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We study a $$D$$-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss-Bonnet term and the cosmological constant $$\Lambda$$. We find a class of cosmological type solutions with exponential dependence of two scale factors on the variable $$u$$ (either cosmological time or a spatial coordinate), governed by two Hubble-like parameters $$H\neq 0$$ and $$h$$, corresponding to factor spaces of dimensions $$m>2$$ and $$l>2$$, respectively, and depending on the sign parameter $$\varepsilon=\pm 1$$ ($$\varepsilon=1$$ corresponds to cosmological solutions and $$\varepsilon=-1$$ to static ones). These solutions are governed by a certain master equation $$\Lambda\alpha=\lambda(x)$$ and the restriction $$\alpha\varepsilon(x-x_{+})(x-x_{-})

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 ≠ 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. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter e = ±1 before the scalar field kinetic term. Here e = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when $$\lambda_i^2 \neq 1/2$$ for e = −1. Several integrable cases, corresponding to the Lie algebras A1 + A1, A2, B2 = C2 and G2 are considered. Some physical parameters of the solutions are derived: the 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.

We deal with Einstein-Gauss-Bonnet model in dimension $D$ with a $\Lambda$-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 $\Lambda$., Comment: 9 pages, Latex, certain editing of the text (mainly in Abstract, Introduction and Conclusions) is done; few phrases and words are deleted; one reference is added

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 $\vec{\lambda}_i$ obeying $\vec{\lambda}_i (\vec{\lambda}_1 + \vec{\lambda}_2) > 0$, $i =1,2$. 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 $\vec{\lambda}_i$. For limiting strong ($a = +0$) and weak ($a = 2$) coupling cases, they coincide with the well-known results for the Schwarzschild and Reissner-Nordstr\"om 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., Comment: 13 pages, 5 (double) figures, LaTex. Subsection 3.3 is extended; two typos in formulas (22) and (30) are eliminated; 2 figures and 3 references are added; a paragraph in Sec. 1 and Remark on page 10 are added; several phrases are modified. To be published in EPJC

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 the presence of four Abelian two-form and four scalar fields. The solution is governed by four moduli functions $$H_s(z)$$ ( $$s = 1,\ldots ,4$$ ) of squared radial coordinate $$z=\rho ^2$$ 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 $$\nu $$ 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 two-form flux integrals over a two-dimensional submanifold. Dilatonic black hole analogs of the obtained Melvin-type solutions, e.g. “phantom” ones, are also considered. The phantom black holes are described by fluxbrane polynomials under consideration.

We consider a class of solutions in multidimensional gravity which generalize Melvin’s well-known cylindrically symmetric solution, originally describing the gravitational field of a magnetic flux tube. The solutions considered contain the metric, two Abelian 2-forms and two scalar fields, and are governed by two moduli functions H1(z) and H2(z) (z = ρ2, ρ is a radial coordinate) which have a polynomial structure and obey two differential (Toda-like) master equations with certain boundary conditions. These equations are governed by a certain matrix A which is a Cartan matrix for some Lie algebra. The models for rank-2 Lie algebras A2, C2 and G2 are considered. We study a number of physical and geometric properties of these models. In particular, duality identities are proved, which reveal a certain behavior of the solutions under the transformation ρ → 1/ρ; asymptotic relations for the solutions at large distances are obtained; 2-form flux integrals over 2-dimensional regions and the corresponding Wilson loop factors are calculated, and their convergence is demonstrated. These properties make the solutions potentially applicable in the context of some dual holographic models. The duality identities can also be understood in terms of the Z2 symmetry on vertices of the Dynkin diagram for the corresponding Lie algebra.

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 $z=\rho^2$ 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 $\nu$ 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., Comment: 16 pages, 1 figure, LaTex, a semi-review paper. The changes in the v2 version: two paragraphs were added into the end of Introduction with a footnote and 8 references, several typos in the text were eliminated. arXiv admin note: text overlap with arXiv:1709.09663

We study exact cosmological solutions in $D$-dimensional Einstein-Gauss-Bonnet model (with zero cosmological term) governed by two non-zero constants: $\alpha_1$ and $\alpha_2$. 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 $\alpha = \alpha_2/\alpha_1 > 0$ 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 $\alpha < 0$ 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 $(m, l) = (9, l > 2), (12, 11), (11,16), (15, 6)$., Comment: 21 pages, Latex, 3 figures, revised version, Appendix is added

A D-dimensional gravitational model with Gauss–Bonnet and cosmological terms is considered. When an ansatz with a diagonal cosmological metric is adopted, we find new examples of solutions for Λ Λ ≠ 0 and D = 8 with an exponential dependence of the scale factors, which describe expansion of our 3D factor-space and contraction of 4D internal space. We also study the stability of the solutions with static Hubble-like parameters hi and prove that two solutions with Λ = 0 in dimensions D = 22, 28, which were found earlier, are stable. For both solutions we find asymptotic relations for the effective gravitational constant.

