arXiv subjects

K. K. Ernazarov

Publications and source records attributed to K. K. Ernazarov.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Fisher-Janis-Newman-Winicour (FJNW) and Yilmaz-Rosen solutions in the higher-dimensional scalar-tensor theory with nonminimal coupling

This paper investigates higher-dimensional scalar-tensor theories of gravity with nonminimal coupling, focusing on the reconstruction of exact spherically symmetric solutions. We systematically apply the formalism developed in previous works, which demonstrates that any static spherically symmetric metric can be represented as an exact solution of a scalar-tensor theory with specific coupling functions $f(ϕ)$ and potential $U(ϕ)$. Our analysis centers on two important classes of solutions in arbitrary spacetime dimensions: the Fisher-Janis-Newman-Winicour (FJNW) metric and its limiting case, the generalized Yilmaz-Rosen metric. We derive the key relations for the coupling function $f(ϕ)$ and the scalar field potential $U(ϕ)$ for both solution families using the master equation formalism in the Jordan frame. For the FJNW metric, we find that in the special case $s = 2$, $D = 6$, the coupling function $f(ϕ)$ is positive in the domain $u^3 > M$, corresponding to gravitational attraction and a canonical scalar field with vanishing potential $U(ϕ) = 0$. In contrast, for the generalized Yilmaz-Rosen metric in arbitrary dimensions $D > 4$, the reconstructed coupling function is always negative, $f(ϕ) < 0$, indicating a phantom scalar field with negative kinetic energy and repulsive gravity.

gr-qc↗

arXiv2026

Reconstructed black hole solutions in the scalar-tensor theory with nonminimal coupling

We consider the scalar-tensor theory witn non-minimal coupling in the Jordan frame. The action of the model contains a potential term $U(φ)$, a coupling function $f(φ)$. We explore a reconstruction procedure for a generic static spherically symmetric metric written in the Buchdahl parametrization: $ds^2 = \left(A(u)\right)^{-1}du^2 - A(u)dt^2 + C(u)dΩ^2$, with given $A(u) > 0$ and $C(u) > 0$. The procedure gives the relations for $U(φ(u))$, $f(φ(u))$ and $dφ/du$, which lead to exact solutions to equations of motion with a given metric. A key role in this approach is played by the solutions to a first order linear differential equation for the function $f(φ(u))$. The formalism is illustrated by two examples when: a) the Reissner-Nordström-(Anti-)de Sitter metric and b) the Bocharova-Bronnikov-Melnikov-Bekenstein-(Anti)de-Sitter metric are chosen as a starting point.

gr-qc↗

arXiv2025

The asymptotically Schwarzschild-like metric solutions

In this article we investigate the properties of the asymptotically Schwarzschild-like metric as an alternative to the Schwarzschild solution in General Relativity. While asymptotically flat and similar to Schwarzschild at large distances $r$, this metric exhibits a fundamentally different strong-field behavior: it lacks an event horizon and is best interpreted as a traversable wormhole or a black hole surrounded by a specific anisotropic fluid, rather than a true vacuum solution. We analyze key phenomenological features, demonstrating significant deviations from Schwarzschild in the radii of the photon sphere and the Innermost Stable Circular Orbit (ISCO). Furthermore, we derive the Regge-Wheeler equation for gravitational and electromagnetic perturbations and compute the black hole shadow, providing a direct comparison with the Schwarzschild metric. Despite being ruled out by solar system tests, the exponential metric remains relevant for theories beyond standard GR, regular black hole models, and its connection to screened Yukawa potentials.

gr-qc↗

arXiv2025

The Yilmaz-Rosen and Janis-Newman-Winicour metric solutions in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model

We consider the scalar-Einstein-Gauss-Bonnet (sEGB) $4d$ gravitational model with a scalar field $φ\left(u\right)$, Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\left(φ\right)$, a Gauss-Bonnet coupling function $f\left(φ\right)$ and a parameter $\varepsilon = \pm 1$, where $\varepsilon = 1$ corresponds to the ordinary scalar field, and $\varepsilon = -1$ to the phantom field. In this paper we applied the sEGB reconstruction procedure from our previous work \cite{Er_Ivash} to the Yılmaz-Rosen metric, a solution potentially describing a quasi-black hole without an event horizon. Within this framework, we also derived analytical solutions based on scalar-tensor theory with minimal coupling. Our results indicate that for this configuration, the potential $U$ vanishes and the scalar field is phantom-like. Furthermore, an analysis of the Einstein equations in the Yılmaz-Rosen metric reveals that all energy conditions are violated. The corresponding energy-momentum tensor suggests the presence of exotic matter with negative pressure, as indicated by the negative value of $T_u^u$. This could originate from a scalar field (such as the Higgs field or another nonlinear field), or from phenomena like dark energy or quintessence. In addition, we considered the application of our reconstruction method in the sEGB model in the Janis-Newman-Winicour (JNW) metric. As noted in this paper, the Yılmaz-Rosen metric is a limiting case of the Janus metric (as $s \to +\infty$). Furthermore, we obtained some exact solutions of scalar-tensor theory with minimal coupling in the JNW metric.

