Foliation-generating observers under Lorentz transformations

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.

18 pages, more examples added, accepted for publication

References in corpus (19)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Teleparallel Gravity: From Theory to Cosmology
• The covariant formulation of f(T) gravity
• Good and bad tetrads in f(T) gravity
• Modified Gravity and Cosmology: An Update by the CANTATA Network
• Cosmological perturbations in modified teleparallel gravity models
• Beyond Einstein-Cartan gravity: Quadratic torsion and curvature invariants with even and odd parity including all boundary terms
• General Teleparallel Quadratic Gravity
• Regularizing role of teleparallelism
• Remnant group of local Lorentz transformations in f(T) theories
• A special exact spherically symmetric solution in f(T) gravity theories
• The $3+1$ Formalism in the Geometric Trinity of Gravity
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Regularization of $f(T)$ gravity theories and local Lorentz transformation
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• New proper tetrad for teleparallel gravities in non-flat spacetime
• On the space-times admitting two shear-free geodesic null congruences
• Darboux coordinates for the Hamiltonian of first order Einstein-Cartan gravity
• Kinematics in Metric-Affine Geometry