arXiv subjects

Kirill A. Bronnikov

Publications and source records attributed to Kirill A. Bronnikov.

At least 37 records · Page 2Linked to original sources

arXiv2022

Arbitrary static, spherically symmetric space-times as solutions of scalar-tensor gravity

It is shown that an arbitrary static, spherically symmetric metric can be presented as an exact solution of a scalar-tensor theory (STT) of gravity with certain nonminimal coupling function $f(ϕ)$ and potential $U(ϕ)$. The scalar field in this representation can change its nature from canonical to phantom on certain coordinate spheres. This representation, however, is valid in general not in the full range of the radial coordinate but only piecewise. Two examples of STT representations are discussed: for the Reissner-Nordström metric and for the Simpson-Visser regularization of the Schwarzschild metric (the so-called black bounce space-time).

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arXiv2022

Regular black holes sourced by nonlinear electrodynamics

The paper is a brief review on the existence and basic properties of static, spherically symmetric regular black hole solutions of general relativity, where the source of gravity is represented by nonlinear electromagnetic fields with the Lagrangian function $L$ depending on the single invariant $f = F_{μν}F^{μν}$ or on two variables: either $L(f, h)$, where $h = {^*}F_{μν} F^{μν}$, where ${^*}F_{μν}$ is the Hodge dual of $F_{μν}$, or $L(f, J)$, where $J = F_{μν}F^{νρ} F_{ρσ} F^{σμ}$. A number of no-go theorems are discussed, revealing the conditions under which the space-time cannot have a regular center, among which the theorems concerning $L(f,J)$ theories are probably new. These results concern both regular black holes and regular particlelike or starlike objects (solitons) without horizons. Thus, a regular center in solutions with an electric charge $q_e\ne 0$ is only possible with nonlinear electrodynamics (NED) having no Maxwell weak field limit. Regular solutions with $L(f)$ and $L(f, J)$ NED, possessing a correct (Maxwell) weak-field limit, are possible if the system contains only a magnetic charge $q_m \ne 0$. It is shown, however, that in such solutions the causality and unitarity as well as dynamic stability conditions are inevitably violated in a neighborhood of the center. Some particular examples are discussed.

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arXiv2021

Field sources for Simpson-Visser space-times

Simpson-Visser (SV) space-times are the simplest globally regular modifications of the Schwarzschild, Reissner-Nordstrom and other blak-hole solutions of general relativity. They smoothly interpolate between these black holes and traversable wormholes. After a brief presentation of the Schwarzschild-like and Reissner-Nordstrom-like SV geometries, including their Carter-Penrose diagrams, we show that any static, spherically symmetric SV metric can be obtained as an exact solution to the Einstein field equations sourced by a combination of a minimally coupled phantom scalar field with a nonzero potential $V(ϕ)$ and a magnetic field in the framework of nonlinear electrodynamics with the Lagrangian $\mathcal {L(F)}$, $\mathcal{F} = F_{μν} F^{μν}$ (in standard notations). Explicit forms of $V(ϕ)$ and $\mathcal {L(F)}$ are presented for the cases of Schwarzschild-like and Reissner-Nordstrom-like SV metrics.

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arXiv2021

General parametrization of wormhole spacetimes and its application to shadows and quasinormal modes

The general parametrization for spacetimes of spherically symmetric Lorentzian, traversable wormholes in an arbitrary metric theory of gravity is presented. The parametrization is similar in spirit to the post-Newtonian parametrized formalism, but with validity that extends beyond the weak field region and covers the whole space. Our method is based on a continued-fraction expansion in terms of a compactified radial coordinate. Calculations of shadows and quasinormal modes for various examples of parametrization of known wormhole metrics that we have performed show that, for most cases, the parametrization provides excellent accuracy already at the first order. Therefore, only a few parameters are dominant and important for finding potentially observable quantities in a wormhole background. We have also extended the analysis to the regime of slow rotation.

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arXiv2021

Magnetized dusty black holes and wormholes

We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions $f(R)$, $F(R)$ and $τ_0(R)$, where $R$ is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic ($f >0$), parabolic ($f=0$) and elliptic ($f < 0$) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus if such a dust cloud is placed between two empty (Reissner-Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.

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arXiv2021

Local regions with expanding extra dimensions

We study possible spatial domains containing expanding extra dimensions. We show that they are predicted in the framework of $f(R)$ gravity and could appear due to quantum fluctuations during inflation. Their interior is characterized by the multidimensional curvature ultimately tending to zero and a slowly growing size of the extra dimensions.

