A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity

Abstract

We present a novel derivation of the boundary term for the action in Lanczos-Lovelock gravity, starting from the boundary contribution in the variation of the Lanczos-Lovelock action. The derivation presented here is straightforward, i.e., one starts from the Lanczos-Lovelock action principle and the action itself dictates the boundary structure and hence the boundary term one needs to add to the action to make it well-posed. It also gives the full structure of the contribution at the boundary of the complete action, enabling us to read off the degrees of freedom to be fixed at the boundary, their corresponding conjugate momenta and the total derivative contribution on the boundary. We also provide a separate derivation of the Gauss-Bonnet case.

28 pages

References in corpus (6)

• The Confrontation between General Relativity and Experiment
• Gravitational action with null boundaries
• Counterterms in Dimensionally Continued AdS Gravity
• On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations
• Boundary terms of the Einstein-Hilbert action
• Boundary and Corner Terms in the Action for General Relativity

Cited by in corpus (25)

• Inflation driven by Einstein-Gauss-Bonnet gravity
• Surface term, corner term, and action growth in F(Riemann) gravity theory
• Horndeski theories confront the Gravity Probe B experiment
• Generalized Pure Lovelock Gravity
• Lovelock action with nonsmooth boundaries
• Complexity growth of rotating black holes with a probe string
• Inverting a normal harmonic oscillator: Physical interpretation and applications
• Null boundary terms for Lanczos-Lovelock gravity
• Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term
• Comments on Joint Terms in Gravitational Action
• Weiss variation for general boundaries
• On variational principle and canonical structure of gravitational theory in double-foliation formalism
• Eddington gravity with matter: An emergent perspective
• Quasi-local energy and ADM mass in pure Lovelock gravity
• Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity
• Chern-Weil theorem, Lovelock Lagrangians in critical dimensions and boundary terms in gravity actions
• First-order Lagrangian and Hamiltonian of Lovelock gravity
• Conical defects and holography in topological AdS gravity
• Holographic BCFT Spectra from Brane Mergers
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces
• Thin shell dynamics in Lovelock gravity
• Holographic relationships in Lovelock type brane gravity
• Junction conditions for higher order gravity theories from a Gibbons-Hawking-York boundary term
• Validity of the Background Subtraction Method for Black Hole Thermodynamics in Matter-Coupled Gravity Theories
• Lovelock type brane gravity from a minimal surface perspective