arXiv subjects

V. D. Ivashchuk

Publications and source records attributed to V. D. Ivashchuk.

At least 19 recordsLinked to original sources

arXiv2026

Generalized pp-wave solutions on product of Ricci-flat spaces

A multidimensional gravitational model with several scalar fields and form fields is considered. A wide class of generalized pp-wave solutions defined on a product of n+1 Ricci-flat spaces is obtained. Certain examples of solutions (e.g. in supergravitational theories) are singled out. For special cone-type internal factor spaces the solutions are written in Brinkmann form. An example of pp-wave solution is obtained using Penrose limit of a solution defined on a product of two Einstein spaces.

hep-th↗

arXiv2026

Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field

Dilatonic dyon black hole solution with gravitational radius $2 μ$ and two charges $Q_1$ and $Q_2$ (electric and magnetic ones) in the gravitational $4d$ model with one scalar field and one 2-form is considered. Dilatonic coupling constant $λ$ obeys $λ^2 = \frac{1}{2}$. The circular orbits for null geodesics are explored. The 3rd order polynomial master equation for radius $R_0$ of photon sphere is studied. It has only one solution which obeys $R_0 > 2 μ$. The circular null geodesics are shown to be unstable. The black hole shadow is studied and relations for shadow angle and critical impact parameter are obtained.

gr-qc↗

arXiv2026

On generalized black brane solutions in the model with multicomponent anisotropic fluid

A family of spherically $O(d_0 + 1)$-symmetric solutions in the model with $m$-component anisotropic fluid is obtained. The metrics are defined on a manifold which contains a product of $n-1$ Ricci-flat ``internal'' spaces. The equation of state for any $s$-th component is defined by a vector $U^s = (U^s_i)$ belonging to $R^{n + 1}$ and obeying inequalities $U^s_1 = q_s > 0$, $s = 1, \ldots,m$. The solutions are governed by moduli functions $H_s$ which are solutions to (master) non-linear differential equations with certain boundary conditions imposed. It is shown that for coinciding $q_s = q$ there exists a subclass of solutions with a horizon when $q = 1, 2, \ldots$ and $U^s$-vectors correspond to certain semisimple Lie algebras. An extension of these solutions to block-orthogonal set of vectors $U^s$ with natural parameters $q_s$ coinciding inside blocks is also proposed. $q$-analogues of black brane/hole solutions are presented, e.g. generalising $M_2 \cap M_5$ dyonic solution in $D =11$ supergravity and Myers-Perry charged black hole solution in dimension $D = 2 + d_0$.

hep-th↗

arXiv2025

Dyon-like black hole solutions in the model with two Abelian gauge fields

Dilatonic black hole dyon-like solutions in the gravitational $4d$ model with a scalar field, two 2-forms, two dilatonic coupling constants $λ_i \neq 0$, $i =1,2$, obeying $λ_1 \neq - λ_2$ and the sign parameter $\varepsilon = \pm 1$ for scalar field kinetic term are overviewed. Here $\varepsilon = - 1$ corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when $λ^2_i \neq 1/2$ for $\varepsilon = - 1$. Several integrable cases corresponding to Lie algebras $A_1 + A_1$, $A_2$, $B_2 = C_2$ and $G_2$ are considered. Some physical parameters of the solutions are derived: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters $β$ and $γ$. Bounds on the gravitational mass and scalar charge (based on a certain conjecture) are presented.

hep-th↗

arXiv2025

Photon spheres near black holes in a model with anisotropic fluid

The semi-review paper studies the null geodesics which appear for black hole solutions in the gravitational $4d$ model with anisotropic fluid. The equations of state for the fluid and solutions itselves depend upon integer parameter $q = 1, 2, ...$: $p_r = -ρc^2 (2q-1)^{-1}, \quad p_t = - p_r$, where $ρ$ is the mass density, $c$ is speed of light, $p_r$ and $p_t$ are pressures in radial and transverse to radial directions, respectively. The circular null geodesics are explored and the master equation for radius $r_*$ of photon sphere is outlined as well as the proposition on existence and uniqueness of the solution to master equation obeying $r_* > r_h$, where $r_h$ is horizon radius. The relations for spectrum of quasinormal modes for a test massless scalar field in the eikonal approximation are overviewed and compared with cyclic frequencies of circular null geodesics. The shadow angles are explored.

