scholarly journals BPS Skyrme submodels of the five-dimensional Skyrme model

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Emir Syahreza Fadhilla ◽  
Bobby Eka Gunara ◽  
Ardian Nata Atmaja
Keyword(s):  
Topological Charge ◽  
Skyrme Model ◽  
Symmetric Case ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Full Field ◽  
Potential Term ◽  
Effective Lagrangian ◽  
Dimensional Spacetime ◽  
Static Energy

Abstract In this paper, we search for the BPS skyrmions in some BPS submodels of the generalized Skyrme model in five-dimensional spacetime using the BPS Lagrangian method. We focus on the static solutions of the Bogomolny’s equations and their corresponding energies with topological charge B > 0 is an integer. We consider two main cases based on the symmetry of the effective Lagrangian of the BPS submodels, i.e. the spherically symmetric and non-spherically symmetric cases. For the spherically symmetric case, we find two BPS submodels. The first BPS submodels consist of a potential term and a term proportional to the square of the topological current. The second BPS submodels consist of only the Skyrme term. The second BPS submodel has BPS skyrmions with the same topological charge B > 1, but with different energies, that we shall call “topological degenerate” BPS skyrmions. It also has the usual BPS skyrmions with equal energies, if the topological charge is a prime number. Another interesting feature of the BPS skyrmions, with B > 1, in this BPS submodel, is that these BPS skyrmions have non-zero pressures in the angular direction. For the non-spherically symmetric case, there is only one BPS submodel, which is similar to the first BPS submodel in the spherically symmetric case. We find that the BPS skyrmions depend on a constant k and for a particular value of k we obtain the BPS skyrmions of the first BPS submodel in the spherically symmetric case. The total static energy and the topological charge of these BPS skyrmions also depend on this constant. We also show that all the results found in this paper satisfy the full field equations of motions of the corresponding BPS submodels.

On the uniqueness of the Møller energy–momentum complex

1970 ◽  
Vol 48 (2) ◽  
pp. 225-228 ◽  
Author(s):  
Leopold Halpern ◽  
Milivoj J. Miketinac
Keyword(s):  
Cp Violation ◽  
Symmetric Case ◽  
Spherically Symmetric ◽  
Meson Field ◽  
Field Equations ◽  
Yang Mills ◽  
Momentum Complex ◽  
Mills Field

Møller's tetrad energy–momentum complex is made unique by introducing a suitable Yang–Mills field. The field equations are given and solved approximately for the spherically symmetric case. The simplest couplings to the K0 meson field are analyzed and it is shown that they cannot be used to resolve the CP violation.

scholarly journals Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Sergio L. Cacciatori ◽  
Fabrizio Canfora ◽  
Marcela Lagos ◽  
Federica Muscolino ◽  
Aldo Vera
Keyword(s):  
Total Energy ◽  
Topological Charge ◽  
Analytic Solutions ◽  
Integrable Equation ◽  
Skyrme Model ◽  
Low Density ◽  
Field Equations ◽  
Complete Set ◽  
Baryonic Charge ◽  
Density Regime

Abstract We construct explicit analytic solutions of the SU(N)-Skyrme model (for generic N) suitable to describe different phases of nuclear pasta at finite volume in (3 + 1) dimensions. The first type are crystals of Baryonic tubes (nuclear spaghetti) while the second type are smooth Baryonic layers (nuclear lasagna). Both, the ansatz for the spaghetti and the ansatz for the lasagna phases, reduce the complete set of Skyrme field equations to just one integrable equation for the profile within sectors of arbitrary high topological charge. We compute explicitly the total energy of both configurations in terms of the flavor number, the density and the Baryonic charge. Remarkably, our analytic results allow to compare explicitly the physical properties of nuclear spaghetti and lasagna phases. Our construction shows explicitly that, at lower densities, configurations with N = 2 light flavors are favored while, at higher densities, configurations with N = 3 are favored. Our construction also proves that in the high density regime (but still well within the range of validity of the Skyrme model) the lasagna configurations are favored while at low density the spaghetti configurations are favored. Moreover, the integrability property of the present configurations is not spoiled by the inclusion of the subleading corrections to the Skyrme model arising in the ’t Hooft expansion. Finally, we briefly discuss the large N limit of our configurations.

scholarly journals NONEXTREME BLACK HOLES FROM INTERSECTING M-BRANES

1998 ◽  
Vol 13 (08) ◽  
pp. 1305-1328 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
TAKASHI SHIMIZU
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Higher Dimensions ◽  
Symmetric Case ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Deformation Parameters ◽  
Special Cases ◽  
Two Parameter ◽  
Black Hole Solutions

