2009/10/19 by Maxim Eingorn, Alexander Zhuk · 15 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dimension (graph theory) #Extra dimensions #Gravitation #Gravitational potential #Limit (mathematics) #Newtonian potential #Noncommutative and Quantum Gravity Theories #Space (punctuation) #Spacetime #Torus #gr-qc
paper · pdf · doi:10.1088/0264-9381/27/5/055002
published in Classical and Quantum Gravity 27(5), 055002 (IOP Publishing) · LaTex file, 18 pages, 4 figures
arxiv created 2009/10/19 · openalex publication_date 2010/02/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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+d3+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 MPl(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.