arXiv subjects

K. A. Bronnikov

Publications and source records attributed to K. A. Bronnikov.

At least 109 records · Page 6Linked to original sources

arXiv2005

f(R) theory of gravity and conformal continuations

We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the equations of f(R) theory are reduced to the ``Einstein picture'', i.e., to the equations of general relativity with a source in the form of a scalar field with a potential. We have obtained necessary and sufficient conditions for the existence of solutions admitting conformal continuations. The latter means that a central singularity that exists in the Einstein picture is mapped, in the Jordan picture (i.e., in the manifold corresponding to the original formulation of the theory), to a certain regular sphere, and the solution to the field equations may be smoothly continued beyond it. The value of the curvature R on the transition sphere corresponds to an extremum of the function f(R). Specific examples are considered.

gr-qc↗

arXiv2004

Quantum theory of scalar field in isotropic world

Fock representations are constructed for a free scalar field in the closed and quasi-Euclidean isotropic cosmological models. Invariance of their cyclic vector (vacuum) under isometries and the correspondence principle single out a class of unitarily equivalent representations.

gr-qc↗

arXiv2004

Conformal continuations and wormhole instability in scalar-tensor gravity

We study the stability of static, spherically symmetric, traversable wormholes existing due to conformal continuations in a class of scalar-tensor theories with zero scalar field potential (so that Fisher's well-known scalar-vacuum solution holds in the Einstein conformal frame). Specific examples of such wormholes are those with nonminimally (e.g., conformally) coupled scalar fields. All boundary conditions for scalar and metric perturbations are taken into account. All such wormholes are shown to be unstable under spherically symmetric perturbations. The instability is proved analytically with the aid of the theory of self-adjoint operators in Hilbert space and is confirmed by a numerical computation.

gr-qc↗

arXiv2004

Nonsingular multidimensional cosmologies with Lobachevsky spatial sections

Examples of nonsingular cosmological models are presented on the basis of exact solutions to multidimensional gravity equations. These examples involve pure imaginary scalar fields, or, in other terms, ``phantom'' fields with an unusual sign of the kinetic term in the Lagrangian. We show that, with such fields, hyperbolic nonsingular models with a cosmological bounce (unlike spherical and spatially flat models) emerge without special relations among the integration constants, i.e., without fine tuning. In such models, the extra-dimension scale factors as well as scalar fields evolve smoothly between different finite asymptotic values. Examples of theories which create phantom scalar fields are obtained from string-inspired multidimensional field models and from theories of gravity in integrable Weyl space-times.

gr-qc↗

arXiv2004

Magneto-dilatonic Bianchi-I cosmology: isotropization and singularity problems

We study the evolution of Bianchi-I space-times filled with a global unidirectional electromagnetic field $F_{mn}$ interacting with a massless scalar dilatonic field according to the law Ψ(ϕ) F^{mn} F_{mn} where Ψ(ϕ) > 0 is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models becoming isotropic at late times and (iii) the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All these features are confirmed for exact solutions found for the usually considered case Ψ= e^{2λϕ}, λ= const. In particular, isotropizing models are found for |λ| > 1/\sqrt{3}. In the special case |λ| = 1, which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric.

gr-qc↗

arXiv2003

Self-gravitating global monopole and nonsingular cosmology

We review some recent results concerning the properties of a spherically symmetric global monopole in $(D=d+2)$-dimensional general relativity. Some common features of monopole solutions are found independently of the choice of the symmetry-breaking potential. Thus, the solutions show six types of qualitative behavior and can contain at most one simple horizon. For the standard Mexican hat potential, we analytically find the $D$-dependent range of $γ$ (the gravitational field strength parameter) in which there exist globally regular solutions with a monotonically growing Higgs field, containing a horizon and a Kantowski-Sachs (KS) cosmology outside it, where the topology of spatial sections is $\R\times §^d$. Their cosmological properties favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition on the Planck energy scale. We have also found families of new solutions with an oscillating Higgs field, parametrized by the number of its knots. All such solutions describe space-times of finite size, possessing a regular center, a horizon and a singularity beyond it.

gr-qc↗

arXiv2003

Conformal frames and D-dimensional gravity

We review some results concerning the properties of static, spherically symmetric solutions of multidimensional theories of gravity: various scalar-tensor theories and a generalized string-motivated model with multiple scalar fields and fields of antisymmetric forms associated with p-branes. A Kaluza-Klein type framework is used: there is no dependence on internal coordinates but multiple internal factor spaces are admitted. We discuss the causal structure and the existence of black holes, wormholes and particle-like configurations in the case of scalar vacuum with arbitrary potentials as well as some observational predictions for exactly solvable systems with p-branes: post-Newtonian coefficients, Coulomb law violation and black hole temperatures. Particular attention is paid to conformal frames in which the theory is initially formulated and which are used for its comparison with observations; it is stressed that, in general, these two kinds of frames do not coincide.

