Warped product spaces and geodesic motion in the neighborhood of branes

@article{Dahia2007WarpedPS,
  title={Warped product spaces and geodesic motion in the neighborhood of branes},
  author={F Dahia and C. Romero and L. F. P. da Silva and Reza Tavakol},
  journal={Journal of Mathematical Physics},
  year={2007},
  volume={48},
  pages={072501-072501}
}
We study the classical geodesic motions of nonzero rest mass test particles and photons in five-dimensional warped product spaces. We show that it is possible to obtain a general picture of these motions using the natural decoupling that occurs in such spaces between the motions in the fifth dimension and the motion in the hypersurfaces. This splitting allows the use of phase space analysis in order to investigate the possible confinement of particles and photons to hypersurfaces in five… 

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References

SHOWING 1-10 OF 40 REFERENCES

Extra force from an extra dimension. Comparison between brane theory, STM and other approaches

We investigate the question of how an observer in 4D perceives the five-dimensional geodesic motion. We consider the interpretation of null and non-null bulk geodesics in the context of brane theory,

Geodesics and Newton's law in brane backgrounds

In brane world models our universe is considered as a brane imbedded into a higher dimensional space. We discuss the behaviour of geodesics in the Randall-Sundrum background and point out that free

Geodesics, the equivalence principle and singularities in higher-dimensional general relativity and braneworlds

The geodesics of a spacetime seldom coincide with those of an embedded submanifold of co-dimension one. We investigate this issue for higher-dimensional general relativity-like models, firstly in the

Extra Force in Brane Worlds

By carefully analyzing the geodesic motion of a test particle in the bulk of brane worlds, we identify an extra force which is recognized in spacetime of one lower dimensions as a non-gravitational

The Einstein Equations on the 3-BRANE World:. a Window to Extra Dimensions

We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with $Z_2$ symmetry. We

Einstein spaces in warped geometries in five dimensions

We investigate five-dimensional Einstein spaces in warped geometries from the point of view of the four-dimensional physically relevant Robertson-Walker-Friedman cosmological metric and the

Modeling the fifth dimension with scalars and gravity

A method for obtaining solutions to the classical equations for scalars plus gravity in five dimensions is applied to some recent suggestions for brane-world phenomenology. The method involves only

On the geometry of warped spacetimes

An invariant characterization of warped spacetimes is given and a classification scheme for them is proposed. Some results on the curvature structure (Petrov and Segre types of the Weyl and Ricci