The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an 1-dimensional interval and n oriented Einstein spaces, is chosen, 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 WDWequation are found in the limit of the formation of billiard walls which reduce the problem to the socalled quantum billiard on (n + l - 1)-dimensional hyperbolic space. Several examples of billiards in the model with {pmn} non-intersecting electric branes, e.g., corresponding to hyperbolic Kac–Moody algebras, are considered. In the classical case, any of these billiards describe a never-ending oscillating behavior of scale factors while approaching to the singularity, which is either spacelike or timelike. For n = 2 the model is completely integrable in the asymptotic regime in the clasical and quantum cases.

We obtain new examples of partially supersymmetric M-brane solutions defined on products of Ricci-flat manifolds, which contain two-dimensional Lorentzian submanifold R^{1,1}_{*}/Z_2 with one parallel spinor. The examples belong to the following configurations: M2, M5, M2-M5 and M5-M5. Among them a M2 solution with N =1/32 fractional number of preserved supersymmetries is presented. The examples with three M-branes were considered earlier in our paper with A.A. Golubtsova., Comment: 8 pages, LaTeX, no figures, 14 refs. are added

We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued 4×4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the Z2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over 2-dimensional discs and corresponding Wilson loop factors over their boundaries.

Recent results of measurements of the Avogadro constant by the method of crystal silicon spheres in connection with the planned transition to a new definition of the basic SI unit, the mole, are discussed.

The role of the fundamental constants and of measurement data on the Planck and Avogadro constants, the kelvin, and the electrical charge in the planned transition to new definitions of the four SI base units (kilogram, mole, ampere, and kelvin) based on fixed values of these constants is discussed.

We study $D$-dimensional Einstein-Gauss-Bonnet gravitational model including the Gauss-Bonnet term and the cosmological term $\Lambda$. 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 $\Lambda = \Lambda (x, m, l, \alpha)$, which depends upon the ratio $h/H = x$, dimensions of factor spaces $m$ and $l$, and the ratio $\alpha = \alpha_2/\alpha_1$ of two constants ($\alpha_2$ and $\alpha_1$) of the model. The master equation $\Lambda(x, m, l,\alpha) = \Lambda$ 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., Comment: 37 pages, Latex, 8 figures, 42 references. One typo in eq. (3.77) is eliminated, one phrase in Introduction and the last reference are omitted. To be published in GERG

A multidimensional generalization of Melvin’s solution for an arbitrary simple Lie algebra $${\mathcal {G}}$$ is considered. The gravitational model in D dimensions, $$D \ge 4$$ , contains n 2-forms and $$l \ge n$$ scalar fields, where n is the rank of $${\mathcal {G}}$$ . 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 $$H_s(z)$$ , $$s = 1,\ldots ,6$$ , for the Lie algebra $$E_6$$ are obtained and a corresponding solution for $$l = n = 6$$ is presented. The polynomials depend upon integration constants $$Q_s$$ , $$s = 1,\ldots ,6$$ . 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 the integer-valued matrix $$\nu = A^{-1} (I + P)$$ , where $$A^{-1}$$ is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the $$Z_2$$ -group of symmetry of the Dynkin diagram. The 2-form fluxes $$\Phi ^s$$ , $$s = 1,\ldots ,6$$ , are calculated.

