arXiv subjects

A. A. Kobtsev

Publications and source records attributed to A. A. Kobtsev.

6 recordsLinked to original sources

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↗

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↗

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↗

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↗

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 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↗