Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field V. D. Ivashchuk, U. S. Kayumov, A. N. Malybayev, G. S. Nurbakova Gravitation and Cosmology, 2025 A dilatonic dyonic black hole solution with the gravitational radius $$2\mu$$ and two charges $$Q_{1}$$ and $$Q_{2}$$ (electric and magnetic ones) is considered in a gravitational 4D model with one scalar field and one 2-form, with the dilatonic coupling constant $$\lambda=\pm 1/\sqrt{2}$$ . Circular null geodesics are explored. The 3rd order polynomial master equation for the radius $$R_{0}$$ of photon sphere is studied. There is only one solution with $$R_{0}>2\mu$$ . The circular null geodesics are shown to be unstable. The black hole shadow is studied, and relations for the shadow angle and critical impact parameter are obtained.
Photon Spheres near Black Holes in a Model with an Anisotropic Fluid V. D. Ivashchuk, S. V. Bolokhov, F. B. Belissarova, N. Kydyrbay, A. N. Malybayev, G. S. Nurbakova, B. Zheng Gravitation and Cosmology, 2025 This semi-review paper studies null geodesics which exist for black hole solutions in a gravitational 4D model with an anisotropic fluid. The equations of state for the fluid and the solutions depends on the integer parameter $$q=1,2,...$$ : $$p_{r}=-\rho c^{2}(2q-1)^{-1},\quad p_{t}=-p_{r}$$ , where $$\rho$$ is the mass density, $$c$$ is the speed of light, $$p_{r}$$ and $$p_{t}$$ are pressures in the radial and transverse directions, respectively. Circular null geodesics are explored, and a master equation for the radius $$r_{*}$$ of a photon sphere is found, as well as the proposition on the existence and uniqueness of a solution to the master equation, obeying $$r_{*}>r_{h}$$ , where $$r_{h}$$ is the horizon radius. Relations for the spectrum of quasinormal modes for a test massless scalar field in the eikonal approximation are overviewed and compared with the cyclic frequencies of circular null geo desics. Shadow angles are explored.
The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model K. K. Ernazarov, V. D. Ivashchuk European Physical Journal C, 2025 We consider the 4D gravitational model with a scalar field $$\\varphi $$ φ , Einstein and Gauss–Bonnet terms. The action of the model contains a potential term $$U(\\varphi )$$ U ( φ ) , Gauss–Bonnet coupling function $$f(\\varphi )$$ f ( φ ) and a parameter $$\\varepsilon = \\pm 1 $$ ε = ± 1 , where $$\\varepsilon = 1$$ ε = 1 corresponds to ordinary scalar field and $$\\varepsilon = -1 $$ ε = - 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: $$ds^2 = \\left( A(u)\\right) ^{-1}du^2 - A(u)dt^2 + C(u)d\\Omega ^2$$ d s 2 = A ( u ) - 1 d u 2 - A ( u ) d t 2 + C ( u ) d Ω 2 , with given $$A(u) > 0$$ A ( u ) > 0 and $$C(u) > 0$$ C ( u ) > 0 . The procedure gives the relations for $$U(\\varphi (u))$$ U ( φ ( u ) ) , $$f(\\varphi (u))$$ f ( φ ( u ) ) and $$d\\varphi /du$$ d φ / d u , 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 $$f(\\varphi (u))$$ 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: $$f(\\varphi ) = c_1 + c_0 ( \\tan ( \\varphi ) + \\frac{1}{3} (\\tan ( \\varphi ))^3)$$ f ( φ ) = c 1 + c 0 ( tan ( φ ) + 1 3 ( tan ( φ ) ) 3 ) , where $$c_1$$ c 1 and $$c_0$$ c 0 are constants.
