Research

17 pages, 664 KiB

Open AccessEditor’s ChoiceArticle

by Rustam Ibadov, Burkhard Kleihaus, Jutta Kunz and Sardor Murodov

Symmetry 2021, 13(1), 89; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010089 - 06 Jan 2021

Cited by 6 | Viewed by 1662

We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following Brihaye, Herdeiro and Radu, who recently studied spontaneously scalarised Schwarzschild-NUT solutions. By varying the coupling parameter and the scalar charge we determine the [...] Read more.

We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following Brihaye, Herdeiro and Radu, who recently studied spontaneously scalarised Schwarzschild-NUT solutions. By varying the coupling parameter and the scalar charge we determine the domain of existence of the scalarized nutty wormholes, and their dependence on the NUT charge. In the Gauss-Bonnet case the known set of scalarized wormholes is reached in the limit of vanishing NUT charge. In the Chern-Simons case, however, the limit is peculiar, since with vanishing NUT charge the coupling constant diverges. We focus on scalarized nutty wormholes with a single throat and study their properties. All these scalarized nutty wormholes feature a critical polar angle, beyond which closed timelike curves are present. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

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13 pages, 355 KiB

Open AccessArticle

Inflation inside Non-Topological Defects and Scalar Black Holes

by Yves Brihaye, Felipe Console and Betti Hartmann

Symmetry 2021, 13(1), 2; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010002 - 22 Dec 2020

Cited by 6 | Viewed by 1468

Abstract

In this paper, we demonstrate that a phenomenon described as topological inflation, during which inflation occurs inside the core of topological defects, has a non–topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as [...] Read more.

In this paper, we demonstrate that a phenomenon described as topological inflation, during which inflation occurs inside the core of topological defects, has a non–topological counterpart. This appears in a simple set-up containing Einstein gravity coupled minimally to an electromagnetic field as well as a self-interacting, complex valued scalar field. The U(1) symmetry of the model is unbroken and leads to the existence of globally regular solutions, so-called boson stars, that develop a horizon for sufficiently strong gravitational coupling. We also find that the same phenomenon exists for black holes with scalar hair. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

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11 pages, 295 KiB

Open AccessFeature PaperArticle

Higgs–Chern–Simons Gravity Models in d = 2n + 1 Dimensions

by Eugen Radu and D. H. Tchrakian

Symmetry 2020, 12(12), 2064; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122064 - 12 Dec 2020

Viewed by 1453

Abstract

We consider a family of new Higgs–Chern–Simons (HCS) gravity models in

2 n + 1

dimensions (

n = 1, 2, 3

). This provides a generalization of the (usual) gravitational Chern–Simons (CS) gravities resulting from non-Abelian CS densities in all [...] Read more.

We consider a family of new Higgs–Chern–Simons (HCS) gravity models in

2 n + 1

dimensions (

n = 1, 2, 3

). This provides a generalization of the (usual) gravitational Chern–Simons (CS) gravities resulting from non-Abelian CS densities in all odd dimensions, which feature vector and scalar fields, in addition to the metric. The derivation of the new HCS gravitational (HCSG) actions follows the same method as in the

u s u a l

-CSG case resulting from the

u s u a l

CS densities. The HCSG result from the HCS densities, which result through a one-step descent of the Higgs–Chern–Pontryagin (HCP), with the latter being descended from Chern-Pontryagin (CP) densities in some even dimension. A preliminary study of the solutions of these models is considered, with exact solutions being reported for spacetime dimensions

d = 3, 5

. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

15 pages, 878 KiB

Open AccessArticle

Critical Solutions of Scalarized Black Holes

by Jose Luis Blázquez-Salcedo, Sarah Kahlen and Jutta Kunz

Symmetry 2020, 12(12), 2057; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122057 - 11 Dec 2020

Cited by 10 | Viewed by 1555

Abstract

We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with [...] Read more.

We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with scalar hair. Scrutinizing the domain of existence of these hairy black holes, we observe a critical behavior. A limiting configuration is encountered at a critical value of the charge, where space time splits into two parts: an inner space time with a finite scalar field and an outer extremal Reissner–Nordström space time. Such a pattern was first observed in the context of gravitating non-Abelian magnetic monopoles and their hairy black holes. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

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15 pages, 391 KiB

Open AccessArticle

Spontaneous Symmetry Breaking and Its Pattern of Scales

by Maurizio Consoli and Leonardo Cosmai

Symmetry 2020, 12(12), 2037; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122037 - 09 Dec 2020

Cited by 7 | Viewed by 1407

Abstract

Spontaneous Symmetry Breaking (SSB) in

λ Φ^{4}

theories is usually described as a 2nd-order phase transition. However, most recent lattice calculations indicate instead a weakly 1st-order phase transition as in the one-loop and Gaussian approximations to the effective potential. This modest change [...] Read more.

