Derrick’s theorem in curved spacetime

Carloni, Sante; Rosa, João Luís

doi:10.1103/physrevd.100.025014

Cited by 15 publications

(10 citation statements)

References 35 publications

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“…Asymptotic flat solutions have been considered with respect to gravitational lensing in [42] and rotating and expanding solutions are presented in [43]. The inner star objects with spin and torsion are considered in [44] and mass bounds in [45].…”

Section: Introductionmentioning

confidence: 99%

Consistent solution of Einstein–Cartan equations with torsion outside matter

Morawetz

2021

Class. Quantum Grav.

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The Einstein–Cartan equations in first-order action of torsion are considered. From Belinfante–Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion is given by the spin which leads to an extended Oppenhaimer–Volkov equation. Outside matter a second solution is found besides the torsion-free Schwarzschild one with the torsion completely determined by the metric and vice versa. This solution is shown to be of non-spherical origin and its uniqueness with respect to the consistence is demonstrated. Unusual properties are discussed in different coordinate systems where the cosmological constant assumes the role of the Friedman parameter in Friedman–Lamaître–Robertson–Walker cosmoses. Parameters are specified where wormholes are possible. Transformations are presented to explore and map regions of expanding and contracting universes to the form of static metrics. The autoparallel equations are solved exactly and compared with geodesic motion. The Weyl tensor reveals that the here found solution is of Petrov-D type.

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Section: Introductionmentioning

confidence: 99%

Consistent solution of Einstein–Cartan equations with torsion outside matter

Morawetz

2021

Class. Quantum Grav.

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“…Note that in Minkowski space-time the existence of real, static scalar field solutions of this simple model is forbidden by Derrick's theorem [10]. Moreover, in a curved space-time background, solutions do not exist if the spacetime is asymptotically flat [22]. However, in the spatially compact space-time that we are studying here, the additional length scale-the radius of the three-sphere R 0leads to the existence of solitonic solutions.…”

Section: The Modelmentioning

confidence: 88%

“…When extending these models to curved space-time, self-gravitating counterparts of Q-balls, socalled boson stars exist [15][16][17][18][19][20][21]. In curved space-time, no general direct extension of Derrick's theorem seems to restrict the solitonic solutions, and the possibility of finding them is open for exploration, although there has been recent progress for asymptotically flat space-times [22].…”

Section: Introductionmentioning

confidence: 99%

Real scalar field kinks and antikinks and their perturbation spectra in a closed universe

Hartmann

Luchini²,

Constantinidis³

et al. 2020

Phys. Rev. D

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We demonstrate that solitons of a simple real scalar field model that are static and linearly stable do exist when considered in a (3 þ 1)-dimensional, spatially compact space-time background, the static Einstein universe, which is a good approximation to the observed Universe for sufficiently small time intervals. We study the properties of these solutions for a Φ 4-potential and demonstrate that next to the fundamental solutions, excited configurations exist. We also investigate general perturbations about the solitons, determine their eigenfrequency spectra, and compare them to those of the perturbations about the vacua of the model. We find that the degeneracy with respect to the multipoles of the perturbation, which is present for the vacua, no longer exists in the presence of the soliton. Moreover, specific perturbations correspond to zero modes of the system. Our results have applications in condensed matter physics as well as computations of quantum effects (e.g., the Casimir energy) in spatially compact space-times in the presence of solitonlike objects.

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“…Further, Derrick's theorem is not valid in curved spacetime due to the coupling between matter and the metric of the background geometry. In [30][31][32], Derrick's theorem is extended to field theories in a class of curved spacetimes. The existence of soliton configuration is also shown numerically in [19].…”

Section: Derrick's Theoremmentioning

confidence: 99%

Solitons in curved spacetime

Mandal

2022

Preprint

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Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling transformation. According to this theorem, the 2 + 1 dimension is the critical dimension for the existence of solitons in scalar field theories without the gauge fields. In the present article, Derrick's theorem is extended in a generic curved spacetime in a covariant manner. Moreover, the existence of solitons in conformally flat spacetimes and spherically symmetric spacetimes is also shown using the approach presented in this article. Further, the approach shown in the present article in order to derive the soliton configurations is not restricted to a particular form of the field potential or curved spacetime.

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Derrick’s theorem in curved spacetime

Cited by 15 publications

References 35 publications

Consistent solution of Einstein–Cartan equations with torsion outside matter

Consistent solution of Einstein–Cartan equations with torsion outside matter

Real scalar field kinks and antikinks and their perturbation spectra in a closed universe

Solitons in curved spacetime

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