Espaços-tempos estáticos e esfericamente simétricos na teoria de Rastall acoplado à um campo escalar - Santos, Edison Cesar de Oliveira (2016)
The non-conservative Rastall theory of gravity showed identical results to the ?CDM model in cosmological scales. Furthermore, in vacuum, the only non-trivial static and spherically symmetric solution are the same of general realtivity, except in a very specific case. This work presents new solutions for a canonical massless scalar field coupled to the gravity sector in terms of Rastall’s parameter a, where a = 1 returns to general relativity. It was shown that for a = -1 and a = 0 the same solutions as in the k-essence theory were retrieved, yet, the scalar field function behaves differently. For a = 3/2, implying R = 0, a potential independent solution was obtained. Regular solutions for the potential V(f) recovered exactly the same result replicated in general relativity coupled with scalar fields, however it’s intrinsically dependent on the parameter a.