On a Reconstruction Procedure for Special Spherically Symmetric Metrics in the Scalar-Einstein–Gauss–Bonnet Model: the Schwarzschild Metric Test K. K. Ernazarov, V. D. Ivashchuk Gravitation and Cosmology, 2024 The 4D gravitational model with a real scalar field $$\varphi$$ , Einstein and Gauss–Bonnet terms is considered. The action contains the potential $$U(\varphi)$$ and the Gauss–Bonnet coupling function $$f(\varphi)$$ . For a special static spherically symmetric metric $$ds^{2}=(A(u))^{-1}du^{2}-A(u)dt^{2}+u^{2}d\Omega^{2}$$ , 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 $$U(\varphi)$$ and $$f(\varphi)$$ 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 $$f(\varphi(u))$$ and $$\varphi(u)$$ are correct, but the relation for $$U(\varphi(u))$$ contains a typo which is eliminated in this paper. Here we apply the procedure to the (external) Schwarzschild metric with the gravitational radius $$2\mu$$ and $$u>2\mu$$ . Using the “no-ghost” restriction (i.e., reality of $$\varphi(u)$$ ), we find two families of $$(U(\varphi),f(\varphi))$$ . The first one gives us the Schwarzschild metric defined for $$u>3\mu$$ , while the second one describes the Schwarzschild metric defined for $$2\mu<u<3\mu$$ ( $$3\mu$$ is the radius of the photon sphere). In both cases the potential $$U(\varphi)$$ is negative.
Circular geodesics in the field of double-charged dilatonic black holes K. Boshkayev, G. Suliyeva, V. Ivashchuk, A. Urazalina European Physical Journal C, 2024 A non-extreme dilatonic charged (by two “color electric” charges) black hole solution is examined within a four-dimensional gravity model that incorporates two scalar (dilaton) fields and two Abelian vector fields. The scalar and vector fields interact through exponential terms containing two dilatonic coupling vectors. The solution is characterized by a dimensionless parameter a$$(0< a < 2)$$ ( 0 < a < 2 ) , which is a specific function of dilatonic coupling vectors. The paper presents solutions for timelike and null circular geodesics that may play a crucial role in different astrophysical scenarios, including quasinormal modes of various test fields in the eikonal approximation. For $$a = 1/2,1, 3/2,2 $$ a = 1 / 2 , 1 , 3 / 2 , 2 , the radii of the innermost stable circular orbit are presented and analyzed.
Photon Spheres near Dilatonic Dyon-Like Black Holes in a Model with Two Abelian Gauge Fields and Two Scalar Fields V. D. Ivashchuk, A. N. Malybayev, G. S. Nurbakova, G. Takey Gravitation and Cosmology, 2023 Dilatonic dyon-like black hole solutions with two (color) charges $$Q_{1}$$ and $$Q_{2}$$ (electric and magnetic ones) are considered in a gravitational 4D model with two scalar fields and two 2-forms. Two-dimensional dilatonic coupling vectors $$\vec{\lambda}_{i}$$ , $$i=1,2$$ , determining the model, obey the relation $$\vec{\lambda}_{1}\vec{\lambda}_{2}=1/2$$ . Circular null geodesics in the field of such black holes are explored. The master equation for the photon sphere radius $$R$$ is derived. A conjecture is suggested on the existence and uniqueness of the solution to the master equation with $$R>R_{g}$$ , where $$R_{g}$$ is the horizon radius. This conjecture is varified for certain special cases, e.g., for a charge symmetric configuration: $$Q_{1}^{2}=Q_{2}^{2}$$ . In this charge symmetric case, we present a relation for the spectrum of quasinormal modes of a test massless scalar field in the eikonal approximation, and an example of circular orbits of a massive particle.
Fluxbrane Polynomials and Melvin-like Solutions for Simple Lie Algebras Sergey V. Bolokhov, Vladimir D. Ivashchuk Symmetry, 2023 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 Hs(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 ps>0, s=1,…,n. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks n=1,2,3,4,5 and exceptional algebra E6. 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.
Exact (1 + 3 + 6)-Dimensional Cosmological-Type Solutions in Gravitational Model with Yang–Mills Field, Gauss–Bonnet Term and Λ Term V. D. Ivashchuk, K. K. Ernazarov, A. A. Kobtsev Symmetry, 2023 We consider a 10-dimensional gravitational model with an SO(6)Yang–Mills field, Gauss–Bonnet term, and Λ term. We study so-called cosmological-type solutions defined on the product manifold M=R×R3×K, where K is 6d a Calabi–Yau manifold. By setting the gauge field 1-form to coincide with the 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 and h obeying H+2h≠0. We also present static analogs of these cosmological solutions (for H≠0, h≠H, and H+2h≠0). The islands of stability for both classes of solutions are outlined.
