Hypersurface-deformation algebroids and effective spacetime models

Abstract

In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie algebroid morphisms therefore allow one to relate different versions of the brackets that correspond to the same space-time structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can in some cases map the space-time structure back to the classical Riemannian form after a field redefinition. For one type of quantum corrections (holonomies), signature change appears to be a generic feature of effective space-time, and is shown here to be a new quantum space-time phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions prove the existence of classical space-time structures assumed elsewhere in models of loop quantum cosmology, but also shows the existence of additional quantum corrections that have not always been included.

Deformed General Relativity and Quantum Black Holes Interior

“…otherwise there is an anomaly and the Hamiltonian constraint is no more first class, which means that it does not generate any symmetries. This conclusion is consistent with what has already been found in the literature [62,66,68,87]. Before going further and discuss this condition, notice that in general relativity the Hamiltonian constraint is of the form (3.34) with (3.41) where the functions A and B are explicitly given by 45) which obviously satisfy the closeness condition (3.44).…”

“…Interestingly, it was realized in a series of articles [49][50][51][52][53][54] that under suitable conditions, one can construct regularizations where the deformed algebra of constraints remain closed 3 . The consequences of this deformed covariance was then investigated in depth in the context of spherically symmetric backgrounds [60][61][62] and then extended to more general symmetry reduced models in [63][64][65][66][67][68]. Phenomenological implications were explored both for inhomogeneous cosmological backgrounds as well as for black holes in [69][70][71].…”

Critical Evaluation of Common Claims in Loop Quantum Cosmology

“…A possible solution to this problem is to implement holonomy modifications in an anomaly-free way which does not break any gauge transformations but may deform the classical structure of hypersurface deformations given in [63,64]. Consistent deformations are possible in spherically symmetric models with holonomy modifications [71,72,73,74,75,76,77], but they imply a non-classical space-time structure which is related to slicing independence only in some cases, and after field redefinitions [78,79]. The latter feature not only resolves the contradiction between holonomy modifications and covariance pointed out in [11], it also shows why singularities can be resolved in loop quantum cosmology even for matter obeying the usual energy conditions: Not only the dynamics but also space-time structure become non-classical as a consequence of holonomy modifications, unhinging the mathematical foundation of singularity theorems.…”

Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity

“…Several independent studies have shown that holonomy and inverse-triad corrections from loop quantum gravity (LQG) modify hypersurface-deformation brackets for spherically symmetric gravity and related midisuperspace models [1][2][3][4][5][6][7][8][9][10], thereby realizing a deformation of general covariance [11][12][13]. These modifications are closely related [14] to anomalyfree models of perturbative cosmological inhomogeneity constructed within the same framework [15][16][17][18][19], suggesting that modified space-time structures may be a generic consequence of quantum-geometry effects in loop quantum gravity.…”