Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

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Regular charged black hole construction in dimensions

Physics Letters A ◽

10.1016/j.physleta.2012.01.001 ◽

2012 ◽

Vol 376 (8-9) ◽

pp. 893-898 ◽

Cited By ~ 10

Author(s):

S. Habib Mazharimousavi ◽

M. Halilsoy ◽

T. Tahamtan

Keyword(s):

Black Hole ◽

Charged Black Hole

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The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽

10.3390/galaxies9010018 ◽

2021 ◽

Vol 9 (1) ◽

pp. 18

Author(s):

Alexander Burinskii

Keyword(s):

Electromagnetic Field ◽

Quantum Theory ◽

Gravitational Field ◽

Dirac Equation ◽

Higgs Field ◽

Vacuum State ◽

Relativistic String ◽

Dirac Equations ◽

Dirac Electron ◽

Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

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New non-extremal and BPS hairy black holes in gauged $$ \mathcal{N} $$ = 2 and $$ \mathcal{N} $$ = 8 supergravity

Journal of High Energy Physics ◽

10.1007/jhep04(2021)047 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Andres Anabalon ◽

Dumitru Astefanesei ◽

Antonio Gallerati ◽

Mario Trigiante

Keyword(s):

Black Holes ◽

Black Hole ◽

Boundary Conditions ◽

Charged Black Hole ◽

Dual Theory ◽

Real Numbers ◽

Hairy Black Holes ◽

Interpolation Parameter ◽

Black Hole Solutions ◽

Extremal Black Holes

Abstract In this article we study a family of four-dimensional, $$ \mathcal{N} $$ N = 2 supergravity theories that interpolates between all the single dilaton truncations of the SO(8) gauged $$ \mathcal{N} $$ N = 8 supergravity. In this infinitely many theories characterized by two real numbers — the interpolation parameter and the dyonic “angle” of the gauging — we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supersymmetric and non-extremal black holes are new examples in the $$ \mathcal{N} $$ N = 8 theory that do not belong to the STU model. We compute the asymptotic charges, thermodynamics and boundary conditions of these black holes and show that all of them, except one, introduce a triple trace deformation in the dual theory.

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