VIOLATION OF γ IN BRANS-DICKE GRAVITY

The Brans Class I solution in Brans-Dicke gravity is a staple in the study of gravitational theories beyond General Relativity. Discovered in 1961, it describes the exterior vacuum of a spherical Brans-Dicke star and is characterized by two adjustable parameters. Surprisingly, the relationship between these parameters and the properties of the star has not been rigorously established. In this Proceeding, we bridge this gap by deriving the complete exterior solution of Brans Class I, expressed in terms of the total energy and total pressure of the spherisymmetric gravity source. The solution allows for the exact derivation of all post-Newtonian parameters in Brans-Dicke gravity for far field regions of a spherical source. Particularly for the gamma parameter, instead of the conventional result gamma PPN=(omega+1)/(omega+2), we obtain the analytical expression gamma exact=(omega+1+(omega+2)Theta)/(omega+2+(omega+1)Theta) where Theta is the ratio of the total pressure P-parallel to(& lowast;)+2P(perpendicular to )(& lowast;)and total energy E-& lowast; contained within the mass source. Our non-perturbative gamma formula is valid for all field strengths and types of matter comprising the mass source. Consequently, observational constraints on gamma thus set joint bounds on omega and Theta, with the latter representing a global characteristic of the mass source. More broadly, our formula highlights the importance of pressure (when Theta not equal 0) in spherical Brans-Dicke stars, and potentially in stars within other modified theories of gravitation.