Finite Action Principle and Horava-Lifshitz Gravity: early universe, black holes and wormholes

Abstract

The destructive interference of the neighbouring field configurations with infinite classical action in the gravitational path integral approach serves as a dynamical mechanism resolving the black hole singularity problem. It also provides an isotropic and homogeneous early universe without the need of inflation. In this work, we elaborate on the finite action in the framework of Horava-Lifshitz gravity-a ghostfree QFT. Assuming the mixmaster chaotic solutions in the projectable H-L theory, we show that the beginning of the universe is homogeneous and isotropic. Furthermore, we show that the H-L gravity action selects only the regular black-hole spacetimes. We also comment on possibility of traversable wormholes in theories with higher curvature invariants.

Action principle selection of regular black holes

“…Therefore, the integration over all possible geometries selects with higher weight the spacetime configurations for which the action is finite. (Earlier considerations on the finite action principle were formulated in [14]; see also [15][16][17][18] for a more recent discussion and further applications.) We remind that in the path integral (1) all kinds of metrics are included, not only those which are solutions of the classical equations of motion.…”