We consider a $D$-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term $\Lambda$. We restrict the metrics to diagonal cosmological ones and find for certain $\Lambda$ 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., Comment: 16 pages, Latex, no figures, prepared for a talk at 16th Russian Gravitational Conference - International Conference on General Relativity, Cosmology and Astrophysics (Kaliningrad, 24-30 June); several typos are eliminated

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., 14 pages, 2 figures, LaTex., 2nd revised version, several words and phrases are changed or added, eq. (3.1) is modified, Remark on p. 4 is inserted. To be published in Eur. Phys. J. C. arXiv admin note: substantial text overlap with arXiv:1612.07178

Two families of composite black brane solutions are overviewed, fluxbrane and black brane ones, in a model with scalar fields and fields of forms. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions $\mathcal{H}_s $ (for fluxbranes) and H s (for black branes), obeying nonlinear differential equations with certain boundary conditions. Themaster equations for $\mathcal{H}_s $ and H s are equivalent to Toda-like equations and depend on a nondegenerate matrix A related to brane intersection rules. The functions H s and $\mathcal{H}_s $ , as was conjectured and confirmed (at least partly) earlier, should be polynomials in proper variables if A is a Cartan matrix of some semisimple finite-dimensional Lie algebra. The fluxbrane polynomials $\mathcal{H}_s $ were shown to be used for the construction of black brane polynomials H s . This approach is illustrated by examples of nonextremal electric black p-brane solutions related to Lie algebras A 2, C 2, and G 2.

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 $H_1(z),H_2(z),H_3(z)$ ($z = \rho^2$ and $\rho$ 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 $\nu$, 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 $\nu = A^{-1} (I + P)$, 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., Comment: 10 pages, Latex, 1 figure; 5th version: the abstract in the Latex file is corrected. arXiv admin note: text overlap with arXiv:1706.07856

A [Formula: see text]-dimensional Einstein–Gauss–Bonnet (EGB) model with the cosmological term [Formula: see text] is considered. We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters [Formula: see text] and [Formula: see text], corresponding to two factor spaces of dimension [Formula: see text] and obeying [Formula: see text]. We prove that the solutions, obeying [Formula: see text], are stable (in a class of cosmological solutions with diagonal metrics) for [Formula: see text] and they are unstable for [Formula: see text]. A subclass of solutions with small enough variation of the effective gravitational constant [Formula: see text] is considered. It is shown that all solutions from this subclass are stable.

We investigate all standard triple composite M-brane intersections defined on products of Ricci-flat manifolds for preserving supersymmetries in eleven-dimensional N =1 supergravity. The explicit formulae for computing the numbers of preserved supersymmetries are obtained, which generalize the relations for topologically trivial flat factor spaces presented in the classification by Bergshoeff et al. We obtain certain examples of configurations preserving some fractions of supersymmetries, e.g. containing such factor spaces as K3, C^2_{*}/Z_2, a four-dimensional pp-wave manifold and the two-dimensional pseudo-Euclidean manifold R^{1,1}_{*}/Z_2., 26 pages, LaTex, 7 figures (are changed), typos and few words are eliminated, certain notations are simplified, several phrases are added. To be published in Nuclear Physics B

Bianchi type I cosmological model in (n+1)-dimensional gravity with several forms is considered. When the electric non-composite brane ansatz is adopted, the Wheeler-DeWitt (WDW) equation for the model, written in a conformally covariant form, is analyzed. Under certain restrictions, asymptotic solutions to the WDW equation near the singularity are found, which reduce the problem to the so-called quantum billiard on the (n-1)-dimensional Lobachevsky space H^{n-1}. Two examples of quantum billiards are considered: a 2-dimensional quantum billiard for a 4D model with three 2-forms and a 9D quantum billiard for an 11D model with 120 4-forms which mimics SM2-brane sector of D=11 supergravity. For certain solutions, vanishing of the wave function at the singularity is proved., Comment: 14 pages, LaTex, no figures, several typos are eliminated

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., 4 pages, Latex, corrected version of the paper published in Grav. Cosmol. Three typos for Lambda corresponding to (m,l) = (6,7), (7,5), (7,6) are eliminated

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., 20 pages, no figures, LaTex; two Remarks (1 and 4) and 7 references are added

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., 31 pages, Latex, no figures, based on a talk at Int. Session-Conf. of the Sect. of Nucl. Phys. of PSD RAN "Physics of Fundamental Interactions", April 12-15, 2016, JINR, Dubna; few typos are eliminated, some references are updated and reordered

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., Comment: 7 pages, Latex, no figures. To be published in: Proceedings of the XII International Conference on Gravitation, Cosmology and Astrophysics, (ICGAC-12, June 28-July 5, 2015, Moscow, PFUR), Eds. J.P. Hsu and V.N. Melnikov, World Scientific Publ., Singapore, 2016

