The lack of rotating black hole models, which are typically found in nature, in loop quantum gravity (LQG) substantially hinders the progress of testing LQG from observations. Starting with a nonrotating LQG black hole as a seed metric, we construct a rotating spacetime using the revised Newman-Janis algorithm. The rotating solution is nonsingular everywhere and it reduces to the Kerr black hole asymptotically. In different regions of the parameter space, the solution describes (1) a wormhole without event horizon (which, we show, is almost ruled out by observations), (2) a black hole with a spacelike transition surface inside the event horizon, or (3) a black hole with a timelike transition region inside the inner horizon. It is shown how fundamental parameters of LQG can be constrained by the observational implications of the shadow cast by this object. The causal structure of our solution depends crucially only on the spacelike transition surface of the nonrotating seed metric, while being agnostic about specific details of the latter, and therefore captures universal features of an effective rotating, nonsingular black hole in LQG.

Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance in an effective Friedmann equation, but there should also be implications for a modified space-time structure. Quantum space-time effects, however, are often ignored in this setting because they are not obvious: they require a careful analysis of gauge transformations and the anomaly problem. It is shown here how modified space-time structures and effective line elements can be derived unambiguously, provided an off-shell anomaly-free system of modified constraints exists. The resulting effective line elements reveal signature change as an inescapable consequence of nonclassical gauge transformations in the presence of holonomy modifications. The general framework is then specialized to black-hole models in loop quantum gravity. In contrast to previous studies, a self-consistent space-time structure is taken into account, leading to a new picture of black-hole interiors.

Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

We show that the entropy of cosmological perturbations originating as quantum vacuum fluctuations in the very early universe, including the contribution of the leading nonlinear interactions, can be viewed as momentum space entanglement entropy between sub- and super-Hubble modes. The interactions between these modes cause decoherence of the super-Hubble fluctuations which, in turn, leads to a nonvanishing entropy of the reduced density matrix corresponding to the super-Hubble inhomogeneities. In particular, applying this to inflationary cosmology reveals that the entanglement entropy produced by leading order nonlinearities dominates over that coming from the squeezing of the vacuum state unless inflation lasts for a very short period. Furthermore, demanding that this entanglement entropy be smaller than the thermal entropy at the beginning of the radiation phase of standard cosmology leads to an upper bound on the duration of inflation which is similar to what is obtained from the trans-Planckian censorship conjecture.