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

[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 → +∞.

[发布机构] Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, Toulouse; 31062, France^1

[效力级别] 数学

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