We consider a D-dimensional model of gravity with non-linear "scalar fields" as a matter source. The model is defined on the product manifold M, which contains n Einstein factor spaces. General cosmological type solutions to the field equations are obtained when n-1 factor spaces are Ricci-flat, e.g. when one space M_1 of dimension d_1 > 1 has nonzero scalar curvature. The solutions are defined up to solutions to geodesic equations corresponding to a sigma model target space. Several examples of sigma models are presented. A subclass of spherically-symmetric solutions is studied and a restricted version of "no-hair theorem" for black holes is proved. For the case d_1 =2 a subclass of latent soliton solutions is singled out., 22 pages, Latex, several phrases and 4 refs. are addes, few typos are eliminated

The latest high-precision experimental results and theoretical calculations to determine the value of the fine-structure constant α are analyzed. These indicate a possible increase in its value by approximately 0.5·10−8α compared with the CODATA data (2006). It is shown that this shift in the value of α may play an important role in the new system of units, including the solution of the problem of matching the results of measurements of the Avogadro and Planck constants obtained by different methods (in the Avogadro project and by means of the watt balance).

We review spherically symmetric solutions with a horizon in two models: (i) with scalar fields and fields of forms, and (ii) with a multi-component anisotropic fluid. The metrics of the solutions are defined on a manifold that contains a product of n − 1 Ricci-flat “internal” spaces. The solutions are governed by functions H s obeying nonlinear differential equations with certain boundary conditions. Simulation of black-brane solutions is considered, and the Hawking temperature is calculated. For the fluid solution, the post-Newtonian parameters β and Γ corresponding to the 4-dimensional section of the metric are found.

A (n + 1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For diagonal cosmological-type metrics, the equations of motion are reduced to a set of Lagrange equations. The effective Lagrangian contains two "minisuperspace" metrics on R^n. The first one is the well-known 2-metric of pseudo-Euclidean signature and the second one is the Finslerian 4-metric that is proportional to n-dimensional Berwald-Moor 4-metric. When a "synchronous-like" time gauge is considered the equations of motion are reduced to an autonomous system of first-order differential equations. For the case of the "pure" Gauss-Bonnet model, two exact solutions with power-law and exponential dependence of scale factors (with respect to "synchronous-like" variable) are obtained. (In the cosmological case the power-law solution was considered earlier in papers of N. Deruelle, A. Toporensky, P. Tretyakov and S. Pavluchenko.) A generalization of the effective Lagrangian to the Lowelock case is conjectured. This hypothesis implies existence of exact solutions with power-law and exponential dependence of scale factors for the "pure" Lowelock model of m-th order., Comment: 24 pages, Latex, typos are eliminated

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., Comment: 21 pages, 12 figures, LaTex; eq. (2.1) is modified, several sentences are added, a typo in eq. (3.13) is eliminated

A family of spherically symmetric solutions in the model with m-component anisotropic fluid is considered. The metric of the solution depends on parameters q_s, s = 1,...,m, relating radial pressures and the densities and contains (n -1)m parameters corresponding to Ricci-flat "internal space" metrics and obeying certain m(m-1)/2 ("orthogonality") relations. For q_s = 1 (for all s) and certian equations of state (p_i^s = \pm \rho^s) the metric coincides with the metric of intersecting black brane solution in the model with antisymmetric forms. A family of solutions with (regular) horizon corresponding to natural numbers q_s = 1,2,... is singled out. Certain examples of "generalized simulation" of intersecting M-branes in D=11 supergravity are considered. The post-Newtonian parameters \beta and \gamma corresponding to the 4-dimensional section of the metric are calculated., Comment: 16 pages, no figures

A family of generalized $S$-brane solutions with orthogonal intersection rules and $n$ Ricci-flat factor spaces in the theory with several scalar fields and antisymmetric forms is considered. Two subclasses of solutions with power-law and exponential behaviour of scale factors are singled out. These subclasses contain sub-families of solutions with accelerated expansion of certain factor spaces. The solutions depend on charge densities of branes, their dimensions and intersections, dilatonic couplings and the number of dilatonic fields., To appear in GRG

Black p-brane solutions for a wide class of intersection rules and Ricci-flat ``internal'' spaces are considered. They are defined up to moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra A_3 is obtained. The functions H_1, H_2 and H_3 for this solution are polynomials of degree 3, 4 and 3, correspondingly. An example of A_3-solution with three 3-branes in 12-dimensional model (suggested by N. Khviengia et al) is presented., 11 pages, Latex, to appear in Phys. Lett. B