Emergent modified gravity: Covariance regained

Abstract

In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism constraints, vanish. Since the specific form taken by Poisson brackets of the constraints and of the gauge transformations and equations of motion they generate is important for general covariance to be realized, modifications of the canonical theory, suggested for instance by approaches to quantum gravity, are not guaranteed to be compatible with the existence of a covariant space-time line element. This caveat applies even if the modification preserves the number of independent gauge transformations and the modified constraints remain first class. Here, a complete derivation of covariance conditions, regained from the canonical constraints without assuming that space-time has its classical structure, is presented and applied in detail to spherically symmetric vacuum models. As a broad application, the presence of structure functions in the constraint brackets plays a crucial role, which in an independent analysis has recently been shown to lead to higher algebraic structures in hypersurface deformations given by an L-infinity bracket. The physical analysis of a related feature presented here demonstrates that, at least within the spherically symmetric setting, new theories of modified gravity are possible that are not of higher-curvature form.

arXiv comment50 pages

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Cited by in corpus (14)

• Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons
• Emergent modified gravity: The perfect fluid and gravitational collapse
• Emergent modified gravity coupled to scalar matter
• Emergent Modified Gravity
• Inequivalence of mimetic gravity with models of loop quantum gravity
• A new type of large-scale signature change in emergent modified gravity
• MONDified Gravity
• Formation of nonsingular spherical black holes with holonomy corrections
• Emergent modified gravity: Polarized Gowdy model on a torus
• Lessons for loop quantum gravity from emergent modified gravity
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• Hypersurface deformations
• Hamiltonian gravity in tetrad-connection variables
• Singularities in loop quantum cosmology