The equivalence principle in Kaluza-Klein gravity
| dc.creator | de Leon, J. Ponce | |
| dc.date | 2007-03-19 | |
| dc.date | 2008-05-08 | |
| dc.date.accessioned | 2026-07-07T13:05:09Z | |
| dc.date.available | 2026-07-07T13:05:09Z | |
| dc.description | In four-dimensional general relativity the spacetime outside of an isolated spherical star is described by a unique line element, which is the Schwarzschild metric. As a consequence, the "gravitational" mass and the "inertial" mass of a star are equal to each other. However, theories that envision our world as embedded in a larger universe, with more than four dimensions, permit a number of possible non-Schwarzschild 4D exteriors, which typically lead to {\it different} masses, violating the weak equivalence principle of ordinary general relativity. Therefore, the question arises of whether the violation of this principle, i.e., the equality of gravitational and inertial mass, is a necessary consequence of the existence of extra dimensions. In this paper, in the context of Kaluza-Klein gravity in 5D, we show that the answer to this question is negative. We find a one-parameter family of asymptotically flat non-Schwarzschild static exteriors for which the inertial and gravitational masses are equal to each other, and equal to the Deser-Soldate mass. This family is consistent with the Newtonian weak-field limit as well as with the general-relativistic Schwarzschild limit. Thus, we conclude that the existence of an extra dimension, and the corresponding non-Schwarzschild exterior, does not necessarily require different masses. However, to an observer in 4D, it does affect the motion of test particles in 4D, which is a consequence of the departure from the usual $(4D)$ law of geodesic motion. | |
| dc.description | V3: The abstract and the Introduction section are improved. V4: Two more references added to the Conclusion section. Accepted for publication in IJMPD | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0703094 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0703094 | |
| dc.identifier | Int.J.Mod.Phys.D18:251-273,2009 | |
| dc.identifier | doi:10.1142/S0218271809014418 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227400 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | The equivalence principle in Kaluza-Klein gravity | |
| dc.type | text |