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

The fine structure constant: a review of measurement results and possible space-time variations

A brief description of the main methods for determining the fine structure constant is given. It is shown that the exact value of the fine structure constant is important for the new International System of Units (SI) and for fundamental metrology. Recent measurement results and theoretical calculations of the fine structure constant, as well as its possible space-time variations, are presented. The results of laboratory experiments on the search for long-term variations of the fine structure constant are described. The astrophysical and cosmological observational data on possible variability of the fine structure constant are displayed. The possibility of slightly lower values of the fine structure constant in the remote past as compared to its modern value, as well as the existence of unresolved problems related to possible space-time variations of the fine structure constant and the spread of the results of its precise laboratory measurements, are mentioned. Despite the absence of experimentally confirmed long-term variations of the fine structure constant at a high level of accuracy, possible practical applications of the results are noted, namely, the construction of an optical frequency standard with high stability and frequency reproduction accuracy based on the ytterbium-171 ion and a laser frequency synthesizer which may replace the caesium frequency standard.

hep-ph↗

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

Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras

This review dealt with generalized Melvin solutions for simple finite-dimensional Lie algebras. Each solution appears in a model which includes a metric and $n$ scalar fields coupled to $n$ Abelian 2-forms with dilatonic coupling vectors determined by simple Lie algebra of rank $n$. The set of $n$ moduli functions $H_s(z)$ comply with $n$ non-linear (ordinary) differential equations (of second order) with certain boundary conditions set. Earlier, it was hypothesized that these moduli functions should be polynomials in $z$ (so-called ``fluxbrane'' polynomials) depending upon certain parameters $p_s > 0$, $s = 1,\dots,n$. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks $n = 1,2,3,4,5$ and exceptional algebra $E_6$. Certain relations for the polynomials (e.g., symmetry and duality ones) were outlined. In a general case where polynomial conjecture holds, 2-form flux integrals are finite. The use of fluxbrane polynomials to dilatonic black hole solutions was also explored.

hep-th↗

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

Fundamental physical constants: current results in search for variations and their description

We consider the current results in search for and description of temporal variations of fundamental physical constants (FPCs) obtained under laboratory and astrophysical conditions. On the basis of fixed values of base constants, those FPCs have been chosen that can exhibit variations of greatest interest from the viewpoints of physics and metrology. An analysis of the current data concerning these constants is performed, and estimates of their variations on large time scales are presented. We point out the significance of studying long-term FPC variations for both practical and fundamental metrology.

hep-ph↗

arXiv2022

On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras

We consider generalized Melvin-like solutions corresponding to Lie algebras of rank $5$ ($A_5$, $B_5$, $C_5$, $D_5$). The solutions take place in $D$-dimensional gravitational model with five Abelian 2-forms and five scalar fields. They are governed by five moduli functions $H_s(z)$ ($s = 1,...,5$) of squared radial coordinate $z=ρ^2$ which obey five differential master equations. The moduli functions are polynomials of powers $(n_1, n_2, n_3, n_4, n_5) = (5,8,9,8,5), (10,18,24,28,15), (9,16,21,24,25), (8,14,18,10,10)$ for Lie algebras $A_5$, $B_5$, $C_5$, $D_5$ respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued $5 \times 5$ matrix $ν$ connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in $A_5$ and $D_5$ cases) with the matrix representing a generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The symmetry and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances.