gr-qc↗

arXiv2025

Generalized Ellis-Bronnikov wormhole solution in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model

We consider the sEGB $4d$ gravitational model with a scalar field $φ\left(u\right)$, Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\left(φ\right)$, a Gauss-Bonnet coupling function $f\left(φ\right)$ and a parameter $\varepsilon = \pm 1$, where $\varepsilon = 1$ corresponds to the usual scalar field, and $\varepsilon = -1$ to the phantom field. In this paper, the sEGB reconstruction procedure considered in our previous paper is applied to the metric of the Ellis-Bronnikov solution, which describes a massive wormhole in the model with a phantom field (and zero potential). For this metric, written in the Buchdal parameterization with a radial variable $u$, we find a solution of the master equation for $ f\left(φ\left(u\right)\right)$ with the integration (reconstruction) parameter $C_0$. We also find expressions for $U\left(φ\left(u\right)\right)$ and $\varepsilon \dotφ^2 = h\left(u\right)$ for $\varepsilon = \pm 1$. We prove that for all non-trivial values of the parameter $C_0 \neq 0$ the function $h\left(u\right)$ is not of constant sign for all admissible $u \in \left(-\infty , +\infty\right)$. This means that for a fixed value of the parameter $\varepsilon = \pm 1$ there is no non-trivial sEGB reconstruction in which the scalar field is a purely ordinary field ($\varepsilon = 1$) or a purely phantom field ($\varepsilon = - 1$).

gr-qc↗

arXiv2025

The problem of reconstruction for static spherically-symmetric $4D$ metrics in scalar-Einstein-Gauss-Bonnet model

We consider the $4D$ gravitational model with a scalar field $φ$, Einstein and Gauss-Bonnet terms. The action of the model contains a potential term $U(φ)$, Gauss-Bonnet coupling function $f(φ)$ and a parameter $\varepsilon = \pm1 $, where $\varepsilon = 1$ corresponds to ordinary scalar field and $\varepsilon = -1 $ - to phantom one. Inspired by the recent works of Nojiri and Nashed, we explore a reconstruction procedure for a generic static spherically symmetric metric written in the Buchdal parametrization: $ds^2 = \left(A(u)\right)^{-1}du^2 - A(u)dt^2 + C(u)dΩ^2$, with given $A(u) > 0$ and $C(u) > 0$. The procedure gives the relations for $U(φ(u))$, $f(φ(u))$ and $dφ/du$, which lead to exact solutions to equations of motion with a given metric. A key role in this approach is played by the solutions to a second order linear differential equation for the function $f(φ(u))$. The formalism is illustrated by two examples when: a) the Schwarzschild metric and b) the Ellis wormhole metric, are chosen as a starting point. For the first case a) the black hole solution with a ``trapped ghost'' is found which describes an ordinary scalar field outside the photon sphere and phantom scalar field inside the photon sphere. For the second case b) the sEGB-extension of the Ellis wormhole solution is found when the coupling function reads: $f(φ) = c_1 + c_0 ( \tan ( φ) + \frac{1}{3} (\tan ( φ))^3)$, where $c_1$ and $c_0$ are constants.

gr-qc↗

arXiv2025

On a reconstruction procedure for special spherically symmetric metrics in the scalar-Einstein-Gauss-Bonnet model: the Schwarzschild metric test

The 4D gravitational model with a real scalar field $φ$, Einstein and Gauss-Bonnet terms is considered. The action contains the potential $U(φ)$ and the Gauss-Bonnet coupling function $f(φ)$. For a special static spherically symmetric metric $ds^2 = (A(u))^{-1} du^2 - A(u) dt^2 + u^2 dΩ^2$, with $A(u) > 0$ ($u > 0$ is a radial coordinate), we verify the so-called reconstruction procedure suggested by Nojiri and Nashed. This procedure presents certain implicit relations for $U(φ)$ and $f(φ)$ which lead to exact solutions to the equations of motion for a given metric governed by $A(u)$. We confirm that all relations in the approach of Nojiri and Nashed for $f(φ(u))$ and $φ(u)$ are correct, but the relation for $U(φ(u))$ contains a typo which is eliminated in this paper. Here we apply the procedure to the (external) Schwarzschild metric with the gravitational radius $2 μ$ and $u > 2 μ$. Using the ``no-ghost'' restriction (i.e., reality of $φ(u)$), we find two families of $(U(φ), f(φ))$. The first one gives us the Schwarzschild metric defined for $u > 3 μ$, while the second one describes the Schwarzschild metric defined for $2 μ< u < 3 μ$ ($3 μ$ is the radius of the photon sphere). In both cases the potential $U(φ)$ is negative.

