(3+1)-Formulation for Gravity with Torsion and Non-Metricity II: The Hypermomentum Equation
arXiv:2107.14520 · doi:10.1088/1361-6382/ac2c1c
Abstract
In this article, we consider a special case of Metric-Affine f(R)-gravity for f(R) = R, i.e. the Metric-Affine General Relativity (MAGR). As a companion to the first article in the series, we perform the (3+1) decomposition to the hypermomentum equation, obtained from the minimization of the MAGR action S [g, ω] with respect to the connection ω. Moreover, we show that the hypermomentum tensor H could be constructed completely from 10 hypersurfaces variables that arise from its dilation, shear, and rotational (spin) parts. The (3+1) hypermomentum equations consists of 1 scalar, 3 vector, 3 matrix, and 1 tensor equation of order-(2,1). Together with the (3+1) decomposition of the traceless torsion constraint, consisting of 1 scalar and 1 vector equation, we obtain 10 hypersurface equations, which are the main result in this article. Finally, we consider some special cases of MAGR, namely, the zero hypermomentum, metric, and torsionless cases. For vanishing hypermomentum, we could retrieve the metric compatibility and torsionless condition in the (3+1) framework, hence forcing the affine connection to be Levi-Civita as in the standard General Relativity.
arXiv comment28 pages
References in corpus (41)
- f(R) Theories Of Gravity
- Modified Gravity and Cosmology
- Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
- The Dynamics of General Relativity
- Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
- Palatini Approach to Modified Gravity: f(R) Theories and Beyond
- Modified Gravity and Cosmology: An Update by the CANTATA Network
- 3+1 Formalism and Bases of Numerical Relativity
- Ghosts in metric-affine higher order curvature gravity
- Observable traces of non-metricity: new constraints on metric-affine gravity
- A New Class of Ghost and Tachyon Free Metric Affine Gravities
- Instabilities in Metric-Affine Theories of Gravity
- Constraining Torsion with Gravity Probe B
- The dynamics of metric-affine gravity
- Metric-affine Gravity and Inflation
- On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B
- Cosmological Hyperfluids, Torsion and Non-metricity
- Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
- Dynamical Aspects of Generalized Palatini Theories of Gravity
- Extension of loop quantum gravity to theories
- Constraining f(T) gravity in the Solar System
- Hyperfluid - a model of classical matter with hypermomentum
- Hamiltonian and primary constraints of new general relativity
- A First Experimental Limit on In-matter Torsion from Neutron Spin Rotation in Liquid He-4
- Loop quantum theories
- Various Hamiltonian formulations of f(R) gravity and their canonical relationships
- The Raychaudhuri equation in spacetimes with torsion and non-metricity
- Exactly Solvable Connections in Metric-Affine Gravity
- New models with independent dynamical torsion and nonmetricity fields
- Minimal coupling in presence of non-metricity and torsion
- Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
- Observational Constraints in Metric-Affine Gravity
- Constraining spacetime torsion with LAGEOS
- Cosmological Perturbations in Palatini Formalism
- Conformal inflation in the metric-affine geometry
- The Perfect Hyperfluid of Metric-Affine Gravity: The Foundation
- Linear Transformations on Affine-Connections
- Generalized Ashtekar variables for Palatini f(R) models
- Constraint propagation equations of the 3+1 decomposition of f(R) gravity
- (3+1)-Formulation for Gravity with Torsion and Non-Metricity: The Stress-Energy-Momentum Equation
- Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology