Warped product spaces and geodesic motion in the neighborhood of branes

Dahia, F.; Silva, Lúcio F. P. da; Romero, C.; Tavakol, Reza

doi:10.1063/1.2738750

Cited by 28 publications

(46 citation statements)

References 26 publications

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“…Thus in such co-dimension n cases, one can view the motion in extra dimensions as confined to n-tori. This generalises the case of the centre equilibrium point that was found in the co-dimension one case recently [11] and amounts to a toroidal confinement of particles in the neighbourhood of the spacetime hypersurface.…”

Section: Motion Of Massive Particles In the Neighbourhood Of The Submmentioning

confidence: 99%

“…A great deal of effort has recently gone into the study of geodesic motions in five-dimensional spaces [12]. Recently the authors studied the ability of five-dimensional warped product spaces to provide a mechanism for geodesic confinement on co-dimension one hypersurfaces, purely classically and based on gravitational effects [11]. The aim of this article is to generalise that analysis to the case of co-dimension n warped product spaces [10].…”

Section: Introductionmentioning

confidence: 99%

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Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

et al. 2008

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We study the classical geodesic motions of nonzero rest mass test particles and photons in (3 + 1 + n)-dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between the motions in the (3+1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles and photons to the (3 + 1)-spacetime submanifold. In addition to providing information regarding the motion of photons, we also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces with codimension one.

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Section: Motion Of Massive Particles In the Neighbourhood Of The Submmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

et al. 2008

Self Cite

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“…Therefore, we find that the results obtained in [17,18] are true even if we include a linear time-dependence of the warping function, provided g yy = 1.…”

Section: Motion Of Particles In the Fifth Dimensionmentioning

confidence: 62%

“…Knowledge of these points along with their stability properties can provide a lot of information about the behavior allowed by this dynamical system. For the warping function considered by us, the analysis is very similar to the one done by Dahia et al [17].…”

Section: Motion Of Particles In the Fifth Dimensionmentioning

confidence: 93%

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

Guha

Chakraborty

2010

Gen Relativ Gravit

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In the "braneworld scenario" ordinary standard model matter and nongravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the 'bulk' (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product spacetime having an exponential warping function which depends both on time as well as on the extra coordinates and a non-compact fifth dimension. Assuming that the lapse function may either be a constant or a function of both time and of the extra coordinates, we have studied the nature of the geodesics of test particles and photons and have analyzed the conditions of stability in this geometrical framework. We have also discussed the possible cosmology of the corresponding (3 + 1)-dimensional hypersurfaces.

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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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Warped product spaces and geodesic motion in the neighborhood of branes

Cited by 28 publications

References 26 publications

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

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

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

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