The Shape of Multidimensional Gravity: Non-relativistic Limit
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Дата
2009
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Видавець
Astroprint
Анотація
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/r1+d
3+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 1TeV 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.
Опис
"Astrophysics and cosmology after Gamow: recent progress and new horizons" (2009, Odessa) Gamow memorial international conference dedicated to 105-th anniversary of George Gamow Program and abstracts..., August 17-23, 2009 / chairman: V.A. Smyntyna. - Odessa: Astroprint, 2009. - 40p.
Ключові слова
Multidimensional gravity, Newton’s law, hierarchy problem