Brane cosmology and motion of test particles in five-dimensional warped product spacetimes

Guha, Sarbari; Chakraborty, Subenoy

doi:10.1007/s10714-010-0945-0

Cited by 11 publications

(7 citation statements)

References 40 publications

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“…G t y ) will vanish iḟ T f = 0. (14) This means that eitherṪ = 0, or f = 0. But the condition f = 0 is inadmissible, since that will represent an unwarped spacetime.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

“…The motion not only depends on t but also on the dt dλ term. It is very much clear that the system is nonautonomous and for a nonautonomous system, generally each point of the phase space is intersected by many distinct trajectories [8]. So to avoid any ambiguity we restrict our study to a particular hypersurface y = y 0 .…”

Section: When N Is Positive and C2 Is Negativementioning

confidence: 99%

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Particle Motion and Perturbed Dynamical System in Warped Product Spacetimes

Bhattacharya

Guha

2016

Int J Theor Phys

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In this paper we have used the dynamical systems analysis to study the dynamics of a fivedimensional universe in the form of a warped product spacetime with a spacelike dynamic extra dimension. We have decomposed the geodesic equations to get the motion along the extra dimension and have studied the associated dynamical system when the cross-diagonal element of the Einstein tensor vanishes, and also when it is non-vanishing. In the first case, introducing the concept of an energy function along the phase path in terms of the extra-dimensional coordinate, we have examined how the energy function depends on the warp factor. The energy function has been used as a measure of the amount of perturbation caused by a brane displacement. Geometrically the effect of brane displacement is manifested in terms of a coordinate translation along the extra dimension, thereby producing a change in the geodesic motion along the extra dimension in the region close to the brane. Then we studied the geodesic motion under a conventional metric perturbation in the form of homothetic motion and conformal motion and examined the nature of critical points for a Mashhoon-Wesson-type metric. Finally we investigated the motion for null and timelike geodesics under the condition when the cross-diagonal element of the Einstein tensor is non-vanishing and examined the effects of perturbation on the critical points of the dynamical system.

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“…G t y ) will vanish iḟ T f = 0. (14) This means that eitherṪ = 0, or f = 0. But the condition f = 0 is inadmissible, since that will represent an unwarped spacetime.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

Section: When N Is Positive and C2 Is Negativementioning

confidence: 99%

Particle Motion and Perturbed Dynamical System in Warped Product Spacetimes

Bhattacharya

Guha

2016

Int J Theor Phys

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“…A number of authors have used this method in various context (Uzan et al 2001;Dahia et al 2007;Wainwright et al 1997). For the analysis of the phase trajectories and the nature of critical points, we use the method adopted earlier (Guha et al 2010).…”

Section: Analysis Of Particle Trajectories Using the Dynamical System...mentioning

confidence: 99%

Particle motion in the field of a five-dimensional charged black hole

Guha,

Bhattacharya,

Chakraborty

2012

Astrophys Space Sci

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In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.

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“…We assume that the fifth dimension is non-compact and curved (i.e. warped) [41,62,63] and the warp factor is a function of both time, as well as of the extra dimensional coordinate [64]. Mathematically, the time dependence of the warp factor does not affect the smooth nature of the function f .…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Five-Dimensional Warped Product Space-Time with Time-Dependent Warp Factor and Cosmology of the Four-Dimensional Universe

Guha

Chakraborty²

2011

Int J Theor Phys

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In this paper, we have studied a 5-dimensional warped product space-time with a time-dependent warp factor. This warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe and leads to a geometric interpretation of dynamical dark energy. The five-dimensional field equations are constructed and its solutions are obtained. The nature of modifications produced by this warp factor in the bulk geometry is discussed. The hypersurface is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the effective cosmological constant of the four-dimensional universe is a variable quantity monitored by the time-dependent warp factor. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times.

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Brane cosmology and motion of test particles in five-dimensional warped product spacetimes

Cited by 11 publications

References 40 publications

Particle Motion and Perturbed Dynamical System in Warped Product Spacetimes

Particle Motion and Perturbed Dynamical System in Warped Product Spacetimes

Particle motion in the field of a five-dimensional charged black hole

Five-Dimensional Warped Product Space-Time with Time-Dependent Warp Factor and Cosmology of the Four-Dimensional Universe

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