Spontaneous Symmetry Breaking (SSB) in

λ Φ^{4}

theories is usually described as a 2nd-order phase transition. However, most recent lattice calculations indicate instead a weakly 1st-order phase transition as in the one-loop and Gaussian approximations to the effective potential. This modest change has non-trivial implications. In fact, in these schemes, the effective potential at the minima has two distinct mass scales: (i) a first mass

m_{h}

associated with its quadratic curvature and (ii) a second mass

M_{h}

associated with the zero-point energy which determines its depth. The two masses describe different momentum regions in the scalar propagator and turn out to be related by

M_{h}^{2} \sim m_{h}^{2} ln (Λ_{s} / M_{h})

, where

Λ_{s}

is the ultraviolet cutoff of the scalar sector. Our lattice simulations of the propagator are consistent with this two-mass picture and, in the Standard Model, point to a value

M_{h} \sim 700

GeV. However, despite its rather large mass, this heavier excitation would interact with longitudinal W’s and Z’s with the same typical coupling of the lower-mass state and would therefore represent a rather narrow resonance. Two main novel implications are emphasized in this paper: (1) since vacuum stability depends on the much larger

M_{h}

, and not on

m_{h}

, SSB could originate within the pure scalar sector regardless of the other parameters of the theory (e.g., the vector-boson and top-quark mass) (2) if the smaller mass were fixed at the value

m_{h} =

125 GeV measured at LHC, the hypothetical heavier state

M_{h}

would then naturally fit with the peak in the 4-lepton final state observed by the ATLAS Collaboration at 700 GeV. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

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23 pages, 595 KiB

Open AccessArticle

Asymptotically Flat, Spherical, Self-Interacting Scalar, Dirac and Proca Stars

by Carlos A. R. Herdeiro and Eugen Radu

Symmetry 2020, 12(12), 2032; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122032 - 08 Dec 2020

Cited by 30 | Viewed by 1617

Abstract

We present a comparative analysis of the self-gravitating solitons that arise in the Einstein–Klein–Gordon, Einstein–Dirac, and Einstein–Proca models, for the particular case of static, spherically symmetric spacetimes. Differently from the previous study by Herdeiro, Pombo and Radu in 2017, the matter fields possess [...] Read more.

We present a comparative analysis of the self-gravitating solitons that arise in the Einstein–Klein–Gordon, Einstein–Dirac, and Einstein–Proca models, for the particular case of static, spherically symmetric spacetimes. Differently from the previous study by Herdeiro, Pombo and Radu in 2017, the matter fields possess suitable self-interacting terms in the Lagrangians, which allow for the existence of Q-ball-type solutions for these models in the flat spacetime limit. In spite of this important difference, our analysis shows that the high degree of universality that was observed by Herdeiro, Pombo and Radu remains, and various spin-independent common patterns are observed. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

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10 pages, 746 KiB

Open AccessArticle

Relativistic Symmetries and Hamiltonian Formalism

by Piotr Kosiński and Paweł Maślanka

Symmetry 2020, 12(11), 1810; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12111810 - 01 Nov 2020

Cited by 3 | Viewed by 1775

Abstract

The relativistic (Poincaré and conformal) symmetries of classical elementary systems are briefly discussed and reviewed. The main framework is provided by the Hamiltonian formalism for dynamical systems exhibiting symmetry described by a given Lie group. The construction of phase space and canonical variables [...] Read more.

The relativistic (Poincaré and conformal) symmetries of classical elementary systems are briefly discussed and reviewed. The main framework is provided by the Hamiltonian formalism for dynamical systems exhibiting symmetry described by a given Lie group. The construction of phase space and canonical variables is given using the tools from the coadjoint orbits method. It is indicated how the “exotic” Lorentz transformation properties for particle coordinates can be derived; they are shown to be the natural consequence of the formalism. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

11 pages, 507 KiB

Open AccessArticle

Gravitating Bubbles of Gluon Plasma above Deconfinement Temperature

by Yves Brihaye and Fabien Buisseret

Symmetry 2020, 12(10), 1668; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101668 - 13 Oct 2020

Cited by 2 | Viewed by 1280

Abstract

The equation of state of SU(3) Yang–Mills theory can be modelled by an effective

Z_{3} -

symmetric potential depending on the temperature and on a complex scalar field

ϕ

. Allowing

ϕ

to be dynamical opens the way to the study of [...] Read more.

The equation of state of SU(3) Yang–Mills theory can be modelled by an effective

Z_{3} -

symmetric potential depending on the temperature and on a complex scalar field

ϕ

. Allowing

ϕ

to be dynamical opens the way to the study of spatially localized classical configurations of the scalar field. We first show that spherically symmetric static Q-balls exist in the range

(1 - 1.21) \times T_{c}

,

T_{c}

being the deconfinement temperature. Then we argue that Q-holes solutions, if any, are unphysical within our framework. Finally, we couple our matter Lagrangian to Einstein gravity and show that spherically symmetric static boson stars exist in the same range of temperature. The Q-ball and boson-star solutions we find can be interpreted as “bubbles” of deconfined gluonic matter; their mean radius is always smaller than 10 fm. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

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