Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit

10th Mexican School on Gravitation and Mathematical Physics: "Reaching a Century: Classical and Modified General Relativity's Attempts to explain de evolution of the Universe"'

物理学;数学

Suárez, Abril^1 ; Chavanis, Pierre-Henri^1

Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, Toulouse

31062, France^1

关键词: Arbitrary potentials;    Einstein equations;    Gravitational potential;    Hydrodynamic equations;    Klein-Gordon equation;    Nonrelativistic;    Scalar fields;    Schrodinger-Poisson equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/654/1/012008/pdf
DOI  :  10.1088/1742-6596/654/1/012008

来源: IOP

【 摘 要 】

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with an arbitrary potential of the form V(|φ|2). We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrodinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c → +∞.