Variational Principle for Gravity with Null and Non-null boundaries: A Unified Boundary Counter-term

Abstract

It is common knowledge that the Einstein-Hilbert action does not furnish a well-posed variational principle. The usual solution to this problem is to add an extra boundary term to the action, called a counter-term, so that the variational principle becomes well-posed. When the boundary is spacelike or timelike, the Gibbons-Hawking-York counter-term is the most widely used. For null boundaries, we had proposed a counter-term in a previous paper. In this paper, we extend the previous analysis and propose a counter-term that can be used to eliminate variations of the "off-the-surface" derivatives of the metric on any boundary, regardless of its spacelike, timelike or null nature.

6 pages, no figures, accepted in Eur. Phys. J. C

Cited by in corpus (48)

• Superrotation Charge and Supertranslation Hair on Black Holes
• Gravity Degrees of Freedom on a Null Surface
• Perturbing the perturbed: Stability of quasinormal modes in presence of a positive cosmological constant
• Null Conservation Laws for Gravity
• Complexity and Behind the Horizon Cut Off
• Boundary terms of the Einstein-Hilbert action
• Boundary and Corner Terms in the Action for General Relativity
• Surface term, corner term, and action growth in F(Riemann) gravity theory
• Excavating black hole continuum spectrum: Possible signatures of scalar hairs and of higher dimensions
• A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity
• Holographic Purification Complexity
• A Dynamical Boundary for Anti-de Sitter Space
• An Alternate Path Integral for Quantum Gravity
• Renormalization of conformal infinity as a stretched horizon
• Systematic analysis of doubly charmed baryons ${\Xi }_{cc}$ and ${\Omega }_{cc}$
• Holographic complexity growth in a FLRW universe
• Entropy of a generic null surface from its associated Virasoro algebra
• de Sitter as a Resonance
• Null boundary terms for Lanczos-Lovelock gravity
• On Symplectic Form for Null Boundary Phase Space
• On the physical process first law for dynamical black holes
• Path Integrals for Causal Diamonds and the Covariant Entropy Principle
• Complexity of Hyperscaling Violating Theories at Finite Cutoff
• Covariant canonical formulations of classical field theories
• Bouncing with shear: Implications from quantum cosmology
• Entropy of a box of gas in an external gravitational field $-$ revisited
• The Weiss Variation of the Gravitational Action
• From path integrals to the Wheeler-DeWitt equation: Time evolution in spacetimes with a spatial boundary
• Weiss variation for general boundaries
• Comments on Joint Terms in Gravitational Action
• de Sitter Harmonies: Cosmological Spacetimes as Resonances
• Foliation-based quantization and black hole information
• Boundary Term in the Gravitational Action is the Heat Content of the Null surfaces
• Eddington gravity with matter: An emergent perspective
• Microscopic origin of Einstein's field equations and the raison d'être for a positive cosmological constant
• Reparameterization Dependence is Useful for Holographic Complexity
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• On the well-posed variational principle in degenerate point particle systems using embeddings of the symplectic manifold
• A novel probe of Einstein-Hilbert action: Dynamic upgradation of metric parameters
• Geometrothermodynamics for Black holes and de Sitter Space
• Complexity as a holographic probe of strong cosmic censorship
• Thin shell dynamics in Lovelock gravity
• The fate of boundary terms in dimensional reductions
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces
• Variational formalism for generic shells in general relativity
• Covariant phase space with null boundaries
• Renormalization of the Einstein-Hilbert action
• Junction conditions in a general field theory