Physics – High Energy Physics
Scientific paper
Jan 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1206..122e&link_type=abstract
ASTROPHYSICS AND COSMOLOGY AFTER GAMOW: Proceedings of the 4th Gamow International Conference on Astrophysics and Cosmology Afte
Physics
High Energy Physics
Poisson Equation, Gravitational Constant, Quantum Gravity, Kaluza-Klein Theory, Electrostatics, Poisson And Laplace Equations, Boundary-Value Problems, Experimental Tests Of Gravitational Theories, Quantum Gravity, Kaluza-Klein Theories
Scientific paper
It is found the exact solution of the Poisson equation for the multidimensional space with topology M3+d = R3×Td. This solution describes smooth transition from the Newtonian behavior 1/r3 for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior 1/r3+d1+d in opposite limit. In the case of one extra dimension d = 1, the gravitational potential is expressed via compact and elegant formula. Obtained formula is applied to an infinitesimally thin shell, a shell, a sphere and two spheres to show deviations from the Newtonian expressions. It is shown that the corrections to the gravitational constant in the Cavendish-type experiment can be within the measurement accuracy of Newton's gravitational constant GN. 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 1 TeV fundamental Planck scale MPl(10). In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the Newtonian one. Nevertheless, the hierarchy problem can be solved in these models.
Eingorn Maxim
Zhuk Alexander
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