Kaluza-Klein Multidimensional Models with Ricci-Flat Internal Spaces: The Absence of the KK Particles

Author:

Chopovsky Alexey12,Eingorn Maxim3ORCID,Zhuk Alexander2ORCID

Affiliation:

1. Department of Theoretical Physics, Odessa National University, Dvoryanskaya Street 2, Odessa 65082, Ukraine

2. Astronomical Observatory, Odessa National University, Dvoryanskaya Street 2, Odessa 65082, Ukraine

3. North Carolina Central University, CREST and NASA Research Centers, Fayetteville Street 1801, Durham, NC 27707, USA

Abstract

We consider a multidimensional Kaluza-Klein (KK) model with a Ricci-flat internal space, for example, a Calabi-Yau manifold. We perturb this background metrics by a system of gravitating masses, for example, astrophysical objects such as our Sun. We suppose that these masses are pressureless in the external space but they have relativistic pressure in the internal space. We show that metric perturbations do not depend on coordinates of the internal space and gravitating masses should be uniformly smeared over the internal space. This means, first, that KK modes corresponding to the metric fluctuations are absent and, second, particles should be only in the ground quantum state with respect to the internal space. In our opinion, these results look very unnatural. According to statistical physics, any nonzero temperature should result in fluctuations, that is, in KK modes. We also get formulae for the metric correction terms which enable us to calculate the gravitational tests: the deflection of light, the time-delay of the radar echoes, and the perihelion advance.

Funder

National Academy of Sciences of Ukraine

Publisher

Hindawi Limited

Subject

Nuclear and High Energy Physics

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