Nonrelativistic isothermal fluid in the presence of a chameleon scalar field: Static and collapsing configurations

We consider a gravitating spherically symmetric nonrelativistic configuration consisting of a massless chameleon scalar field nonminimally coupled to a perfect isothermal fluid. The object of this paper is to show the influence of the chameleon scalar field on the structure and evolution of an isothermal sphere. For this system we find static, singular and regular solutions depending on the form of the coupling function. A preliminary stability analysis indicates that both stable and unstable solutions exist. For unstable configurations, by choosing the special form of the coupling function, we consider the problem of the gravitational collapse by applying the similarity method.Comment: 16 pages, 3 figures, minor corrections to content, references added, matches PRD accepted versio

Anisotropic neutron stars in R2R^2 gravity

We consider static neutron stars within the framework of $R^2$ gravity. The neutron fluid is described by three different types of realistic equations of state (soft, moderately stiff, and stiff). Using the observational data on the neutron star mass-radius relation, it is demonstrated that the characteristics of the objects supported by the isotropic fluid agree with the observations only if one uses the soft equation of state. We show that the inclusion of the fluid anisotropy enables one also to employ more stiff equations of state to model configurations that will satisfy the observational constraints sufficiently. Also, using the standard thin accretion disk model, we demonstrate potentially observable differences, which allow us to distinguish the neutron stars constructed within the modified gravity framework from those described in Einstein's general relativity.Comment: 14 pages, 4 figures, minor corrections to content, new references added, version published in PR

Thick brane solutions supported by two spinor fields

Stationary thick brane solutions supported by two spinor fields are considered. Two spinor fields are used here to exclude the off-diagonal components of the energy-momentum tensor of the spinor fields. The trapping of a test scalar field on the brane is also considered.Comment: 6 pages, 2 fig'

Kaluza-Klein wormholes with the compactified fifth dimension

We consider wormhole solutions in five-dimensional Kaluza-Klein gravity in the presence of a massless ghost four-dimensional scalar field. The system possesses two types of topological nontriviality connected with the presence of the scalar field and of a magnetic charge. Mathematically, the presence of the charge appears in the fact that the $S^3$ part of a spacetime metric is the Hopf bundle $S^3 \rightarrow S^2$ with fibre $S^1$. We show that the fifth dimension spanned on the sphere $S^1$ is compactified in the sense that asymptotically, at large distances from the throat, the size of $S^1$ is equal to some constant, the value of which can be chosen to lie, say, in the Planck region. Then, from the four-dimensional point of view, such a wormhole contains a radial magnetic (monopole) field, and an asymptotic four-dimensional observer sees a wormhole with the compactified fifth dimension.Comment: 6 pages, 3 figure

Dirac stars supported by nonlinear spinor fields

We study configurations consisting of a gravitating spinor field $\psi$ with a nonlinearity of the type $\lambda\left(\bar\psi\psi\right)^2$. To ensure spherical symmetry of the configurations, we use two spin-$\frac{1}{2}$ fields forming a spin singlet. For such systems, we find regular stationary asymptotically flat solutions describing compact objects. For negative values of the coupling constant $\lambda$, it is shown that, by choosing physically reasonable values of this constant, it is possible to obtain configurations with masses comparable to the Chandrasekhar mass. It enables us to speak of an astrophysical interpretation of the obtained systems, regarding them as Dirac stars.Comment: 8 pages, 4 figures, minor corrections to content, new reference added, version published in PR

Spinor field solutions in F(B2)F\left(B^2\right) modified Weyl gravity

We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating spinor field. It is shown that such a theory contains solutions for a class of metrics which are conformally equivalent to the Hopf metric on the Hopf fibration. For this case, we obtain a full discrete spectrum of the solutions and show that they can be related to the Hopf invariant on the Hopf fibration. The expression for the spin operator in the Hopf coordinates is obtained. It is demonstrated that this class of conformally equivalent metrics contains: (a) a metric describing a toroidal wormhole without exotic matter; (b) a cosmological solution with a bounce and inflation; and (c) a transition with a change in metric signature. A physical discussion of the results is given. \end{abstract}Comment: 11page

Scalar model of SU(N) glueball \`a la Heisenberg

Nonperturbative model of glueball is studied. The model is based on the nonperturbative quantization technique suggested by Heisenberg. 2- and 4-point Green functions for a gauge potential are expressed in terms of two scalar fields. The first scalar field describes quantum fluctuations of the subgroup $SU(n) \subset SU(N)$, and the second one describes quantum fluctuations of the coset $SU(N) / SU(n)$. An effective Lagrangian for the scalar fields is obtained. The coefficients for all terms in the Lagrangian are calculated, and it is shown that they depend on $\dim SU(n), \dim SU(N)$. It is demonstrated that a spherically symmetric solution describing the glueball does exist.Comment: 2 figures, 8 page

Energy spectrum and the mass gap from nonperturbative quantization \`a la Heisenberg

Using approximate methods of nonperturbative quantization \`a la Heisenberg and taking into account the interaction of gauge fields with quarks, we find regular solutions describing the following configurations: (i) a spinball consisting of two virtual quarks with opposite spins; (ii) a quantum monopole; (iii) a spinball-plus-quantum-monopole system; and (iv) a spinball-plus-quantum-dyon system. A comparison with quasi-particles obtained by lattice and phenomenological analytical calculations is carried out. All these objects (except the spinball) are embedded in a bag created by the quantum coset condensate consisting of the SU(3)/(SU(2)~$\times$~U(1)) gauge fields. The existence of these objects is due to the Meissner effect, which implies that the SU(2)~$\times$~U(1) gauge fields are expelled from the condensate. The physical interpretation of these solutions is proposed in two different forms: (i) an approximate glueball model; and (ii) quantum fluctuations in the coset condensate of the nonperturbative vacuum or in a quark-gluon plasma. For the spinball and the spinball-plus-quantum-monopole configuration, we obtain energy spectra, in which mass gaps are present. The process of deconfinement is discussed qualitatively. It is shown that the quantum chromodynamics constant $\Lambda_{\text{QCD}}$ appears in the nonperturbative quantization \`a la Heisenberg as some constant controlling the correlation length of quantum fields in a spacelike direction.Comment: 19 pages, 19 figure

Quantum Evolution of the Dilaton-Inflaton Model

The quantum evolution of a model of the universe with account of two scalar fields ({\it dilaton} and {\it inflaton}) is considered. For this case, the closed and flat models has been examined. It is shown that in both cases the realization of conditions necessary for inflation is strongly depends on coupling constant for dilaton and inflaton fields.Comment: 11 pages, 4 figure

Spinor brane

The thick brane model supported by a nonlinear spinor field is constructed. The different cases with the various values of the cosmological constant $\Lambda () 0$ are investigated. It is shown that regular analytical spinor thick brane solutions with asymptotically Minkowski (at $\Lambda=0$) or anti-de Sitter spacetimes (at $\Lambda<0$) do exist.Comment: errors are correcte