A Galileon Primer
  Elementary features of galileon models are discussed at an introductory level. Following a simple example, a general formalism leading to a hierarchy of field equations and Lagrangians is developed for flat spacetimes. Legendre duality is discussed. Implicit and explicit solutions are then constructed and analyzed in some detail. Galileon shock fronts are conjectured to exist. Finally, some interesting general relativistic effects are studied for galileons coupled minimally to gravity. Spherically symmetric galileon and metric solutions with naked curvature singularities are obtained and are shown to be separated from solutions which exhibit event horizons by a critical curve in the space of boundary data. 
Thomas L. Curtright, David B. Fairlie, and Hassan Alshal
hep-th gr-qc math-ph math.MP