arXiv subjects

V. D. Ivashchuk

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

At least 37 records · Page 2Linked to original sources

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↗

arXiv2020

Regularization by $\varepsilon$-metric. II. Limit $\varepsilon = + 0$

In a wide class of propagators regularized by the $\varepsilon$-metric [1], the $R$-operation is formulated. It is proved that the limit of renormalized Feynman integrals exists and is covariant. Possible applications in gravity are discussed. (The paper is an English translation of the second of two articles in Russian published by the author in 1987-88: V.D. Ivashchuk, Regularization by $\varepsilon$-metric. II. Limit $\varepsilon = +0$, Izvestiya Akademii Nauk Moldavskoy SSR, Ser. fiziko-tekhnicheskih i matematicheskih nauk, No. 1, p. 10-20 (1988) [in Russian] .)

hep-th↗

arXiv2019

Exponential cosmological solutions with two factor spaces in EGB model with $Λ= 0$ revisited

We study exact cosmological solutions in $D$-dimensional Einstein-Gauss-Bonnet model (with zero cosmological term) governed by two non-zero constants: $α_1$ and $α_2$. We deal with exponential dependence (in time) of two scale factors governed by Hubble-like parameters $H > 0$ and $h$, which correspond to factor spaces of dimensions $m > 2$ and $l > 2$, respectively, and $D = 1 + m + l$. We put $h \neq H$ and $m H + l h \neq 0$. We show that for $α= α_2/α_1 > 0$ there are two (real) solutions with two sets of Hubble-like parameters: $(H_1, h_1)$ and $(H_2, h_2)$, which obey: $ h_1/ H_1 < - m/l < h_2/ H_2 < 0$, while for $α< 0$ the (real) solutions are absent. We prove that the cosmological solution corresponding to $(H_2, h_2)$ is stable in a class of cosmological solutions with diagonal metrics, while the solution corresponding to $(H_1, h_1)$ is unstable. We present several examples of analytical solutions, e.g. stable ones with small enough variation of the effective gravitational constant $G$, for $(m, l) = (9, l > 2), (12, 11), (11,16), (15, 6)$.

gr-qc↗

arXiv2019

Regularization by ε-metric

The regularization of propagators by means of a complex metric is considered. (The paper is an English translation of the first of two articles in Russian published by the author in 1987-88: V.D. Ivashchuk, Regularization by ε-metric. I, Izvestiya Akademii Nauk Moldavskoy SSR, Ser. Fiziko-tekhnicheskih i matematicheskih nauk, No 3, p. 8-17 (1987) [in Russian] .)

hep-th↗

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↗

arXiv2018

On generalized Melvin solutions for Lie algebras of rank 3

Generalized Melvin solutions for rank-$3$ Lie algebras $A_3$, $B_3$ and $C_3$ are considered. Any solution contains metric, three Abelian 2-forms and three scalar fields. It is governed by three moduli functions $H_1(z),H_2(z),H_3(z)$ ($z = ρ^2$ and $ρ$ is a radial variable), obeying three differential equations with certain boundary conditions imposed. These functions are polynomials with powers $(n_1,n_2, n_3) = (3,4,3), (6,10,6), (5,8,9)$ for Lie algebras $A_3$, $B_3$, $C_3$, respectively. The solutions depend upon integration constants $q_1, q_2, q_3 \neq 0$. The power-law asymptotic relations for polynomials at large $z$ are governed by integer-valued $3 \times 3$ matrix $ν$, which coincides with twice the inverse Cartan matrix $2 A^{-1}$ for Lie algebras $B_3$ and $C_3$, while in the $A_3$ case $ν= A^{-1} (I + P)$, where $I$ is the identity matrix and $P$ is a permutation matrix, corresponding to a generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The duality identities for polynomials and asymptotic relations for solutions at large distances are obtained. 2-form flux integrals over a $2$-dimensional disc of radius $R$ and corresponding Wilson loop factors over a circle of radius $R$ are presented.

hep-th↗

arXiv2018

Stable exponential cosmological solutions with two factor spaces in the Einstein-Gauss-Bonnet model with a $Λ$-term

We study $D$-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term $Λ$. We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters $H >0$ and $h$, corresponding to factor spaces of dimensions $m >2$ and $l > 2$, respectively. These solutions contain a fine-tuned $Λ= Λ(x, m, l, α)$, which depends upon the ratio $h/H = x$, dimensions of factor spaces $m$ and $l$, and the ratio $α= α_2/α_1$ of two constants ($α_2$ and $α_1$) of the model. The master equation $Λ(x, m, l,α) = Λ$ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. The explicit solution for $m = l$ is presented in Appendix. Imposing certain restrictions on $x$, we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. We also consider a subclass of solutions with small enough variation of the effective gravitational constant $G$ and show the stability of all solutions from this subclass.

gr-qc↗

arXiv2017

On generalized Melvin solution for the Lie algebra $E_6$

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra $\cal G$ is considered. The gravitational model in $D$ dimensions, $D \geq 4$, contains $n$ 2-forms and $l \geq n$ scalar fields, where $n$ is the rank of $\cal G$. The solution is governed by a set of $n$ functions $H_s(z)$ obeying $n$ ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials $H_s(z)$, $s = 1,\dots,6$, for the Lie algebra $E_6$ are obtained and a corresponding solution for $l = n = 6$ is presented. The polynomials depend upon integration constants $Q_s$, $s = 1,\dots,6$. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for $E_6$-polynomials at large $z$ are governed by integer-valued matrix $ν= A^{-1} (I + P)$, where $A^{-1}$ is the inverse Cartan matrix, $I$ is the identity matrix and $P$ is permutation matrix, corresponding to a generator of the $Z_2$-group of symmetry of the Dynkin diagram. The 2-form fluxes $Φ^s$, $s = 1,\dots,6$, are calculated.

