and the generalized Kodama states.

Classical general relativity from quantum gravity and the generalized Kodama states. Abstract In this paper we investigate the relation between the CDJ matrix used for construction of the generalized Kodama states and the Weyl curvature tensor. By exploiting special self-duality relations unique to four dimensional spacetime, we show that the effects of quantum gravity in Ashtekar variables are neither in contradiction with the Einstein metric field equations of classical general relativity nor the semiclas-sical limit, and could potentially be used to corroborate both. We correlate the degrees of freedom in the quantized CDJ matrix with the corresponding degrees of freedom of the Riemann curvature tensor of spacetime for both the pure and for the generalized Kodama states. The implication is that quantum gravity in Ashtekar variables predicts distinguishable effects in the limit below the Planck scale through various consistency conditions, including a matter-induced distortion of the Weyl curvature tensor which is the main result of this work.