Black-brane solution for A3 algebra M.A. Grebeniuk, V.D. Ivashchuk, V.N. Melnikov Physics Letters Section B Nuclear Elementary Particle and High Energy Physics, 2002
Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field VD Ivashchuk, US Kayumov, AN Malybayev, GS Nurbakova Gravitation and Cosmology 31 (4), 591-599 , 2025 2025
Photon Spheres near Black Holes in a Model with an Anisotropic Fluid VD Ivashchuk, SV Bolokhov, FB Belissarova, N Kydyrbay, AN Malybayev, ... Gravitation and Cosmology 31 (3), 392-400 , 2025 2025 Citations: 3
The problem of reconstruction for static spherically-symmetric 4D metrics in scalar-Einstein–Gauss–Bonnet model KK Ernazarov, VD Ivashchuk The European Physical Journal C 85 (7), 756 , 2025 2025 Citations: 4
The fine-structure constant: a review of measurement results and possible space-time variations KA Bronnikov, VD Ivashchuk, VV Khruschov Measurement Techniques 68 (3), 125-134 , 2025 2025
Stability analysis of circular geodesics in dyonic dilatonic black hole spacetimes K Boshkayev, G Takey, VD Ivashchuk, AN Malybayev, GS Nurbakova, ... Physics of the Dark Universe 48, 101862 , 2025 2025 Citations: 7
On a Reconstruction Procedure for Special Spherically Symmetric Metrics in the Scalar-Einstein–Gauss–Bonnet Model: the Schwarzschild Metric Test KK Ernazarov, VD Ivashchuk Gravitation and Cosmology 30 (3), 344-352 , 2024 2024 Citations: 4
Circular geodesics in the field of double-charged dilatonic black holes K Boshkayev, G Suliyeva, V Ivashchuk, A Urazalina The European Physical Journal C 84 (1), 19 , 2024 2024 Citations: 14
Photon spheres near dilatonic dyon-like black holes in a model with two Abelian gauge fields and two scalar fields VD Ivashchuk, AN Malybayev, GS Nurbakova, G Takey Gravitation and Cosmology 29 (4), 411-418 , 2023 2023 Citations: 4
Exact (1+ 3+ 6)-Dimensional Cosmological-Type Solutions in Gravitational Model with Yang–Mills Field, Gauss–Bonnet Term and Λ Term VD Ivashchuk, KK Ernazarov, AA Kobtsev Symmetry 15 (4), 783 , 2023 2023 Citations: 2
On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras SV Bolokhov, VD Ivashchuk Symmetry 14 (10), 2145 , 2022 2022 Citations: 1
On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid SV Bolokhov, VD Ivashchuk Eur. Phys. J. C 82 (624), 1-13 , 2022 2022 Citations: 12
Stable exponential cosmological type solutions with three factor spaces in EGB Model with a Λ-Term KK Ernazarov, VD Ivashchuk Symmetry 14 (7), 1296 , 2022 2022 Citations: 2
Fundamental physical constants: search results and variation descriptions KA Bronnikov, VD Ivashchuk, VV Khrushchev Measurement Techniques 65 (3), 151-156 , 2022 2022 Citations: 6
On stable exponential cosmological solutions with two factor spaces in (1+ m+ 2)-dimensional Einstein–Gauss–Bonnet model with Λ-term VD Ivashchuk, AA Kobtsev Philosophical Transactions of the Royal Society A: Mathematical, Physical … , 2022 2022 Citations: 3
Quasinormal modes in the field of a dyon-like dilatonic black hole AN Malybayev, KA Boshkayev, VD Ivashchuk The European Physical Journal C 81 (5), 475 , 2021 2021 Citations: 29
Special dyon-like black hole solution in the model with two Abelian gauge fields and two scalar fields FB Belissarova, KA Boshkayev, VD Ivashchuk, AN Malybayev Journal of Physics: Conference Series 1690 (1), 012143 , 2020 2020 Citations: 9
On stable exponential cosmological solutions with two factor spaces in -dimensional EGB model with -term VD Ivashchuk, AA Kobtsev arXiv preprint arXiv:2009.10204 , 2020 2020
Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a -term KK Ernazarov, VD Ivashchuk The European Physical Journal C 80 (6), 543 , 2020 2020 Citations: 6