gr-qc↗

arXiv2003

Self-gravitating stringlike configurations from nonlinear electodynamics

We consider static, cylindrically symmetric configurations in general relativity coupled to nonlinear electrodynamics (NED) with an arbitrary gauge-invariant Lagrangian of the form $L_{em}= Φ(F)$, $F =F_{mn}F^{mn}$. We study electric and magnetic fields with three possible orientations: radial (R), longitudinal (L) and azimuthal (A), and try to find solitonic stringlike solutions, having a regular axis and a flat metric at large $r$, with a possible angular defect. Assuming the function $Φ(F)$ to be regular at small $F$, it is shown that a regular axis is impossible in R-fields if there is a nonzero effective electric charge and in A-fields if there is a nonzero effective electric current along the axis. Solitonic solutions are only possible for purely magnetic R-fields and purely electric A-fields, in cases when $Φ(F)$ tends to a finite limit at large $F$. For both R- and A-fields, the desired large $r$ asymptotic is only possible with a non- Maxwell behaviour of $Φ(F)$ at small $F$. For L-fields, solutions with a regular axis are easily obtained (and can be found by quadratures) whereas a desired large $r$ asymptotic is only possible in an exceptional solution; the latter gives rise to solitonic configurations in case $Φ(F) = \const \cdot \sqrt{F}$. We give an explicit example of such a solution.

gr-qc↗

arXiv2003

Scalar field in a minimally coupled brane world: no-hair and other no-go theorems

In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian $(\dϕ)^2/2 - V(ϕ)$, confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the usual stress tensor $T\mN$, the tensor $Π\mN$, quadratic in $T\mN$, and $E\mN$ describing interaction with the bulk. For models under study, the tensor $Π\mN$ has zero divergence, so we can consider a "minimally coupled" brane with $E\mN = 0$, whose 4D gravity is decoupled from the bulk geometry. Assuming $E\mN =0$, we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a $Lambda$ term in GR: Minkowski, Schwarzschild, (A)dS and Schwarzschild-(A)dS. A no-hair theorem, saying that, given a potential $V\geq 0$, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region.

gr-qc↗

arXiv2003

On a general class of brane-world black holes

We use the general solution to the trace of the 4-dimensional Einstein equations for static, spherically symmetric configurations as a basis for finding a general class of black hole (BH) metrics, containing one arbitrary function $g_{tt} = A(r)$ which vanishes at some $r = r_h > 0$, the horizon radius. Under certain reasonable restrictions, BH metrics are found with or without matter and, depending on the boundary conditions, can be asymptotically flat or have any other prescribed large $r$ behaviour. It is shown that this procedure generically leads to families of solutions unifying non-extremal globally regular BHs with a Kerr-like global structure, extremal BHs and symmetric wormholes. Horizons in space-times with zero scalar curvature are shown to be either simple or double. The same is generically true for horizons inside a matter distribution, but in special cases there can be horizons of any order. A few simple examples are discussed. A natural application of the above results is the brane world concept, in which the trace of the 4D gravity equations is the only unambiguous equation for the 4D metric, and its solutions can be continued into the 5D bulk according to the embedding theorems.

gr-qc↗

arXiv2003

Nonsingular vacuum cosmologies with a variable cosmological term

We present nonsingular cosmological models with a variable cosmological term described by the second-rank symmetric tensor $Λ_{mn}$ evolving from $Λg_{mn}$ to $λg_{mn}$ with $λ< Λ$. All $Λ_{mn}$ dominated cosmologies belong to Lemaitre type models for an anisotropic perfect fluid. The expansion starts from a nonsingular nonsimultaneous de Sitter bang, with $Λ$ on the scale responsible for the earliest accelerated expansion, which is followed by an anisotropic Kasner type stage. For a certain class of observers these models can be also identified as Kantowski-Sachs models with regular R regions. For Kantowski-Sachs observers the cosmological evolution starts from horizons with a highly anisotropic ``null bang'' where the volume of the spatial section vanishes. We study in detail the spherically symmetric case and consider the general features of cosmologies with planar and pseudospherical symmetries. Nonsingular $Λ_{mn}$ dominated cosmologies are Bianchi type I in the planar case and hyperbolic analogs of the Kantowski-Sachs models in the pseudospherical case. At late times all models approach a de Sitter asymptotic with small $λ$.