hep-th↗

arXiv2022

On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid

We consider a family of 4-dimensional black hole solutions from Dehnen et al. ( Grav. Cosmol. 9:153, arXiv: gr-qc/0211049, 2003) governed by natural number $q= 1, 2, 3 , \dots$, which appear in the model with anisotropic fluid and the equations of state: $p_r = -ρ(2q-1)^{-1}$, $p_t = - p_r$, where $p_r$ and $p_t$ are pressures in radial and transverse directions, respectively, and $ρ> 0$ is the density. These equations of state obey weak, strong and dominant energy conditions. For $q = 1$ the metric of the solution coincides with that of the Reissner-Nordström one. The global structure of solutions is outlined, giving rise to Carter-Penrose diagram of Reissner-Nordström or Schwarzschild types for odd $q = 2k + 1$ or even $q = 2k$, respectively. Certain physical parameters corresponding to BH solutions (gravitational mass, PPN parameters, Hawking temperature and entropy) are calculated. We obtain and analyse the quasinormal modes for a test massless scalar field in the eikonal approximation. For limiting case $q = + \infty$, they coincide with the well-known results for the Schwarzschild solution. We show that the Hod conjecture which connect the Hawking temperature and the damping rate is obeyed for all $q \geq 2$ and all (allowed) values of parameters.

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↗

arXiv2021

Quasinormal modes in the field of a dyon-like dilatonic black hole

Quasinormal modes of massless test scalar field in the background of gravitational field for a non-extremal dilatonic dyonic black hole are explored. The dyon-like black hole solution is considered in the gravitational $4d$ model involving two scalar fields and two 2-forms. It is governed by two 2-dimensional dilatonic coupling vectors $\vecλ_i$ obeying $\vecλ_i (\vecλ_1 + \vecλ_2) > 0$, $i =1,2$. The first law of black hole thermodynamics is given and the Smarr relation is verified. Quasinormal modes for a massless scalar (test) field in the eikonal approximation are obtained and analysed. These modes depend upon a dimensionless parameter $a$ ($0 < a \leq 2$) which is a function of $\vecλ_i$. For limiting strong ($a = +0$) and weak ($a = 2$) coupling cases, they coincide with the well-known results for the Schwarzschild and Reissner-Nordström solutions. It is shown that the Hod conjecture, connecting the damping rate and the Hawking temperature, is satisfied for $0 < a \leq 1$ and all allowed values of parameters.

gr-qc↗

arXiv2021

On generalized Melvin solutions for Lie algebras of rank 4

We deal with generalized Melvin-like solutions associated with Lie algebras of rank $4$ ($A_4$, $B_4$, $C_4$, $D_4$, $F_4$). Any solution has static cylindrically-symmetric metric in $D$ dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions $H_s(z)$ ($s = 1,...,4$) of squared radial coordinate $z=ρ^2$ obeying four differential equations of the Toda chain type. These functions are polynomials of powers $(n_1,n_2, n_3, n_4) = (4,6,6,4), (8,14,18,10), (7,12,15,16), (6,10,6,6), (22,42,30,16)$ for Lie algebras $A_4$, $B_4$, $C_4$, $D_4$, $F_4$, respectively. The asymptotic behaviour for the polynomials at large $z$ is governed by an integer-valued $4 \times 4$ matrix $ν$ connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in $A_4$ case) the matrix representing a generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are studied. We also present 2-form flux integrals over a $2$-dimensional submanifold. Dilatonic black hole analogs of the obtained Melvin-type solutions, e.g. "fantom" ones, are also considered. The phantom black holes are described by fluxbrane polynomials under consideration.

hep-th↗

arXiv2020

On stable exponential cosmological solutions with two factor spaces in $(1+ m + 2)$-dimensional EGB model with $Λ$-term

A $(m+ 3)$-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term $Λ$ is considered. Exact solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters $H >0$ and $h \neq H$, corresponding to factor spaces of dimensions $m >2$ and $l = 2$, respectively, are found. Under certain restrictions on $x = h/H $, the stability of the solutions in a class of cosmological solutions with diagonal metrics is proved. A subclass of solutions with small enough variation of the effective gravitational constant $G$ is considered and the stability of all solutions from this subclass is shown.

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↗