Circular orbits in cosmic string and Schwarzschild–AdS spacetime with Fermi–Walker transport

In this paper we discuss parallel transport of vectors and spinors around circular orbits in Schwarzschild–AdS spacetime. We study the global properties of this spacetime via loop variables or holonomy. A set of paths in this background is considered. We demonstrate that for some special radii there appears the so-called quantized band structure of holonomy invariance. This analysis is also extended to parallel transport of a spinor in this spacetime.

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MULTI-BLACK HOLES SOLUTION WITH COSMIC STRINGS

International Journal of Modern Physics A ◽

10.1142/s0217751x04017756 ◽

2004 ◽

Vol 19 (10) ◽

pp. 1549-1557 ◽

Cited By ~ 8

Author(s):

F. ÖZDEMIR ◽

N. ÖZDEMIR ◽

B. T. KAYNAK

Keyword(s):

Black Holes ◽

Black Hole ◽

Angular Momentum ◽

Cosmic String ◽

Circular Orbit ◽

Cosmic Strings ◽

De Sitter ◽

Circular Orbits ◽

Small Oscillations ◽

String Models

Some black hole-cosmic string models such as Reissner–Nordström, RN–de Sitter, Kerr–Newman and multi-black holes with cosmic string are given. Energy and angular momentum of a timelike particle in circular orbits in multi-black hole space–time are calculated. The geodesic equations for the timelike particles for the far region of the multi-black hole sources are calculated and small oscillations around the circular orbit obtained. It is seen that the particle's orbit precesses like the Lens–Thirring effect.

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Induced current in high-dimensional AdS spacetime in the presence of a cosmic string and a compactified extra dimension

Physical Review D ◽

10.1103/physrevd.99.045005 ◽

2019 ◽

Vol 99 (4) ◽

Cited By ~ 5

Author(s):

W. Oliveira dos Santos ◽

H. F. Mota ◽

E. R. Bezerra de Mello

Keyword(s):

Cosmic String ◽

Extra Dimension ◽

High Dimensional ◽

Induced Current ◽

Ads Spacetime

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Induced fermionic current in AdS spacetime in the presence of a cosmic string and a compactified dimension

The European Physical Journal C ◽

10.1140/epjc/s10052-020-08505-7 ◽

2020 ◽

Vol 80 (10) ◽

Author(s):

S. Bellucci ◽

W. Oliveira dos Santos ◽

E. R. Bezerra de Mello

Keyword(s):

Magnetic Flux ◽

Cosmic String ◽

Vacuum Expectation ◽

Vacuum Expectation Value ◽

Axial Current ◽

De Sitter ◽

Twisted Field ◽

Compact Dimension ◽

Ads Spacetime ◽

Current Densities

AbstractIn this paper, we consider a massive charged fermionic quantum field and investigate the current densities induced by a magnetic flux running along the core of an idealized cosmic string in the background geometry of a 5-dimensional anti-de Sitter spacetime, assuming that an extra dimension is compactified. Along the compact dimension quasi-periodicity condition is imposed on the field with a general phase. Moreover, we admit the presence of a magnetic flux enclosed by the compactified axis. The latter gives rise to Ahanorov–Bohm-like effect on the vacuum expectation value of the currents. In this setup, only azimuthal and axial current densities take place. The former presents two contributions, with the first one due to the cosmic string in a 5-dimensional AdS spacetime without compact dimension, and the second one being induced by the compactification itself. The latter is an odd function of the magnetic flux along the cosmic string and an even function of the magnetic flux enclosed by the compactified axis with period equal to the quantum flux. As to the induced axial current, it is an even function of the magnetic flux along the string’s core and an odd function of the magnetic flux enclosed by the compactification perimeter. For untwisted and twisted field along compact dimension, the axial current vanishes. The massless field case is presented as well some asymptotic limits for the parameters of the model.

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Fermionic vacuum polarization around a cosmic string in compactified AdS spacetime

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2022/01/010 ◽

2022 ◽

Vol 2022 (01) ◽

pp. 010

Author(s):

S. Bellucci ◽

W. Oliveira dos Santos ◽

E.R. Bezerra de Mello ◽

A.A. Saharian

Keyword(s):

Energy Density ◽

Cosmic String ◽

Vacuum Energy ◽

Energy Momentum Tensor ◽

Minkowski Spacetime ◽

Vacuum Expectation ◽

Vacuum Expectation Value ◽

Momentum Tensor ◽

Vacuum Energy Density ◽

Ads Spacetime

Abstract We investigate topological effects of a cosmic string and compactification of a spatial dimension on the vacuum expectation value (VEV) of the energy-momentum tensor for a fermionic field in (4+1)-dimensional locally AdS spacetime. The contribution induced by the compactification is explicitly extracted by using the Abel-Plana summation formula. The mean energy-momentum tensor is diagonal and the vacuum stresses along the direction perpendicular to the AdS boundary and along the cosmic string are equal to the energy density. All the components are even periodic functions of the magnetic fluxes inside the string core and enclosed by compact dimension, with the period equal to the flux quantum. The vacuum energy density can be either positive or negative, depending on the values of the parameters and the distance from the string. The topological contributions in the VEV of the energy-momentum tensor vanish on the AdS boundary. Near the string the effects of compactification and gravitational field are weak and the leading term in the asymptotic expansion coincides with the corresponding VEV in (4+1)-dimensional Minkowski spacetime. At large distances, the decay of the cosmic string induced contribution in the vacuum energy-momentum tensor, as a function of the proper distance from the string, follows a power law. For a cosmic string in the Minkowski bulk and for massive fields the corresponding fall off is exponential. Within the framework of the AdS/CFT correspondence, the geometry for conformal field theory on the AdS boundary corresponds to the standard cosmic string in (3+1)-dimensional Minkowski spacetime compactified along its axis.

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The evolutions of the innermost stable circular orbits in dynamical spacetimes

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09623-6 ◽

2021 ◽

Vol 81 (10) ◽

Author(s):

Yong Song

Keyword(s):

Angular Momentum ◽

Orbital Angular Momentum ◽

Effective Potential ◽

Potential Method ◽

Orbital Energy ◽

Slow Rotation ◽

Schwarzschild Spacetime ◽

Circular Orbits ◽

Ads Spacetime ◽

Stationary Spacetimes

AbstractIn this paper, we studied the evolutions of the innermost stable circular orbits (ISCOs) in dynamical spacetimes. At first, we reviewed the method to obtain the ISCO in Schwarzschild spacetime by varying its conserved orbital angular momentum. Then, we demonstrated this method is equivalent to the effective potential method in general static and stationary spacetimes. Unlike the effective potential method, which depends on the presence of the conserved orbital energy, this method requires the existence of conserved orbital angular momentum in spacetime. So it can be easily generalized to the dynamical spacetimes where there exists conserved orbital angular momentum. From this generalization, we studied the evolutions of the ISCOs in Vaidya spacetime, Vaidya-AdS spacetime and the slow rotation limit of Kerr–Vaidya spacetime. The results given by these examples are all reasonable and can be compared with the evolutions of the photon spheres in dynamical spacetimes.

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