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arXiv2021

The simplest wormhole in Rastall and k-essence theories

The geometry of the Ellis-Bronnikov wormhole is implemented in the Rastall and k-essence theories of gravity with a self-interacting scalar field. The form of the scalar field potential is determined in both cases. A stability analysis with respect to spherically symmetric time-dependent perturbations is carried out, and it shows that in k-essence theory the wormhole is unstable, like the original version of this geometry supported by a massless phantom scalar field in general relativity. In Rastall's theory, it turns out that a perturbative approach reveals the same inconsistency that was found previously for black hole solutions: time-dependent perturbations of the static configuration prove to be excluded by the equations of motion, and the wormhole is, in this sense, stable under spherical perturbations.

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arXiv2020

Inhomogeneous compact extra dimensions and de Sitter cosmology

In the framework of multidimensional $f(R)$ gravity, we study the metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, varying in the extra factor space $\mathbb{M}_2$, it is possible to obtain a variety of inhomogeneous metrics in $\mathbb{M}_2$. Each of these metrics leads to a certain value of the 4D cosmological constant $Λ_4$, and in particular, it is possible to obtain $Λ_4 =0$, as is confirmed by numerically obtained solutions. A nontrivial scalar field distribution in the extra dimensions is an important feature of this family of models.

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arXiv2019

Echoes in brane worlds: ringing at a black hole--wormhole transition

Echoes are known as modifications of the usual quasinormal ringing of a black hole at late times because of the deviation of space-time from the initial black-hole geometry in a small region near its event horizon. We consider a class of brane-world model solutions of the Shiromizu-Maeda-Sasaki equations, which describe both black holes and wormholes and interpolate between them via a continuous parameter. In this way the brane-world scenario provides a natural model for wormholes mimicking the black hole behavior if the continuous parameter is chosen near the threshold with a black-hole solution. We show that in the vicinity of this threshold interpolating between black holes and wormholes, quasinormal ringing of the wormholes at the initial stage is indistinguishable from that of the black holes with nearby values of the above parameter, but at later times the signal is modified by intensive echoes. We notice that the black-hole mimickers that are wormholes near the threshold have the largest quality factor and are therefore the best oscillators among the considered examples.

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arXiv2018

Scalar fields as sources for wormholes and regular black holes

We review nonsingular static, spherically symmetric solutions of general relativity with a minimally coupled scalar field $ϕ$ as a source. Considered are wormholes and regular black holes without a center, including black universes (black holes with an expanding cosmology beyond the horizon). Such configurations require a "ghost" field with negative kinetic energy, but it may be negative in a restricted (strong-field) region of space and positive outside it ("trapped ghost") thus explaining why no ghosts are observed under usual conditions. Another possible explanation of the same may be a rapid decay of a ghost field at large radii. Before discussing particular examples, some general results are presented, such as the necessity of anisotropic matter for obtaining asymptotically flat or anti-de Sitter wormholes, no-hair and global structure theorems for black holes with scalar fields. The stability properties of scalar wormholes and regular black holes are discussed for perturbations preserving spherical symmetry. It is stressed that the effective potential $V_{eff}$ for perturbations has universal shapes near generic wormhole throats (a positive pole regularizable by a Darboux transformation) and near transition surfaces from canonical to ghost behavior of the scalar field (a negative pole at which the perturbation finiteness requirement plays a stabilizing role). It is also found that positive poles of $V_{eff}$ emerging at "long throats" (with the spherical radius $r \approx r_0 + {\rm const} \cdot x^{2n}$, $n > 1$, if $x=0$ is the throat) may be regularized by repeated Darboux transformations for some values of $n$.

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arXiv2017

Duality between k-essence and Rastall gravity

The k-essence theory with a power-law function of $(\partialϕ)^2$ and Rastall's non-conservative theory of gravity with a scalar field are shown to have the same solutions for the metric under the assumption that both the metric and the scalar fields depend on a single coordinate. This equivalence (called k-R duality) holds for static configurations with various symmetries (spherical, plane, cylindrical, etc.) and all homogeneous cosmologies. In the presence of matter, Rastall's theory requires additional assumptions on how the stress-energy tensor non-conservation is distributed between different contributions. Two versions of such non-conservation are considered in the case of isotropic spatially flat cosmological models with a perfect fluid: one (R1) in which there is no coupling between the scalar field and the fluid, and another (R2) in which the fluid separately obeys the usual conservation law. In version R1 it is shown that k-R duality holds not only for the cosmological models themselves but also for their adiabatic perturbations. In version R2, among other results, a particular model is singled out that reproduces the same cosmological expansion history as the standard $Λ$CDM model but predicts different behaviors of small fluctuations in the k-essence and Rastall frameworks.