Regularization by -metric. II. Limit VD Ivashchuk arXiv preprint arXiv:2002.10527 , 2020 2020 Citations: 7
MOST CITED SCHOLAR PUBLICATIONS
On Wheeler-De Witt equation in multidimensional cosmology VD Ivashchuk, VN Melnikov, AI Zhuk Il Nuovo Cimento B (1971-1996) 104 (5), 575-582 , 1989 1989 Citations: 169
Exact solutions in multidimensional gravity with antisymmetric forms VD Ivashchuk, VN Melnikov Classical and Quantum Gravity 18 (20), R87-R152 , 2001 2001 Citations: 153
Multidimensional classical and quantum cosmology with intersecting -branes VD Ivashchuk, VN Melnikov Journal of Mathematical Physics 39 (5), 2866-2888 , 1998 1998 Citations: 124
Multidimensional cosmology with m-component perfect fluid VD Ivashchuk, VN Melnikov International Journal of Modern Physics D 3 (04), 795-811 , 1994 1994 Citations: 117
Sigma-model for generalized composite p -branes VD Ivashchuk, VN Melnikov Classical and Quantum Gravity 14 (11), 3001-3029 , 1997 1997 Citations: 109
Billiard representation for multidimensional cosmology with multicomponent perfect fluid near the singularity VD Ivashchuk, VN Melnikov Classical and Quantum Gravity 12 (3), 809-826 , 1995 1995 Citations: 98
Integrable pseudo‐Euclidean Toda‐like systems in multidimensional cosmology with multicomponent perfect fluid VR Gavrilov, VD Ivashchuk, VN Melnikov Journal of Mathematical Physics 36 (10), 5829-5847 , 1995 1995 Citations: 97
Multidimensional classical and quantum wormholes in models with cosmological constant U Bleyer, VD Ivashchuk, VN Melnikov, A Zhuk Nuclear Physics B 429 (1), 177-204 , 1994 1994 Citations: 85
Intersecting p-brane solutions in multidimensional gravity and M-theory VD Ivashchuk, VN Melnikov arXiv preprint hep-th/9612089 , 1996 1996 Citations: 82
The Reissner-Nordstrom problem for intersecting electric and magnetic P-branes KA Bronnikov, VD Ivashchuk, VN Melnikov arXiv preprint gr-qc/9710054 , 1997 1997 Citations: 81
Perfect-fluid type solution in multidimensional cosmology VD Ivashchuk, VN Melnikov Physics Letters A 136 (9), 465-467 , 1989 1989 Citations: 80
Time variation of gravitational constant in multidimensional cosmology KA Bronnikov, VD Ivashchuk, VN Melnikov Il Nuovo Cimento B (1971-1996) 102 (2), 209-215 , 1988 1988 Citations: 79
Billiard representation for multidimensional cosmology with intersecting p -branes near the singularity VD Ivashchuk, VN Melnikov Journal of Mathematical Physics 41 (9), 6341-6363 , 2000 2000 Citations: 77
Composite S -brane solutions related to Toda-type systems VD Ivashchuk Classical and Quantum Gravity 20 (2), 261-275 , 2003 2003 Citations: 69
Multidimensional cosmology and Toda-like systems VD Ivashchuk Physics Letters A 170 (1), 16-20 , 1992 1992 Citations: 68
On cosmological-type solutions in multi-dimensional model with Gauss–Bonnet term VD Ivashchuk International Journal of Geometric Methods in Modern Physics 7 (05), 797-819 , 2010 2010 Citations: 63
Cosmological solutions in multidimensional model with multiple exponential potential VD Ivashchuk, VN Melnikov, AB Selivanov Journal of High Energy Physics 2003 (09), 059-059 , 2003 2003 Citations: 55
Solutions with intersecting p -branes related to Toda chains VD Ivashchuk, SW Kim Journal of Mathematical Physics 41 (1), 444-460 , 2000 2000 Citations: 55
Multidimensional integrable vacuum cosmology with two curvatures VR Gavrilov, VD Ivashchuk, VN Melnikov Classical and Quantum Gravity 13 (11), 3039-3056 , 1996 1996 Citations: 55
On time variation of gravitational constant in superstring theories VD Ivashchuk, VN Melnikov Il Nuovo Cimento B (1971-1996) 102 (2), 131-138 , 1988 1988 Citations: 55
