Gravitational polarization of testmass potential in equilibrium polytropic sheets with nonnegative polytropic indexes
Abstract
Gravitational polarization is examined for equilibrium selfgravitating polytropic sheets perturbed by gravitational field due to test mass sheet. We find equilibrium solutions to the corresponding perturbed LaneEmden equations for nonnegative polytropic indexes. It is shown that gravitational polarization may be observed even in a finite extent of selfgravitating systems in addition to previously discussed infinite systems. In the polytropic sheets, the maximum gravitational amplification gets greater with a higher polytropic index while the height at which the maximum amplification occurs gets lower. The ratio of height change to the original height increases with polytropic index. The last result constrains the linear approximation method used for the present perturbation method.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.14876
 arXiv:
 arXiv:2303.14876
 Bibcode:
 2023arXiv230314876I
 Keywords:

 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Solar and Stellar Astrophysics;
 Condensed Matter  Statistical Mechanics;
 Physics  Fluid Dynamics