gr-qc↗

arXiv2002

Possible wormholes in a brane world

The condition R=0, where R is the four-dimensional scalar curvature, is used for obtaining a large class (with an arbitrary function of r) of static, spherically symmetric Lorentzian wormhole metrics. The wormholes are globally regular and traversable, can have throats of arbitrary size and can be both symmetric and asymmetric. These metrics may be treated as possible wormhole solutions in a brane world since they satisfy the vacuum Einstein equations on the brane where effective stress-energy is induced by interaction with the bulk gravitational field. Some particular examples are discussed.

gr-qc↗

arXiv2002

Scalar fields in multidimensional gravity. No-hair and other no-go theorems

Global properties of static, spherically symmetric configurations of scalar fields of sigma-model type with arbitrary potentials are studied in $D$ dimensions, including space-times containing multiple internal factor spaces. The latter are assumed to be Einstein spaces, not necessarily Ricci-flat, and the potential $V$ includes contributions from their curvatures. The following results generalize those known in four dimensions: (A) a no-hair theorem: in case $V\geq 0$, an asymptotically flat black hole cannot have varying scalar fields or moduli fields outside the event horizon; (B) nonexistence of particlelike solutions in models with $V\geq 0$; (C) nonexistence of wormholes under very general conditions; (D) a restriction on possible global causal structures (represented by Carter-Penrose diagrams). The list of structures in all models under consideration is the same as is known for vacuum with a cosmological constant in general relativity: Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild--de Sitter, and horizons which bound a static region are always simple. The results are applicable to a wide range of Kaluza-Klein, supergravity and stringy models with multiple dilaton and moduli fields.

gr-qc↗

arXiv2002

Possible time variations of G in scalar-tensor theories of gravity

We estimate the possible variations of the gravitational constant G in the framework of a generalized (Bergmann-Wagoner-Nordtvedt) scalar-tensor theory of gravity on the basis of the field equations, without using their special solutions. Specific estimates are essentially related to the values of other cosmological parameters (the Hubble and acceleration parameters, the dark matter density etc.), but the values of G-dot/G compatible with modern observations do not exceed 10^{-12}.

gr-qc↗

arXiv2002

Nonsingular multidimensional cosmologies without fine tuning

Exact cosmological solutions for effective actions in D dimensions inspired by the tree-level superstring action are studied. For a certain range of free parameters existing in the model, nonsingular bouncing solutions are found. Among them, of particular interest can be open hyperbolic models, in which, without any fine tuning, the internal scale factor and the dilaton field (connected with string coupling in string theories) tend to constant values at late times. A cosmological singularity is avoided due to nonminimal dilaton-gravity coupling and, for D > 11, due to pure imaginary nature of the dilaton, which conforms to currently discussed unification models. The existence of such and similar solutions supports the opinion that the Universe had never undergone a stage driven by full-scale quantum gravity.

hep-th↗

arXiv2002

Charged wormholes with non-minimally coupled scalar fields. Existence and stability

Static, spherically symmetric, traversable wormhole solutions with electric or magnetic charges are shown to exist in general relativity in the presence of scalar fields nonminimally coupled to gravity. These wormholes, however, turn out to be unstable under spherically symmetric perturbations. The instability is related to blowing-up of the effective gravitational constant on a certain sphere.

gr-qc↗

arXiv2002

Instability of wormholes with a nonminimally coupled scalar field

Static, spherically symmetric, traversable wormholes, induced by massless, nonminimally coupled scalar fields in general relativity, are shown to be unstable under spherically symmetric perturbations. The instability is related to blowing-up of the effective gravitational constant on a certain sphere.

gr-qc↗

arXiv2001

Spherically symmetric scalar vacuum: no-go theorems, black holes and solitons

We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not necessarily positive-definite. The results are extended to sigma models, scalar-tensor and curvature-nonlinear theories of gravity. We show that the list of all possible types of space-time causal structure in the models under study is the same as for a constant scalar field, namely, Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and all horizons are simple. In particular, these theories do not admit regular black holes with any asymptotics. Some special features of (2+1)D gravity are revealed. We give examples of two types of asymptotically flat configurations with positive mass in GR, admitted by the above theorems: (i) a black hole with nontrivial ``scalar hair'' and (ii) a particlelike solution with a regular centre; in both cases, the potential $V$ must be at least partly negative. We also discuss the global effects of conformal mappings that connect different theories. Such effects are illustrated for solutions with a conformal scalar field in GR.

gr-qc↗