Classical solutions of the gravitating Abelian Higgs model

Brihaye, Yves; Lubo, Musongela

doi:10.1103/physrevd.62.085004

Cited by 31 publications

(51 citation statements)

References 13 publications

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“…Note that there is also another notion of energy in this space-time, namely that of the Tolman energy [24,25]. This defines the gravitationally active mass.…”

Section: The Model a The Space-time Of A (Pq)-stringmentioning

confidence: 99%

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Detection of cosmic superstrings by geodesic test particle motion

2011

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(p,q)-strings are bound states of p F-strings and q D-strings and are predicted to form at the end of brane inflation. As such these cosmic superstrings should be detectable in the universe. In this paper we argue that they can be detected by the way that massive and massless test particles move in the space-time of these cosmic superstrings, in particular we study solutions to the geodesic equation in the space-time of field theoretical (p,q)-strings. The geodesics can be classified according to the test particle's energy, angular momentum and momentum in the direction of the string axis. We discuss how the change of the magnetic fluxes, the ratio between the symmetry breaking scale and the Planck mass, the Higgs to gauge boson mass ratios and the binding between the F-and D-strings, respectively, influence the motion of the test particles. While massless test particles can only move on escape orbits, a new feature as compared to the infinitely thin string limit is the existence of bound orbits for massive test particles. In particular, we observe that -in contrast to the space-time of a single Abelian-Higgs string -bound orbits for massive test particles in (p,q)-string space-times are possible if the Higgs boson mass is larger than the gauge boson mass. We also compute the effect of the binding between the p-and the q-string on observables such as the light deflection and the perihelion shift. While light deflection can also be caused by other matter distributions, the possibility of a negative perihelion shift seems to be a feature of finite width cosmic strings that could lead to the unmistakable identification of such objects. In Melvin space-times, which are asymptotically non-conical, massive test particles have to move on bound orbits, while massless test particles can only escape to infinity if their angular momentum vanishes.

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“…Note that there is also another notion of energy in this space-time, namely that of the Tolman energy [24,25]. This defines the gravitationally active mass.…”

Section: The Model a The Space-time Of A (Pq)-stringmentioning

confidence: 99%

“…For β 3 = 0 it has been found [24,25] that c 1 > 1 for β 1 = β 2 ≡ β < 2, c 1 < 1 for β 1 = β 2 ≡ β > 2 and c 1 = 1 in the BPS limit…”

Section: String Solutionsmentioning

confidence: 99%

Detection of cosmic superstrings by geodesic test particle motion

2011

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“…For α > α max no globally regular string solutions exist, but only solutions with singularities (so-called "supermassive" or "inverted" string solutions). These supermassive solutions possess a singularity at some finite value of the radial coordinate r = r max,1 at which L(r max,1 ) = 0, while N (r max,1 ) stays finite [25,26].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Now, we require the respective terms in the brackets to vanish. This gives the equations (25) and (26). We believe that this is a suitable choice for our model.…”

Section: Appendix: the Conservation Lawmentioning

confidence: 99%

Abelian–Higgs strings in Rastall gravity

Mello

Fabris

Hartmann

2015

Class. Quantum Grav.

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In this paper we analyze Abelian-Higgs strings in a phenomenological model that takes quantum effects in curved space-time into account. This model, first introduced by Rastall, cannot be derived from an action principle. We formulate phenomenological equations of motion under the guiding principle of minimal possible deformation of the standard equations. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to 2π at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map S 1 → S 1 . Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.

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“…Although both types of geometries present different asymptotic behaviors, they are solutions of the same set of differential equations. This apparent contradiction was clarified in the papers [13,14], where the authors pointed out that the coexistence of two different kinds of solutions are consequence of boundary conditions imposed on the metric fields. In fact the two different kinds of asymptotic behaviors for the metric tensor correspond to the two different branches of cylindrically symmetric vacuum solutions of the Einstein equations [15].…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian cosmic strings in de Sitter and anti–de Sitter space

Santos

Mello

2016

Phys. Rev. D

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In this paper we investigate the non-Abelian cosmic string in de Sitter and anti-de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also for the metric tensor for specific values of the physical parameters of the theory. For de Sitter case, we find the appearance of horizons that although being consequence of the presence of the cosmological constant it strongly depends on the value of the gravitational coupling. In the anti-de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (00) and (zz) components of the metric tensor. They present a strongly increasing for large distance from the string.

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Classical solutions of the gravitating Abelian Higgs model

Cited by 31 publications

References 13 publications

Detection of cosmic superstrings by geodesic test particle motion

Detection of cosmic superstrings by geodesic test particle motion

Abelian–Higgs strings in Rastall gravity

Non-Abelian cosmic strings in de Sitter and anti–de Sitter space

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