gr-qc↗

arXiv2023

Exact $(1 + 3 + 6)$-dimensional cosmological-type solutions in gravitational model with Yang-Mills field, Gauss-Bonnet term and $Λ$-term

We consider $10$-dimensional gravitational model with $SO(6)$ Yang-Mills field, Gauss-Bonnet term and $Λ$-term. We study so-called cosmological type solutions defined on product manifold $M = R \times R^3 \times K$, where $K$ is $6d$ Calabi-Yau manifold. By putting the gauge field 1-form to be coinciding with 1-form spin connection on $K$, we obtain exact cosmological solutions with exponential dependence of scale factors (upon $t$-variable), governed by two non-coinciding Hubble-like parameters: $H >0$, $h$, obeying $ H + 2 h \neq 0$. We also present static analogs of these cosmological solutions (for $H \neq 0$, $h \neq H$ and $ H + 2 h \neq 0$). The islands of stability for both classes of solutions are outlined.

gr-qc↗

arXiv2022

Examples of exact exponential cosmological solutions with three isotropic subspaces in the Einstein-Gauss-Bonnet gravity

We consider $(1+ 8)$- and $(1+10)$-dimensional Einstein-Gauss-Bonnet models with the cosmological $Λ$-term. Some new examples of exact solutions with three constant Hubble-like parameters in this model are obtained, governed by three non-coinciding Hubble-like parameters: $H \neq 0$, $h_1$ and $h_2$, obeying $m H + k_1 h_1 + k_2 h_2 \neq 0$, corresponding to factor spaces of dimensions $m\geqslant 3$, $ k_1 > 1$ and $ k_2\geqslant 1$. In this case, the multidimensional cosmological model deals with three factor spaces: the external 3-dimensional "our" world and internal subspaces with dimensions $ (m-3)$, $k_1$ and $k_2$.

gr-qc↗

arXiv2022

Stable exponential cosmological type solutions with three factor spaces in EGB model with a $Λ$-term

We study a $D$-dimensional Einstein-Gauss-Bonnet model which includes the Gauss-Bonnet term, the cosmological term $Λ$ and two non-zero constants: $α_1$ and $α_2$. Under imposing the metric to be diagonal one, we find cosmological type solutions with exponential dependence of three scale factors in a variable $u$, governed by three non-coinciding Hubble-like parameters: $H \neq 0$, $h_1$ and $h_2$, obeying $m H + k_1 h_1 + k_2 h_2 \neq 0$, corresponding to factor spaces of dimensions $m > 1$, $k_1 > 1$ and $k_2 > 1$, respectively, and depending upon sign parameter $\varepsilon = \pm 1$, where $\varepsilon = 1$ corresponds to cosmological case and $\varepsilon = - 1$ - to static one). We deal with two cases: i) $m < k_1 < k_2$ and ii) $1< k_1 = k_2 = k$, $k \neq m$. We show that in both cases the solutions exist if $\varepsilon α= \varepsilon α_2 / α_1 > 0$ and $αΛ> 0$ satisfies certain (upper and lower) bounds. The solutions are defined up to solutions of certain polynomial master equation of order four (or less) which may be solved in radicals. In case ii) explicit solutions are presented. In both cases we single out stable and non-stable solutions as $u \to \pm \infty$. The case $H = 0$ is also considered.

gr-qc↗

arXiv2020

Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a $Λ$-term

We consider a $D$-dimensional Einstein-Gauss-Bonnet model with a cosmological term $Λ$ and two non-zero constants: $α_1$ and $α_2$. We restrict the metrics to be diagonal ones and study a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: $H \neq 0$, $h_1$ and $h_2$, obeying $m H + k_1 h_1 + k_2 h_2 \neq 0$ and corresponding to factor spaces of dimensions $m > 1$, $k_1 > 1$ and $k_2 > 1$, respectively ($D = 1 + m + k_1 + k_2$). We analyse two cases: i) $m < k_1 < k_2$ and ii) $1< k_1 = k_2 = k$, $k \neq m$. We show that in both cases the solutions exist if $α= α_2 / α_1 > 0$ and $αΛ> 0$ satisfies certain restrictions, e.g. upper and lower bounds. In case ii) explicit relations for exact solutions are found. In both cases the subclasses of stable and non-stable solutions are singled out. For $m > 3$ the case i) contains a subclass of solutions describing an exponential expansion of $3$-dimensional subspace with Hubble parameter $H > 0$ and zero variation of the effective gravitational constant $G$. The case $H = 0$ is also considered.

