Gravitational dynamics in a 2+1+1 decomposed spacetime along nonorthogonal double foliations: Hamiltonian evolution and gauge fixing
arXiv:1905.00039 · doi:10.1103/PhysRevD.99.104071
Abstract
Motivated by situations with temporal evolution and spatial symmetries both singled out, we develop a new 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation. Time evolution proceeds along the leaves of the spatial foliation. We identify the gravitational variables in the velocity phase-space as the 2-metric (induced on the intersection of the hypersurfaces of the foliations), the 2+1 components of the spatial shift vector, together with the extrinsic curvature, normal fundamental form and normal fundamental scalar of , all constructed with the normal to the temporal foliation. This work generalizes a previous decomposition based on orthogonal foliations, a formalism lacking one metric variable, now reintroduced. The new metric variable is related to (i) the angle of a Lorentz-rotation between the nonorthogonal bases adapted to the foliations, and (ii) to the vorticity of these basis vectors. As a first application of the formalism, we work out the Hamiltonian dynamics of general relativity in terms of the variables identified as canonical, generalizing previous work. As a second application we present the unambiguous gauge-fixing suitable to discuss the even sector scalar-type perturbations of spherically symmetric and static spacetimes in generic scalar-tensor gravitational theories, which has been obstructed in the formalism of orthogonal double foliation.
arXiv comment16 pages, 4 figures, to appear in Phys. Rev. D
References in corpus (35)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
- GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
- GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
- GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
- GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
- Tests of general relativity with GW150914
- GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
- Generalized G-inflation: Inflation with the most general second-order field equations
- From k-essence to generalised Galileons
- Dark Energy after GW170817: dead ends and the road ahead
- Strong constraints on cosmological gravity from GW170817 and GRB 170817A
- Dark Energy after GW170817 and GRB170817A
- Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
- Healthy theories beyond Horndeski
- Essential Building Blocks of Dark Energy
- A 3+1 perspective on null hypersurfaces and isolated horizons
- Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models
- Constraining Lorentz-violating, Modified Dispersion Relations with Gravitational Waves
- Vainshtein screening in a cosmological background in the most general second-order scalar-tensor theory
- Black hole perturbation in the most general scalar-tensor theory with second-order field equations I: The odd-parity sector
- Black hole perturbation in the most general scalar-tensor theory with second-order field equations II: the even-parity sector
- Effective theory for the Vainshtein mechanism from the Horndeski action
- A covariant approach for perturbations of rotationally symmetric spacetimes
- Covariant Perturbations of Schwarzschild Black Holes
- Testing Gravity Using Galaxy Clusters: New Constraints on Beyond Horndeski Theories
- A generalized Damour-Navier-Stokes equation applied to trapping horizons
- Effective field theory of modified gravity with two scalar fields: dark energy and dark matter
- Screening the fifth force in the Horndeski's most general scalar-tensor theories
- Midi-superspace Models of Canonical Quantum Gravity
- Effective field theory of modified gravity on the spherically symmetric background: leading order dynamics and the odd-type perturbations
- Constraints as evolutionary systems
- Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory
- Gravitational dynamics in s+1+1 dimensions