The equivalence principle in Kaluza-Klein gravity

Abstract

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.

arXiv commentV3: The abstract and the Introduction section are improved. V4: Two more references added to the Conclusion section. Accepted for publication in IJMPD

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Cited by in corpus (9)

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• Massive test particles motion in Kaluza-Klein gravity
• Effective spacetime from multi-dimensional gravity
• Signatures of modified gravity from the gravitational Aharonov-Bohm effect
• Stars in five dimensional Kaluza Klein gravity
• Schwarzschild-like exteriors for stars in Kaluza-Klein gravity
• Astrophysical evidence for an extra dimension: phenomenology of a Kaluza Klein theory
• On the electromagnetic emission from charged test particles in a five dimensional spacetime