hep-th↗

arXiv2017

On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra

A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra $\cal G$ is considered. The solution contains a metric, $n$ Abelian 2-forms and $n$ scalar fields, where $n$ is the rank of $\cal G$. It is governed by a set of $n$ moduli functions $H_s(z)$ obeying $n$ ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants $q_s$, $s = 1,\dots,n$. In the case when the conjecture on the polynomial structure for the Lie algebra $\cal G$ is satisfied, it is proved that 2-form flux integrals $Φ^s$ over a proper $2d$ submanifold are finite and obey the relations: $q_s Φ^s = 4 πn_s h_s$, where $h_s > 0$ are certain constants (related to dilatonic coupling vectors) and $n_s$ are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, $s = 1,\dots,n$. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra $\cal G$. Examples of polynomials and fluxes for the Lie algebras $A_1$, $A_2$, $A_3$, $C_2$, $G_2$ and $A_1 + A_1$ are presented.

hep-th↗

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

Dilatonic 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 considered. Here $\varepsilon = - 1$ corresponds to a ghost scalar field. These solutions are defined up to solutions of two master equations for two moduli functions, when $λ^2_i \neq 1/2$ for $\varepsilon = - 1$. Some physical parameters of the solutions are obtained: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters $β$ and $γ$. The PPN parameters do not depend on the couplings $λ_i$ and $\varepsilon$. A set of bounds on the gravitational mass and scalar charge are found by using a certain conjecture on the parameters of solutions, when $1 +2 λ_i^2 \varepsilon > 0$, $i =1,2$.

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↗

arXiv2016

On stable exponential solutions in Einstein-Gauss-Bonnet cosmology with zero variation of G

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Lambda is considered. Assuming diagonal cosmological metrics, we find, for certain non-zero Lambda new examples of solutions with an exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to submanifolds of dimensions m and l, respectively, with (m,l) = (4,2), (5,2), (5,3), (6,7), (7,5), (7,6) and D = 1 + m + l. Any of these solutions describes an exponential expansion of "our" 3-dimensional factor-space with Hubble parameter H and zero variation of the effective gravitational constant G. We also prove the stability of these solutions in the class of cosmological solutions with diagonal metrics.

gr-qc↗

arXiv2016

On exponential cosmological type solutions in the model with Gauss-Bonnet term and variation of gravitational constant

A D-dimensional gravitational model with Gauss-Bonnet term is considered. When ansatz with diagonal cosmological type metrics is adopted, we find solutions with exponential dependence of scale factors (with respect to "synchronous-like" variable) which describe an exponential expansion of "our" 3-dimensional factor-space and obey the observational constraints on the temporal variation of effective gravitational constant G. Among them there are two exact solutions in dimensions D = 22, 28 with constant G and also an infinite series of solutions in dimensions D \ge 2690 with the variation of G obeying the observational data.

gr-qc↗

arXiv2016

On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

A (n+1)-dimensional gravitational model with Gauss-Bonnet term and cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with exponential dependence of scale factors: a_i ~ exp( v^i t), i = 1, ..., n, are analysed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = \sum_{k = 1}^{n} v^k \neq 0. We prove that under certain restriction R imposed solutions with K(v) > 0 are stable while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 = v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.

hep-th↗

arXiv2016

Quantum billiards with branes on product of Einstein spaces

We consider a gravitational model in dimension D with several forms, l scalar fields and a Lambda-term. We study cosmological-type block-diagonal metrics defined on a product of an 1-dimensional interval and n oriented Einstein spaces. As an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed the conformally covariant Wheeler-DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDW equation are found in the limit of the formation of the billiard walls. These solutions reduce the problem to the so-called quantum billiard in (n + l - 1)-dimensional hyperbolic space. Several examples of quantum billiards in the model with electric and magnetic branes, e.g. corresponding to hyperbolic Kac-Moody algebras, are considered. In the case n=2 we find a set of basis asymptotic solutions to the WDW equation and derive asymptotic solutions for the metric in the classical case.

hep-th↗

arXiv2016

On multidimensional solutions in the Einstein-Gauss-Bonnet model with a cosmological term

A D-dimensional gravitational model with Gauss-Bonnet and cosmological term is considered. When ansatz with diagonal cosmological metrics is adopted, we overview recent solutions for zero cosmological term and find new examples of solutions for non-zero cosmological term and D = 8 with exponential dependence of scale factors which describe an expansion of our 3-dimensional factor-space and contraction of 4-dimensional internal space.

gr-qc↗

arXiv2015

Dilatonic dyon black hole solutions

Dilatonic black hole dyon solutions with arbitrary dilatonic coupling constant $λ\neq 0$ and canonical sign $\varepsilon = +1$ for scalar field kynetic term are considered. These solutions are defined up to solutions of two master equations for moduli funtions. For $λ^2 \neq 1/2$ the solutions are extended to $\varepsilon = \pm 1$, where $\varepsilon = -1$ corresponds to ghost (phantom) scalar field. Some physical parameters of the solutions: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters $β$ and $γ$ are obtained. It is shown that PPN parameters do not depend on scalar field coupling $λ$ and $\varepsilon$. Two group of bounds on gravitational mass and scalar charge (for fixed and arbitrary extremality parameter $μ>0$) are found by using a certain conjecture on parameters of solutions when $1 +2 λ^2 \varepsilon > 0$. These bounds are verified numerically for certain examples. By product we are led to well-known lower bound on mass which was obtained earlier by Gibbons, Kastor, London, Townsend and Traschen by using spinor techniques.

gr-qc↗