On the Nordtvedt effect in Minkowski spacetime with nonlinear connection

Abstract

The Lunar Laser Ranging (LLR) experiment provided precise data which brought the possibility to make more stringent conclusions for the foundations of gravitational theories, i.e. the Equivalence Principles. Beside some effects of non - gravitational origin, the LLR data was fitted with the well-known gravitational effects such as the apsidal and geodetic precessions, the time delay, etc. The Nordtvedt effect in General Relativity (GR) vanishes, while the LLR experiment data of the Earth-Moon distance and the laboratory experiments with experimental bodies made of different chemical compositions measured a variation of distance in millimeters. According to the mathematical model of gravitation in Minkowski space endowed with a nonlinear connection we obtained a result closer to the experimental measurements. More precisely, we obtained a difference of 0.17 mm (or 0.28 mm, depending on the value of the scaling factor) from the LLR measurements of the variation of the Earth-Moon distance, while the corresponding result in GR makes a difference from the LLR measurements of 5.7 mm. The gravitational theory with nonlinear connection in Minkowski space gives the same results for the confirmed GR effects, nevertheless it yields some additional variations of the distance concerning the Nordtvedt effect.