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arXiv2016

On Black Hole Structures in Scalar-Tensor Theories of Gravity

We review some properties of black hole structures appearing in gravity with a massless scalar field, with both minimal and nonminimal coupling. The main properties of the resulting cold black holes are described. The study of black holes in scalar-gravity systems is extended to $k$-essence theories, and some examples are explicitly worked out. In these cases, even while the existence of horizons is possible, the metric regularity requirement on the horizon implies either a cold black type structure or a singular behavior of the scalar field.

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arXiv2013

Rotating cylindrical wormholes

We consider stationary, cylindrically symmetric configurations in general relativity and formulate necessary conditions for the existence of rotating cylindrical wormholes. It is shown that in a comoving reference frame the rotational part of the gravitational field is separated from its static part and forms an effective stress-energy tensor with exotic properties, which favors the existence of wormhole throats. Exact vacuum and scalar-vacuum solutions (with a massless scalar) are considered as examples, and it turns out that even vacuum solutions can be of wormhole nature. However, solutions obtainable in this manner cannot have well-behaved asymptotic regions, which excludes the existence of wormhole entrances appearing as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions by the cut-and-paste procedure: on both sides of the throat, a wormhole solution is matched to a properly chosen region of flat space at some surfaces $Σ_-$ and $Σ_+$. It is shown, however, that if we describe the throat region with vacuum or scalar-vacuum solutions, one or both thin shells appearing on $Σ_-$ and $Σ_+$ inevitably violate the null energy condition. In other words, although rotating wormhole solutions are easily found without exotic matter, such matter is still necessary for obtaining asymptotic flatness.

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arXiv2010

Trapped ghosts: a new class of wormholes

We construct examples of static, spherically symmetric wormhole solutions in general relativity with a minimally coupled scalar field $ϕ$ whose kinetic energy is negative in a restricted region of space near the throat (of arbitrary size) and positive far from it. Thus in such configurations a "ghost" is trapped in the strong-field region, which may in principle explain why no ghosts are observed under usual conditions. Some properties of general wormhole models with the $ϕ$ field are revealed: it is shown that (i) trapped-ghost wormholes are only possible with nonzero potentials $V(ϕ)$; (ii) in twice asymptotically flat wormholes, a nontrivial potential $V(ϕ)$ has an alternate sign, and (iii) a twice asymptotically flat wormhole which is mirror-symmetric with respect to its throat has necessarily a zero Schwarzschild mass at both asymptotics.

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arXiv2009

Once again on thin-shell wormholes in scalar-tensor gravity

It is proved that all thin-shell wormholes built from two identical regions of vacuum static, spherically symmetric space-times have a negative shell surface energy density in any scalar-tensor theory of gravity with a non-ghost massless scalar field and a non-ghost graviton.

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arXiv2009

Cylindrical wormholes

It is shown that the existence of static, cylindrically symmetric wormholes does not require violation of the weak or null energy conditions near the throat, and cylindrically symmetric wormhole geometries can appear with less exotic sources than wormholes whose throats have a spherical topology. Examples of exact wormhole solutions are given with scalar, spinor and electromagnetic fields as sources, and these fields are not necessarily phantom. In particular, there are wormhole solutions for a massless, minimally coupled scalar field in the presence of a negative cosmological constant, and for an azimuthal Maxwell electromagnetic field. All these solutions are not asymptotically flat. A no-go theorem is proved, according to which a flat (or string) asymptotic behavior on both sides of a cylindrical wormhole throat is impossible if the energy density of matter is everywhere nonnegative.

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arXiv2006

No realistic wormholes from ghost-free scalar-tensor phantom dark energy

It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(Φ)$ is everywhere positive and the scalar field $Φ$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(Φ)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions require severe fine tuning and a very peculiar kind of model. If $f < 0$ is allowed, it is argued (and confirmed by previous investigations) that such solutions are generically unstable under non-static perturbations, the instability appearing right near transition surfaces to negative $f$.

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arXiv2004

A general thick brane supported by a scalar field

A thick Z_2-symmetric domain wall supported by a scalar field with an arbitrary potential V(ϕ) in 5D general relativity is considered as a candidate brane world. We show that, under the global regularity requirement, such a configuration (i) has always an AdS asymptotic far from the brane, (ii) is only possible if V(ϕ) has an alternating sign and (iii) V(ϕ) satisfies a certain fine-tuning type equality. The thin brane limit is well defined and conforms to the Randall-Sundrum (RS2) brane world model if the asymptotic value of V(ϕ) (related to Λ, the effective cosmological constant) is kept thickness-independent. Universality of such a transition is demonstrated using as an example exact solutions for stepwise potentials of different shapes. Also, due to scale invariance of the Einstein-scalar equations, any given regular solution creates a one-parameter family of solutions with different potentials. In such families, a thin brane limit does not exist while the ratio Λ/(brane tension)^2 is thickness-independent and is in general different from its value in the RS2 model.

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