Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories
arXiv:0705.0019
Abstract
The field-theoretical approach is reviewed. Perturbations in general relativity as well as in an arbitrary -dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory. Lagrangian for perturbations is defined, and field equations for perturbations are derived from the variational principle. These equations are exact and equivalent to the equations in the standard formulation, but can be approximate also. The field-theoretical description is invariant under gauge (inner) transformations, which can be presented both in exact and approximate forms. Following the usual field-theoretical prescription, conserved quantities for perturbations are constructed. Conserved currents are expressed through divergences of superpotentials -- antisymmetric tensor densities. This form allows to relate a necessity to consider local properties of perturbations with a theoretical representation of the quasi-local nature of conserved quantities in metric theories. Applications of the formalism in general relativity are discussed. Generalized formulae for an arbitrary metric -dimensional theory are tested in the Einstein-Gauss-Bonnet gravity.
81 pages, LaTeX, 5 figures
References in corpus (81)
- A Large Mass Hierarchy from a Small Extra Dimension
- The Dynamics of General Relativity
- Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
- Non-Gaussianity from Inflation: Theory and Observations
- Gauss-Bonnet Black Holes in AdS Spaces
- Large and infinite extra dimensions
- Self-Interaction and Gauge Invariance
- Black Hole Thermodynamics and Negative Entropy in deSitter and Anti-deSitter Einstein-Gauss-Bonnet gravity
- The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes
- The General Kerr-de Sitter Metrics in All Dimensions
- Energy in Generic Higher Curvature Gravity Theories
- Entropy of Lovelock Black Holes
- Asymptotically Anti-de Sitter Space-times: Conserved Quantities
- Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
- Gravitational Energy in Quadratic Curvature Gravities
- Brane World Cosmology - Gauge-Invariant Formalism for Perturbation
- The Energy-Momentum Tensor for Cosmological Perturbations
- Asymptotic Structure of Symmetry Reduced General Relativity
- Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
- An Early Proposal of "Brane World"
- Cosmological and black hole brane-world Universes in higher derivative gravity
- Cosmological Perturbations in Brane-World Theories: Formalism
- Cosmological perturbations from multi-field inflation in generalized Einstein theories
- Relativistic conservation laws and integral constraints for large cosmological perturbations
- Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
- Gauge invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates
- Energy in Topologically Massive Gravity
- Entropy of gravitons produced in the early Universe
- Scattering of scalar waves by rotating black holes
- Asymptotically Flat Initial Data with Prescribed Regularity at Infinity
- Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes
- Vacuum energy in Einstein-Gauss-Bonnet AdS gravity
- Energy and momentum of cylindrical gravitational waves. II
- Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy
- Canonical Quasilocal Energy and Small Spheres
- Gravity waves from inflating brane or Mirrors moving in adS
- Lightcone reference for total gravitational energy
- Relic Gravitational Waves and Their Detection
- Conserved Charges of Higher D Kerr-AdS Spacetimes
- Billiard Representation for Multidimensional Cosmology with Intersecting p-branes near the Singularity
- Møller Energy for the Kerr-Newman metric
- Cosmological Dynamics
- Perturbations of brane worlds
- Quasilocal Energy-Momentum for Geometric Gravity Theories
- On Superpotentials and Charge Algebras of Gauge Theories
- On boundary conditions in three-dimensional AdS gravity
- Energy Distribution of a Charged Regular Black Hole
- Comment about quasi-isotropic solution of Einstein equations near cosmological singularity
- Relativistic Conservation Laws on Curved Backgrounds and the Theory of Cosmological Perturbations
- Slightly Bimetric Gravitation
- Hamiltonian thermodynamics of a Lovelock black hole
- On the Canonical Reduction of Spherically Symmetric Gravity
- Energy and angular momentum of the weak gravitational waves on the Schwarzschild background -- quasilocal gauge-invariant formulation
- Conservation Laws and Cosmological Perturbations in Curved Universes
- Charges and Energy in Chern-Simons Theories and Lovelock Gravity
- On Global Conservation Laws at Null Infinity
- Integrable Multidimensional Cosmology for Intersecting -Branes
- Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves
- A Time-Like Naked Singularity
- Energy Localization Invariance of Tidal Work in General Relativity
- Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies
- Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations
- Models for the Brane-Bulk Interaction: Toward Understanding Braneworld Cosmological Perturbation
- Quasilocal Center-of-Mass for Teleparallel Gravity
- Cosmological perturbations: a new gauge-invariant approach
- A note on the Deser-Tekin charges
- Null Cones in Lorentz-Covariant General Relativity
- Mass and angular momenta of Kerr anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory
- Multidimensional Cosmology for Intersecting p-Branes with Static Internal Spaces
- Spinors and the reference point of quasilocal energy
- Integral Constraints On cosmological Perturbations and their Energy
- Belinfante Tensors Induced by Matter-Gravity Couplings
- Some exact solutions in general relativity
- Physical vacuum and cosmic coincidence problem
- Observable form of pulses emitted from relativistic collapsing objects
- Backscattering of electromagnetic and gravitational waves off Schwarzschild geometry
- Conserved currents in -dimensional gravity and brane cosmology
- Waves in Schwarzschild spacetimes: How strong can imprints of the spacetime curvature be
- Perturbations in the Einstein theory of gravity: Conserved currents
- Remarks on the Bergmann-Thomsom Expression on Angular Momentum in General Relativity
- The Energy Distribution of the Bianchi Type I Universe
Cited by in corpus (19)
- Universal regularization prescription for Lovelock AdS gravity
- Gauge-Invariant Localization of Infinitely Many Gravitational Energies from All Possible Auxiliary Structures
- Gravitational Energy for GR and Poincare Gauge Theories: a Covariant Hamiltonian Approach
- Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity
- Gauge-covariant canonical formalism revisited with application to the proton spin decomposition
- Empirical Equivalence, Artificial Gauge Freedom and a Generalized Kretschmann Objection
- Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. I. General Consideration
- Noether's theorems and conserved currents in gauge theories in the presence of fixed fields
- The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review
- Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. II. Manifestly Generally Covariant Theories
- A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity
- Covariant conserved currents for scalar-tensor Horndeski theory
- Energy-momentum tensor and duality symmetry of linearized gravity in the Fierz formalism
- Gauge-Invariant Localization of Infinitely Many Gravitational Energies from all Possible Auxiliary Structures, Or, Why Pseudotensors are Okay
- On creating mass/matter by extra dimensions in the Einstein-Gauss-Bonnet gravity
- A point mass and continuous collapse to a point mass in general relativity
- Constant curvature black holes in Einstein AdS gravity: conserved quantities
- Perturbation theory of spherically symmetric self-similar black holes
- Definitions of energy for the description of gravity as the splitting theory