Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations

Abstract

We report on an old computation of propagators of massless scalar fields on an ensemble of configurations in 4D Euclidean dynamical triangulations in the collapsed (crumpled) phase. The resulting quantum average is used to construct the scale factor of a 4-D rotational invariant metric. This new scale factor is non-zero at the origin, which we assume to be caused the presence of the well-known singular structure in the collapsed phase. The scale factor depends on an overall integration constant, which is determined by comparison with the implied volume at intermediate distances. We construct a transformation to a 3-D rotational invariant metric, which reveals Euclidean black hole features at an instant in time, with a horizon separating interior and exterior parts. Effective Einstein equations in the presence of a `geometric condensate' are assumed, and computed with the software OGRe. Also explored briefly is a qualitatively different (not preferred) interpretation of the data which follows from comparison with an inversely transformed Euclidean regular black hole metric.

v4: 27 pages, 36 figures, incorporates companion "Coordinate transformations ..." (2305.16011 [gr-qc]) into one article; matches published version

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