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Foliation-generating observers under Lorentz transformations

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arxiv 2408.16513 v2 pith:LXSMVT5L submitted 2024-08-29 gr-qc math-phmath.DGmath.MP

Daniel Blixt , Alejandro Jiménez Cano , Aneta Wojnar This is my paper · ORCID
classification gr-qcmath-phmath.DGmath.MP
keywords observersexistencefoliationslorentztheoriestransformationsactingaffect
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abstract

In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic characteristics of timelike congruences (observers) and the existence of foliations orthogonal to them. We then explore how local Lorentz transformations acting on observers affect the existence of transversal foliations, provide examples, and discuss the implications of these results for the $3+1$ formulation of tetrad modified theories of gravity.

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  1. Intrinsic Torsion, Extrinsic Torsion, and the Hubble Parameter

    gr-qc 2024-12 conditional novelty 5.0 of 10

    The second fundamental form of a spatial slice in a torsional spacetime is a sum of the Hubble term and an extrinsic torsion term, producing a negative bias in Hubble estimates when torsion is neglected.

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