zbMATH — the first resource for mathematics

Gravitationally non-degenerate Petrov type-I cosmological model filled with viscous fluid in modified Brans-Dicke cosmology. (English) Zbl 1300.83046
Summary: Adding the cosmological term, which is assumed to be variable in Brans-Dicke theory, we have discussed about a cylindrically symmetric cosmological model filled with viscous fluid with free gravitational field of a non-degenerate Petrov type-I. The effect of viscosity on various kinematical parameters has been discussed. Finally, this model has been transformed to the original form [C. Brans and R. H. Dicke, Phys. Rev., II. Ser. 124, 925–935 (1961; Zbl 0103.21402)] of Brans-Dicke theory (including a variable cosmological term).
83F05 Cosmology
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
Full Text: DOI
[1] Petrosian, V, No article title, Int. Astron. Union Symp., 63, 31, (1975)
[2] Zel’dovich, YB, The cosmological constant and the theory of elementary particles, Sov. Phys. Usp., 11, 381-393, (1968)
[3] Linde, AD, Is the Lee constant a cosmological constant, JETP Lett., 19, 183, (1974)
[4] Drietlein, J, Broken symmetry and the cosmological constant, Phys. Rev. Lett., 33, 1243-1244, (1974)
[5] Brans, CH; Dicke, RH, Mach’s principle and a relativistic theory of gravitation, Phys. Rev., 124, 925-935, (1961) · Zbl 0103.21402
[6] Morganstern, RE, Brans-Dicke cosmologies in arbitrary units: solutions in flat Friedmann universes, Phys. Rev. D, 4, 278-282, (1971)
[7] Morganstern, RE, Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes, Phys. Rev. D, 4, 946-954, (1971) · Zbl 1107.83328
[8] Morganstern, RE, Exact solutions to radiation-filled Brans-Dicke cosmologies, Phys. Rev. D, 4, 282-286, (1971)
[9] Morganstern, RE, Cosmological upper limit on the time variation of G, Nature, 232, 109-110, (1971)
[10] Morganstern, RE, Observational constraints imposed by Brans-Dicke cosmologies, Phys. Rev. D, 7, 1570-1579, (1973)
[11] Miyazaki, A, Cosmological solutions for the homogeneous isotropic universe in the Brans-Dicke theory, Prog. Theor. Phys., 60, 321-323, (1978)
[12] Milne, E.A., Mc Crea, W.H.: Newtonian universes and the curvature of space. Quart. J. Math. Oxford Ser. 5, 73-80 · Zbl 0009.04203
[13] Fujii, Y, Scalar-tensor theory of gravitation and spontaneous breakdown of scale invariance, Phys. Rev., D9, 874-876, (1974)
[14] Endo, M; Fukui, T, The cosmological term and a modified Brans-Dicke cosmology gen, Relativ. Gravit., 8, 833-839, (1977)
[15] Dirac, PAM, The cosmological constants, Nature, 139, 323, (1937) · Zbl 0016.18504
[16] Dirac, PAM, Long range forces and broken symmetries, Proc. R. Soc. Lond. A, 333, 403-418, (1973)
[17] Ellis, G.F.R.: In: Sachs, R.K. (ed.) General Relativity and Cosmology, p. 124. Academic, New York and London (1971)
[18] Bergmann, PG, Comments on the scalar-tensor theory, Int. J. Theor. Phys., 1, 25-36, (1968)
[19] Wagoner, RV, Scalar-tensor theory and gravitational waves, Phys. Rev. D, 1, 3209-3216, (1970) · Zbl 06749961
[20] Landau, L.D., Lifschitz, E.M.: Courses of theoretical physics. In: Fluid Mechanics, vol. 6, p. 505. Pergamon Press, Oxford (1963)
[21] Dicke, RH, Mach’s principle and invariance under transformation of units, Phys. Rev., 125, 2163-2167, (1962) · Zbl 0113.45101
[22] Marder, L, Gravitational waves in general relativity. II. the reflexion of cylindrical waves. proc, R. Soc. Lond. A, 246, 133-143, (1958) · Zbl 0080.21801
[23] Roy, SR; Singh, PN, Some viscous fluid cosmological models of plane symmetry, J. Phys. A: Math. Gen., 9, 255-268, (1976)
[24] Ellis, G.F.R.: In: Sachs, R.K. (ed.) General relativity and cosmology, p. 117. Academic, New York and London (1971)
[25] Roy, SR; Prakash, S, A gravitationally non-degerate viscous fluid cosmological model in general relativity, Indian J. Pure Appl. Math., 8, 723-727, (1977)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.