2005/04/02 by Andrew Randono, Randono, Andrew
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0504010
16 pages
arxiv created 2005/04/02 · arxiv updated 2009/12/01
The Kodama State for Lorentzian gravity presupposes a particular value for the Immirzi-parameter, namely β=-i. However, the derivation of black hole entropy in Loop Quantum Gravity suggests that the Immirzi parameter is a fixed value whose magnitude is on the order of unity but larger than one. Since the Kodama state has de-Sitter spacetime as its classical limit, to get the proper radiation temperature, the Kodama state should be extended to incorporate a more physical value for β. Thus, we present an extension of the Kodama state for arbitrary values of the Immirzi parameter, β, that reduces to the ordinary Chern-Simons state for the particular value β=-i. The state for real values of β is free of several of the outstanding problems that cast doubts on the original Kodama state as a ground state for quantum general relativity. We show that for real values of β, the state is invariant under large gauge transformations, it is CPT invariant (but not CP invariant), and it is expected to be delta-function normalizable with respect to the kinematical inner product. To aid in the construction, we first present a general method for solving the Hamiltonian constraint for imaginary values of β that allows one to use the simpler self-dual and anti-self-dual forms of the constraint as an intermediate step.