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  • 1
    Electronic Resource
    Electronic Resource
    Billiard representation for multidimensional cosmology with intersecting p-branes near the singularity (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 6341-6363 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electromagnetic composite p-brane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N−1)-dimensional Lobachevsky space HN−1, N=n+l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of (N−2)-dimensional sphere SN−2 by pointlike sources. Some examples with billiards of finite volume and hence oscillating behavior near the singularity are considered. Among them examples with square and triangle two-dimensional billiards (e.g., that of the Bianchi-IX model) and a four-dimensional billiard in "truncated" D=11 supergravity model (without the Chern–Simons term) are considered. It is shown that the inclusion of the Chern–Simons term destroys the confining of a billiard. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1286671
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  • 2
    Electronic Resource
    Electronic Resource
    Dually charged mesoatom on the space of constant negative curvature (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 1642-1649 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The discrete spectrum solutions corresponding to dually charged mesoatom on the space of constant negative curvature are obtained. The discrete spectrum of energies is finite and vanishes when the magnetic charge of the nucleus exceeds the critical value. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531474
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  • 3
    Electronic Resource
    Electronic Resource
    Cosmological and spherically symmetric solutions with intersecting p-branes (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6558-6576 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Multidimensional model describing the cosmological evolution and/or spherically symmetric configuration with n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n "internal" spaces are Ricci-flat, one space M0 has a nonzero curvature, and all p-branes do not "live" in M0, a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically symmetric solutions (containing nonextremal p-brane black holes) is considered. Post-Newtonian parameters are calculated. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533106
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  • 4
    Electronic Resource
    Electronic Resource
    Integrable pseudo-Euclidean Toda-like systems in multidimensional cosmology with multicomponent perfect fluid (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 5829-5847 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is considered. When the vectors corresponding to the equations of state of the components are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrated and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda-like system connected with some Lie algebra G. For G=A2 exact solutions are explicitly written. A certain family of wormhole solutions is also obtained. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531290
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  • 5
    Electronic Resource
    Electronic Resource
    Multidimensional classical and quantum cosmology with intersecting p-branes (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2866-2888 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A multidimensional cosmological model describing the evolution of (n+1) Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane ansatz is adopted the field equations are reduced to the equations for the Toda-like system. The Wheeler–De Witt equation is obtained. In the case when n "internal" spaces are Ricci-flat, one space M0 has a non-zero curvature, and all p-branes do not "live" in M0; the classical and quantum solutions are obtained if certain orthogonality relations on parameters are imposed. Spherically symmetric solutions with intersecting non-extremal p-branes are singled out. A non-orthogonal generalization of intersection rules corresponding to (open, closed) Toda lattices is obtained. A chain of bosonic D≥11 models (that may be related to hypothetical higher dimensional supergravities and F-theories) is suggested. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532427
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  • 6
    Electronic Resource
    Electronic Resource
    The Birkhoff theorem in multidimensional gravity (1995)
    Springer
    General relativity and gravitation 27 (1995), S. 465-474 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The validity conditions for the extended Birkhoff theorem in multidimensional gravity withn internal spaces are formulated, with no restriction on space-time dimensionality and signature. Examples of matter sources and geometries for which the theorem is valid are given. Further generalization of the theorem is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02105073
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  • 7
    Electronic Resource
    Electronic Resource
    Integrability of Multicomponent Models in Multidimensional Cosmology (1997)
    Springer
    General relativity and gravitation 29 (1997), S. 599-612 
    Details
    ISSN: 1572-9532
    Keywords: INTEGRABLE SYSTEMS ; TODA LATTICES
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is considered. We define vectors related to the equations of state of the components. If they are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrable and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda-like system connected with some Lie algebra. The integrable vacuum (1+5+5)-model with two 5-dimensional Einstein spaces and non-zero Ricci tensors is obtained. Its reduction to a (1+5+3+2)-solution is given. For a special choice of the integration constant and one of the spaces (M1 = S5) a non-singular solution with the topology $$R^6 \times {\text{ }}M_2$$ is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018847419531
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  • 8
    Electronic Resource
    Electronic Resource
    Spontaneously broken symmetries in gravitational fields (1985)
    Springer
    General relativity and gravitation 17 (1985), S. 63-88 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In the present work we study models with material and gravitational fields unified in a self-consistent manner [2, 3]. We use a semiclassical approach, where the gravitational field is classical, but the other fields may be quantum ones. The mechanism of spontaneous symmetry breaking is due to the conformai generalization of the Higgs fields in a curved spacetime. Gravitation will be considered as a gauge field and then in the usual Einstein version.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00760107
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  • 9
    Electronic Resource
    Electronic Resource
    Toda Chains with Type Am Lie Algebra for Multidimensional m-component Perfect Fluid Cosmology (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 139-155 
    Details
    ISSN: 1572-9532
    Keywords: KASNER-LIKE SOLUTIONS ; TODA CHAIN
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a D-dimensional cosmological modeldescribing an evolution of Ricci-flat factor spaces,M1,..., Mn (n ≥ 3), in thepresence of an m-component perfect fluid source (n– 1 ≥ m ≥ 2). We find characteristicvectors, related to the matter constants in thebarotropic equations of state for fluid components ofall factor spaces. We show that, in the case where wecan interpret these vectors as the root vectorsof a Lie algebra of Cartan type A m = sl(m + 1, i), the model reduces tothe classical open m-body Toda chain. Using an eleganttechnique by Anderson for solving this system, weintegrate the Einstein equationsfor the model and present the metric in aKasner-like form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018879807859
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  • 10
    Electronic Resource
    Electronic Resource
    Gravitational vacuum hypothesis and cosmology with variable particle number (1981)
    Springer
    International journal of theoretical physics 20 (1981), S. 831-841 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We discuss a heurisitic model of gravitational vacuum as a set of virtual, radiating planckeons, particles with Planck size (L) and mass (ħ/cL). Combined with Dirac's large number hypothesis, this gives the minimum universe scale factor valuea min∼10−13 cm, the strong interaction length (a = L just whena=a min ). Taking this state as an initial one using standard quantum techniques, we consider particle creation by planckeons. Under some reasonable assumptions we obtain the present number of particles with nucleon mass close to observations,N ∼ 1080. A criterion for gravitational stability of particles is formulated and some applications of the corresponding mass formula are considered. In particular, Fermi's weak interaction constant is expressed in terms ofa andL and a finite value for the neutrino mass is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00673693
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