gr-qc↗

arXiv2019

Stable exponential cosmological solutions with three factor spaces of dimensions $m=3$, $k_1=k$ and $k_2 = k$ in the Einstein-Gauss-Bonnet model with a $Λ$-term

We consider a $(4 + 2k)$ - dimensional Einstein-Gauss-Bonnet model with the cosmological $Λ$-term. Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional cosmological model deals with three factor spaces: the external 3-dimensional "our" world and internal subspaces with dimensions $k_1 = k$ and $k_2=k$.

gr-qc↗

arXiv2019

Scale Factors of Homogeneous Anisotropic Cosmological Models with Perfect Fluid

The article is devoted to cosmology. It deals with homogeneous anisotropic cosmological models. Scale factors have been evaluated for the multicomponent models with perfect fluid, taking account of its expansion, rotation and shear. The cosmological fluid components are as follows: phantom matter, de Sitter vacuum, domain walls, strings, dust, radiation, perfect gas, stiff matter and ekpyrotic matter. The scale factor dependences on the equation of state and kinematic invariants of the perfect fluid have been analysed. The paper is aimed at finding exact solutions of Friedmann and Raychaudhuri equations for different combination of matter components and kinematic invariants.

gr-qc↗

arXiv2019

On non-exponential cosmological solutions with two factor spaces of dimensions $m$ and $ 1$ in the Einstein-Gauss-Bonnet model with a $Λ$-term

We consider a $(m+2)$-dimensional Einstein-Gauss-Bonnet model with the cosmological $Λ$-term. We restrict the metrics to be diagonal ones and find for certain $Λ= Λ(m)$ class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions $m > 2$ and $1$. Any solutions from this class describes an accelerated expansion of $m$-dimensional subspace and tends asymptotically to isotropic solution with exponental dependence of scale factors.

gr-qc↗

arXiv2019

Stable exponential cosmological solutions with three factor spaces in $(1+ 3 + 3 +k)$-dimensional Einstein-Gauss-Bonnet model with a $Λ$-term

We consider a $(7 + k)$-dimensional Einstein-Gauss-Bonnet model with the cosmological $Λ$-term. A cosmological model with three factor spaces of dimensions $3$, $3$ and $k$, $k > 2$ is considered. Exact stable solutions with three (non-coinciding) Hubble-like parameters in this model are obtained. Some examples of solutions (e.g. with zero variation of the effective gravitational constant $G$) are considered in selected dimensions (for $k = 5, 6$).

gr-qc↗

arXiv2019

Examples of stable exponential cosmological solutions with three factor spaces in EGB model with a $Λ$-term

We deal with Einstein-Gauss-Bonnet model in dimension $D$ with a $Λ$-term. We obtain three stable cosmological solutions with exponential behavior (in time) of three scale factors corresponding to subspaces of dimensions $(l_0,l_1,l_2) = (3, 4, 4), (3, 3, 2), (3, 4, 3)$ and $D = 12, 9, 11$, respectively. Any solution may describe an exponential expansion of $3$-dimensional subspace governed by Hubble parameter $H$. Two of them may also describe a small enough variation of the effective gravitational constant $G$ (in Jordan frame) for certain values of $Λ$.

gr-qc↗

arXiv2017

Stable exponential cosmological solutions with zero variation of $G$ and three different Hubble-like parameters in the Einstein-Gauss-Bonnet model with a $Λ$-term

We consider a $D$-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term $Λ$. We restrict the metrics to diagonal cosmological ones and find for certain $Λ$ a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters $H >0$, $h_1$ and $h_2$, corresponding to factor spaces of dimensions $m > 2$, $k_1 > 1$ and $k_2 > 1$, respectively, with $k_1 \neq k_2$ and $D = 1 + m + k_1 + k_2$. Any of these solutions describes an exponential expansion of $3d$ subspace with Hubble parameter $H$ and zero variation of the effective gravitational constant $G$. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics.

gr-qc↗

arXiv2017

Stable exponential cosmological solutions with zero variation of G in the Einstein-Gauss-Bonnet model with a Lambda-term

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Lambda is considered. By assuming diagonal cosmological metrics, we find, for certain fine-tuned Lambda, a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H >0 and h < 0, corresponding to factor spaces of dimensions m > 3 and l > 1, respectively, with (m,l) non-equal to (6,6), (7,4), (9,3) and D = 1 + m + l. Any of these solutions describes an exponential expansion of 3-dimensional subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics.

gr-qc↗