A Scalar-Tensor Theory of Gravitation in a Modified Riemannian Manifold

“…In consecutive investigations, Sen [3] and Sen and Dunn [4] proposed a new scalar tensor theory of gravitation and constructed an analog of Einstein's field equations based on Lyra's geometry which in normal gauge may be written as ϕ ϕ ϕ ϕ π…”

Section: Introductionmentioning

confidence: 99%

Zel’dovich Cosmological Model in Lyra Manifold

Mete¹

2017

AdAp

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Abstract. This paper deals with the study of five dimensional non -static plane symmetric cosmological model within the framework of Lyra's manifold when the source of the gravitational field is perfect fluid with pressure equal to energy density. The cosmological solutions have been analyzed through various physical and geometrical properties.Keywords: Plane symmetry, higher dimension, Lyra geometry. IntroductionAfter the formulation of general relativity (GR) by Einstein, many alternative geometric theories have been developed in order to explain gravitation phenomena. Inspired by geometrizing gravitation, Weyl [1] proposed a more general theory in which both gravitation and electromagnetism are described geometrically. For a long time, Weyl's theory was not taken seriously due to non-integrability of length of vector under parallel displacement.Lyra [2] proposed a new modification of Riemannian geometry by introducing a gauge function which removes the non-integrability condition of the length of a vector under parallel transport. This modified Riemannian geometry is known as Lyra's geometry.In consecutive investigations, Sen [3] and Sen and Dunn [4] proposed a new scalar tensor theory of gravitation and constructed an analog of Einstein's field equations based on Lyra's geometry which in normal gauge may be written as ϕ ϕ ϕ ϕ πwhere ϕ i is a displacement field and the other symbols have their usual meaning as in Riemannian geometry. According to Halford [5], the present theory predicts the same effects within observational limits, as far as the classical solar system tests are concerned. Soleng [6] has pointed out that the constant displacement field in Lyra's geometry will either include a creation field and be equal to Hoyle's creation field cosmology or contain a special vacuum field which together with the gauge vector term may be considered as a cosmological term.Several authors [7][8][9][10][11][12][13][14][15][16] have investigated various aspects of cosmological models in scalar tensor theory and cosmology within the framework of Lyra's geometry. In general relativity a non-static plane symmetric Zel'dovich universe has been obtained by Reddy and Innaiah [17]. Pradhan et.al [18] studied LRS Bianchi-I cosmological models , Singh [19] obtained a new exact solutions for local cosmic string in Lyra manifold.The unification of gravitational forces with other forces in nature is not possible in the usual four dimensional space times. Hence higher dimensional theory might be useful at early stages of the evolution of the universe. In fact, as time evolves, the standard dimensions expand while the extra dimensions shrink to the planckian dimension , which is beyond our ability to detect with the currently available experimental facilities Chatterjee et. al [20]. This fact has attracted many researchers to investigate the problems in the field of higher dimensions. Appelquist et .al [21], Rahaman et.al [22] studied higher dimensional spherically symmetric perfect fluid model in Lyra geometry, Khadekar et.al [...

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“…Lyra also introduced the notion of a gauge and in the "normal" gauge the curvature scalar is identical to that of Weyl. In subsequent investigations Sen [26], Sen and Dunn [27] proposed a new scalar-tensor theory of gravitation and constructed an analog of the Einstein field equations based on Lyra's geometry. It is, thus, possible [26] to construct a geometrized theory of gravitation and electromagnetism along the lines of Weyl's "unified" field theory without inconvenience of non-integrability length transfer.…”

Section: Introductionmentioning

confidence: 99%

Plane symmetric bulk viscous domain wall in Lyra geometry

Pradhan

Kumar

Yadav³

2007

Braz. J. Phys.

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In this paper general solutions are found for domain walls in Lyra geometry in the plane symmetric spacetime metric given by Taub. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field β. Some physical consequences of the models are also given. Finally, the geodesic equations and acceleration of the test particle are discussed.

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A Scalar-Tensor Theory of Gravitation in a Modified Riemannian Manifold

Cited by 269 publications

References 6 publications

Stiff Fluid Cosmological Models in Five Dimensional Space-Time Based On Lyra Geometry

Stiff Fluid Cosmological Models in Five Dimensional Space-Time Based On Lyra Geometry

Zel’dovich Cosmological Model in Lyra Manifold

Plane symmetric bulk viscous domain wall in Lyra geometry

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