On the degenerate phase boundaries

Abstract

The structure of the phase boundary between degenerate and nondegenerate regions in Ashtekar's gravity has been recently studied by Bengtsson and Jacobson who conjectured that the phase boundary should be always null. In this paper, we reformulate the reparametrization procedure in the mapping language and distinguish a phase boundary ∂M 1 from its image φ[∂M 1 ]. It is shown that φ[∂M 1 ] has to be null, while the nullness of ∂M 1 requires some more suitable criterion.

Classical geometry from a physical state in canonical quantum gravity

“…As there is growing evidence from various descriptions of quantum gravity that degenerate metrics should have an important role [3,15,16], researche has been promoted to study the degenerate metric in the classical Ashtekar theory as it is admitted by the formalism, including the dynamic characters of degenerate triads [17,18,19] and degenerate phase boundaries [20,21,22]. By breaking the causality, a solution to classical Ashtekar's equations was constructed in Ref.…”

Hamiltonian Analysis of 3-Dimensional Connection Dynamics in Bondi-like Coordinates

“…It is very different from the Hamiltonian analysis of gravitational theory in the literatures. Although the Hamiltonian analysis in the Ashtekar formalism permits the degenerate geometry [15,16,17], the non-degenerated geometry is mainly concerned. However, what is degenerate in the formalism is just the induced geometry on each slice, while the 3-dimensional geometry is still non-degenerate.…”

“…As a result, the geometries on the slices are always degenerate though the geometries for the spacetime are not degenerate. This is very different from the ADM formalism in which only non-degenerate geometries on slices are dealt with [1], [2] and from the Ashtekar formalism in which non-degenerate geometries on slices are mainly concerned though the degenerate geometries may be studied as well [15], [16], [17].…”

Causal structure and degenerate phase boundaries

“…Using a "covariant approach", Bengtsson and Jacobson [6] investigated the structure of the "phase boundaries" between degenerate and nondegenerate space-time regions, and conjectured that the phase boundaries should always be null provided that the metric is a "regular" solution to Ashtekar's equations, that is, solutions in which the canonical variables (A I i ,ẽ i I ) , the shift vector N i , and the lapse density, N (weight −1), all take finite value which, except for N, are allowed to vanish. In a recent paper [13], however, a degenerate phase boundary is distinguished from its image, and moreover, it is shown that the definition of the nullness of the image of the phase boundary used in Ref. 6 could not be generalized to the phase boundary itself.…”