We investigate the possibility of extending nonextreme black hole solutions made of intersecting M-branes to those with two nonextreme deformation parameters, similar to Reissner–Nordstrøm solutions. General analysis of possible solutions is carried out to reduce the problem of solving field equations to a simple algebraic one for static spherically-symmetric case in D dimensions. The results are used to show that the extension to two-parameter solutions is possible for D= 4,5 dimensions but not for higher dimensions, and that the area of horizon always vanishes in the extreme limit for black hole solutions for D≥6 except for two very special cases which are identified. Various solutions are also summarized.

scholarly journals Static spherically symmetric three-form stars

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Bruno J. Barros ◽  
Zahra Haghani ◽  
Tiberiu Harko ◽  
Francisco S. N. Lobo
Keyword(s):  
Equations Of State ◽  
Field Potential ◽  
Compact Object ◽  
Momentum Tensor ◽  
Einstein Condensate ◽  
Gravity Theory ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Potential Term ◽  
Form Field

AbstractWe consider interior static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field $$A_{\alpha \beta \gamma }$$ A α β γ , which generates, via the field strength and a potential term, a new component in the total energy-momentum tensor of the gravitational system. We formulate the field equations in Schwarzschild coordinates and investigate their solutions numerically for different equations of state of neutron and quark matter, by assuming that the three-field potential is either a constant or possesses a Higgs-like form. Moreover, stellar models, described by the stiff-fluid, radiation-like, bag model and the Bose–Einstein condensate equations of state are explicitly obtained in both general relativity and three-form gravity, thus allowing an in-depth comparison between the astrophysical predictions of these two gravitational theories. As a general result we find that, for all the considered equations of state, three-form field stars are more massive than their general relativistic counterparts. As a possible astrophysical application, we suggest that the 2.5$$ M_{\odot }$$ M ⊙ mass compact object, associated with the GW190814 gravitational wave event, could be in fact a neutron or a quark star described by the three-form gravity theory.

Collapsing solutions in higher-dimensional spacetime

2019 ◽  
Vol 28 (09) ◽  
pp. 1950117
Author(s):  
Hassan Shah ◽  
Zahid Ahmad ◽  
Suhail Khan
Keyword(s):  
Energy Density ◽  
Higher Dimensions ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Dimensional Spacetime ◽  
Higher Dimensional

We investigate higher-dimensional spherically symmetric anisotropic collapsing solutions of the field equations. Our aim is to check the effects of higher dimensions on the density and pressures profile of the collapsing fluid. It has been observed that the energy density, radial and tangential pressures of the collapsing system are strongly affected by higher dimensions. It also comes out that the anisotropy of the collapsing system becomes constant in higher dimensions.

scholarly journals Quantum scalar field in quantum gravity: the vacuum in the spherically symmetric case

2009 ◽  
Vol 26 (21) ◽  
pp. 215011 ◽  
Author(s):  
Rodolfo Gambini ◽  
Jorge Pullin ◽  
Saeed Rastgoo
Keyword(s):  
Scalar Field ◽  
Quantum Gravity ◽  
Symmetric Case ◽  
Spherically Symmetric

scholarly journals On f(R) Theories in Two-Dimensional Spacetime

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
M. A. Ahmed
Keyword(s):  
Exact Solutions ◽  
Ricci Scalar ◽  
Two Dimensional ◽  
Field Equations ◽  
Dimensional Spacetime ◽  
Set Up

In recent years, theories in which the Einstein-Hilbert Lagrangian is replaced by a function f(R) of the Ricci Scalar have been extensively studied in four-dimensional spacetime. In this paper we carry out an analysis of such theories in two-dimensional spacetime with focus on cosmological implications. Solutions to the cosmological field equations are obtained and their properties are analysed. Inflationary solutions are also obtained and discussed. Quantization is then carried out, the Wheeler-DeWitt equation is set up, and its exact solutions are obtained.

Study of gravitational decoupled anisotropic solution

2019 ◽  
Vol 28 (16) ◽  
pp. 2040004
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Anisotropic Model ◽  
Field Equations ◽  
Anisotropic Solution ◽  
Spherically Symmetric Solution ◽  
Gravitational Source ◽  
The Stability

This paper formulates the exact static anisotropic spherically symmetric solution of the field equations through gravitational decoupling. To accomplish this work, we add a new gravitational source in the energy–momentum tensor of a perfect fluid. The corresponding field equations, hydrostatic equilibrium equation as well as matching conditions are evaluated. We obtain the anisotropic model by extending the known Durgapal and Gehlot isotropic solution and examined the physical viability as well as the stability of the developed model. It is found that the system exhibits viable behavior for all fluid variables as well as energy conditions and the stability criterion is fulfilled.

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