Solutions of the massive Dirac equation in the near-horizon metric of the extremal five dimensional Myers-Perry black hole with equal angular momenta

Blázquez-Salcedo, Jose Luis; Knöll, Christian

doi:10.1103/physrevd.99.024026

Cited by 6 publications

(5 citation statements)

References 50 publications

(66 reference statements)

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“…The angular equation in the five dimensional case turns out to be analytically solvable. Solutions have been already obtained in the near-horizon limit of the extremal case [34]. We use for the representation of the algebra fulfilled by the matrices…”

Section: Solving the Angular Equation In The Myers-perry Backgroundmentioning

confidence: 99%

“…In addition, in [33] the quasinormal modes of a charged, massless Dirac field and a charged, massive scalar field in the background of a spherically symmetric black hole with scalar hair in four dimensions have been studied using the continued fraction method. The massive Dirac field in the near-horizon region of the five dimensional Myers-Perry black hole with equal angular momenta was studied in [34].…”

Section: Introductionmentioning

confidence: 99%

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Quasinormal modes of Dirac spinors in the background of rotating black holes in four and five dimensions

Blázquez-Salcedo

Knöll

2019

Class. Quantum Grav.

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We study the quasinormal modes of massive Dirac spinors in the background of rotating black holes. In particular, we consider the Kerr geometry as well as the five dimensional Myers-Perry spacetime with equal angular momenta. We decouple the equations using the standard methods from the literature. In the five dimensional Myers-Perry black hole the angular equation is solved analytically. Using the continued fraction method, we calculate the spectrum of quasinormal modes for the ground modes and first excited modes. We analyze, in a systematic way, its dependence on the different parameters of the black hole and fermionic field. We compare our values with previous results available in the literature for Kerr and for the static limit. The numerical results show several differences between the four and five dimensional cases. For instance, in five dimensions the symmetry between the positive and negative (real) frequency of the modes breaks down, which results in a richer spectrum.

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Section: Solving the Angular Equation In The Myers-perry Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quasinormal modes of Dirac spinors in the background of rotating black holes in four and five dimensions

Blázquez-Salcedo

Knöll

2019

Class. Quantum Grav.

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“…Since Newton's time, many astronomers and physicists have studied the gravitational properties of stars by considering the moment equations derived from the Euler fluid dynamics equations. It is well known that there are two approaches to study the Dirac equation describing fermions near different types of black holes: one is using the Newman–Penrose method (Kraniotis 2019), and the other is a direct calculation method (Blázquez‐Salcedo & Knoll 2019).…”

Section: Introductionmentioning

confidence: 99%

Dirac spinor scattering states with positive‐energy in rotating spheroid models

Gao,

Chen,

Wang

et al. 2024

Astron Nachr

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There are many rotating spheroids in the universe, and many astronomers and physicists have used theoretical methods to study the characteristics of stellar gravity since Newton's time. This paper derives the solutions of eight scattering states ,, and for the Dirac equation with positive‐energy , and establishes the relationship between the differential scattering cross section and the stellar density . It is found that: (1) For the eight scattering states, their average scattering cross‐sections are proportional to , and depend on the star's radius, and the higher the stellar density , the greater the sensitivity of to the change of ; (2) For the four scattering states , their average scattering amplitudes and depend on the mass of the particles; while for the other four scattering states , , then and are independent of . This study links the gravitational characteristics of stars with the scattering cross section, creating a new method for studying the gravitational characteristics, which helps to reveal the mystery of the gravity of rotating ellipsoidal stars.

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“…As we know, there are two kinds of methods to study Dirac equation describing fermions in the vicinity of different types of black holes. One is the Newman–Penrose formalism, and another is the direct method (Blázquez‐Salcedo & Knoll 2019; Kraniotis 2019).…”

Section: Introductionmentioning

confidence: 99%

Scattering‐state solutions to the Dirac spinors with negative‐energy eigenstates in a rotating spheroid

2023

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Based on the work of Fu et al. (2020), we derive the rest seven scattering-state solutions to the Dirac equation when E = −im and establish a relation between differential scattering cross-section, 𝜎 i * (p, 𝜃, 𝜑), and stellar matter density, 𝜇, using the long-wave approximation. It is found that the sensitivity of average scattering cross-sections 𝜎 i (p, 𝜃) to the change in the stellar matter density is proportional to 𝜇 2 . We find that the average scattering amplitudes f i (p, 𝜃), as well as average scattering cross-sections 𝜎 i (p, 𝜃), are independent of the masses of particles, m, for four scattering states 𝜒 (i) , i = 0, 1, 2 and 3, while f i (p, 𝜃) and 𝜎 i * (p, 𝜃) depend on m, for the rest four scattering states, 𝜙 (i) , i = 0, 1, 2 and 3. By measuring the scattering cross-section, we can determine the density of the ellipsoid and obtain its gravitational properties. This work will be useful in understanding the properties of anti-Dirac spinors and the physical effects in a rotating spheroid.

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Solutions of the massive Dirac equation in the near-horizon metric of the extremal five dimensional Myers-Perry black hole with equal angular momenta

Cited by 6 publications

References 50 publications

Quasinormal modes of Dirac spinors in the background of rotating black holes in four and five dimensions

Quasinormal modes of Dirac spinors in the background of rotating black holes in four and five dimensions

Dirac spinor scattering states with positive‐energy in rotating spheroid models

Scattering‐state solutions to the Dirac spinors with negative‐energy eigenstates in a rotating spheroid

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