On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

Abstract

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.

arXiv commentTo be published in Classical and Quantum Gravity

References in corpus (2)

• Superposition of Weyl solutions: The equilibrium forces
• Two Kerr black holes with axisymmetric spins: An improved Newtonian model for the head-on collision and gravitational radiation

Cited by in corpus (5)

• Gravitating discs around black holes
• Relativistic Multipoles and the Advance of the Perihelia
• Linearized multipole solutions and their representation
• Potential-density pairs for bent bars
• Analytical potential-density pairs for bars