Name: Edison Cesar de Oliveira Santos
Type: MSc dissertation
Publication date: 05/09/2016
Advisor:

Name	Role
Júlio César Fabris	Advisor *

Examining board:

Name	Role
Davi Cabral Rodrigues	Internal Examiner *
Júlio César Fabris	Advisor *
Júnior Diniz Toniato	External Examiner *
Marc Casals Casanellas	External Examiner *
Oliver Fabio Piattella	Internal Examiner *

Summary: The non-conservative Rastall’s theory of gravity has shown interesting results in cosmological scales when compared to the ΛCDM model. Furthermore, in vacuum, the only non-trivial static and spherically symmetric solution is the Schwarzschild one, except in a very specific case. This work presents new solutions for a canonical nonmassive
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(ϕ) recovered exactly the same result replicated in general relativity coupled with scalar fields, however it’s intrinsically dependent on the constant a. Furthermore, it was noted that every solution for a traceless energy-momentum tensor in general relativity can be re-interpreted as a solution to Rastall’s theory.

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