14][15][16][17][18][19][20]. Our present work and the other works in the literature which study the wave equations for the metrics based on the Nutku instanton yield DCH functions as solutions.…”

Section: Introductionmentioning

confidence: 57%

Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

Birkandan¹

2022

Preprint

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We study a charged and massive scalar field in the background of the Nutku-Ghezelbash-Kumar metric which is obtained by the addition of a time coordinate to the Nutku helicoid metric in a non-trivial way. The angular part of the Klein-Gordon equation can be written as a double confluent Heun equation. The radial equation cannot be solved in terms of a known function in its general form. However, in some special cases, the radial equation can also be written explicitly as a double confluent Heun equation. We study the full radial equation numerically and observe that the electromagnetic field parameter defines an effective cut-off on the range of the radial coordinate. Finally, we obtain a quasi-exact solution with an approximation.

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Section: Introductionmentioning

confidence: 57%

Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

Birkandan¹

2022

Preprint

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“…[152] and [153], respectively. For the CTNBH [153], the charged Dirac equations [154,155] that govern the behavior of charged spin-1 2 particles are obtained with the NP formalism. Similarly, the charged KG equation has been employed in order to study the GF of bosons in the CTNBH geometry.…”

Section: B Fermionic Gfs and Qnmsmentioning

confidence: 99%

Topical Review: Greybody Factors and Quasinormal Modes for Black Holes in Various Theories -- Fingerprints of Invisibles

Sakallı,

Kanzi

2022

Preprint

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We give a pedagogical introduction to black holes (BHs) greybody factors (GFs) and quasinormal modes (QNMs) and share the recent developments on those subjects. To this end, we present some particular analytical and approximation techniques for the computations of the GFs and QNMs.We first review the gravitational GFs and show how they are analytically calculated for static and spherically symmetric higher dimensional BHs, consisting the charged BHs and existence of cosmological constant (i.e., de Sitter (dS)/anti-de Sitter (AdS)AdS BHs). The computations performed involve both the low-energy (having real and small frequencies) and the asymptotic (having extremely high frequency of the scattered wave throughout the imaginary axis) cases. A generic method is discussed at low frequencies. This method can be used for all three types of spacetime asymptotics and it is unaffected by the BH's features. For asymptotically dS BHs, GF varies depending on whether the spacetime dimension is even or odd, and is proportional to the ratio of the event and cosmic horizon areas. At asymptotic frequencies, the GFs can be computed by using a matching technique inspired by the monodromy method. In the meantime, we also make a general literature review on the matching technique in a separate section. While the GFs for charged or asymptotically dS BHs are generated by non-trivial functions, the GF for asymptotically AdS BHs is precisely one: pure black-body emission. QNMs, which are solutions to the relevant perturbation equations that satisfy the boundary conditions for purely outgoing (gravitational) waves at spatial infinity and purely ingoing (gravitational) waves at the event horizon, are considered using some particular analytical (like the matching technique) and approximation methods. In this study, our primary focus will be on the bosonic and fermionic GFs and QNMs of various BH and brane geometries and reveal the fingerprints of the invisibles with the radiation spectra to be obtained by the WKB approximation and bounding the Bogoliubov coefficients (together with the Miller-Good transformation) methods.

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“…The quantum motions of spin-zero scalar bosons with scalar and vector potential of various kinds and external magnetic and quantum flux fields have been investigated in the background of curved space-times, such as Gödel universe [1], the Som-Raychaudhri space-time [1,2], Ellis-Bronnikov-type wormhole space-time, charged and rotating black hole space-time [3], the Kerr-Newman black holes background [4], topologically trivial space-time [5], and topologically non-trivial space-time [6]. Moreover, the quantum dynamics of spin-half particles have been studied in curved space-time backgrounds as well as in other space-times, such as charged and rotating black hole metric [7], the Kerr spacetime [8], the Kerr-Newman-AdS black hole metric [9], Rindler space-time [10], the Kerr-Newman Space-time [11], and topologically trivial space-time [12] and many more in the literature. It is worth mentioning that the non-relativistic wave equation in the background of topological defect space-times has also been studied in the literature [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Topological effects on generalized Duffin-Kemmer-Petiau oscillator under Aharonov–Bohm flux field and Coulomb potential

Candemir

Ahmed

2023

Phys. Scr.

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In this paper, we study the relativistic quantum motions of the oscillator field of the wave equation under the influence of the Aharonov-Bohm (AB) flux field with a Coulomb vector potential in the background of the topological defects produced by a cosmic string and global monopole space-time. We derive the radial equation of the generalized Duffin-Kemmer-Petiau (DKP) oscillator in a static cosmic string space-time and solve it through the Heun function equation. Afterwards, we derive the radial equation of the same generalizedDKP oscillator in a point-like global monopole background and obtain the eigenvalue solutions using the same procedure. The generalized oscillator field is studied by substituting the radial momentum operator $∂_{r} →(∂_{r}r + i\,M\,ω\,η^{0}\,f(r))$, where $f(r)$ is an arbitrary function other than linear and introduces a vector potential of Coulomb-types through a minimal substitution via $∂_{µ} → (∂_{µ} − i\,q\,A_{µ})$ in the relativistic wave equation. It is shown that the eigenvalue solutions of the oscillator field are influenced by the topological defects of the cosmic string and point-like global monopole space-times and get them modified. Furthermore, we see that the eigenvalue solutions depend on the geometric quantum phase, and hence, shifted them more in addition to the topological defects that show the gravitational analogue to the Aharonov-Bohm effect for the bound-states

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Dirac Equation on the Kerr–Newman Spacetime and Heun Functions

Cited by 12 publications

References 50 publications

Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

Solutions of a charged scalar field in five-dimensional helicoid solution with electromagnetic field

Topical Review: Greybody Factors and Quasinormal Modes for Black Holes in Various Theories -- Fingerprints of Invisibles

Topological effects on generalized Duffin-Kemmer-Petiau oscillator under Aharonov–Bohm flux field and Coulomb potential

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