Non-relativistic limit of multidimensional gravity: exact solutions and applications

Abstract

It is found the exact solution of the Poisson equation for the multidimensional space with topology $M_{3+d}={\mathbb{R}}^3\times T^d$. This solution describes smooth transition from the newtonian behavior $1/r_3$ for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior $1/r_{3+d}^{1+d}$ in opposite limit. In the case of one extra dimension $d=1$, the gravitational potential is expressed via compact and elegant formula. These exact solutions are applied to some practical problems to get the gravitational potentials for considered configurations. Found potentials are used to calculate the acceleration for point masses and gravitational self-energy.It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale $M_{Pl(10)}$. In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one regardless of size of the extra dimensions. Nevertheless, the hierarchy problem can be solved in these models.

LaTex file, 18 pages, 4 figures

References in corpus (5)

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• Tests of the Gravitational Inverse-Square Law
• A Measurement of Newton's Gravitational Constant
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• Kaluza-Klein multidimensional models with Ricci-flat internal spaces: the absence of the KK particles
• Problematic aspects of Kaluza-Klein excitations in multidimensional models with Einstein internal spaces
• Many-body problem in Kaluza-Klein models with toroidal compactification
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• Accelerating Universe in Higher Dimensional Space Time : an alternative approach