Mach’s principle and hidden matter

Abstract

According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor$\hat \Theta _{ik}$ satisfying the relation$\hat \Theta _{i;k}^k = 0$. The tensor$\hat \Theta _{ik}$ is formed from the Einstein-Cartan torsion field given by the anholonomy objects, F_Aik=2h_A[i,k], and appears together with Hilbert’s energy-momentum tensor T^* _ik and Poincaré’s pressure λg_ik on the right-hand side of Einstein’s equations so that one has

$$R_{ik} - (1/2)g_{ik} R = - \kappa T*_{ik} - \lambda g_{ik} - \hat \Theta _{ik}$$

According to this theory, in the universe and in cosmic systems one must excep “invisible masses” described by the Poincaré and Einstein-Cartan terms to exist. The torsion field F_Aik makes the space-time a Machian universe; it is of the same nature as the “weak interacting matter” discussed in astrophysics.