Variational principle for gravity with null and non-null boundaries: a unified boundary counter-term

  title={Variational principle for gravity with null and non-null boundaries: a unified boundary counter-term},
  author={Krishnamohan Parattu and Sumanta Chakraborty and Thanu Padmanabhan},
  journal={The European Physical Journal C},
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… Expand
Boundary term in the gravitational action is the heat content of the null surfaces
The Einstein-Hilbert Lagrangian has no well-defined variational derivative with respect to the metric. This issue has to be tackled by adding a suitable surface term to the action, which is aExpand
On variational principle and canonical structure of gravitational theory in double-foliation formalism
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematicExpand
A Neumann Boundary Term for Gravity
The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well defined, but no such general term seems to be known for Neumann boundary conditions. In this paper, we viewExpand
Boundary and Corner Terms in the Action for General Relativity
We revisit the action principle for general relativity motivated by the path integral approach to quantum gravity. We consider a spacetime region whose boundary has piecewise $C^2$ components, eachExpand
Dynamical boundary for anti–de Sitter space
We argue that a natural boundary condition for gravity in asymptotically AdS spaces is to hold the {\em renormalized} boundary stress tensor density fixed, instead of the boundary metric. This leadsExpand
Boundary terms of the Einstein-Hilbert action
The Einstein-Hilbert action for general relativity is not well posed in terms of the metric $g_{ab}$ as a dynamical variable. There have been many proposals to obtain an well posed action principleExpand
Surface term, corner term, and action growth in F(Rabcd) gravity theory
After reformulating $F(\mathrm{Riemann})$ gravity theory as a second derivative theory by introducing two auxiliary fields to the bulk action, we derive the surface term as well as the corner termExpand
The Weiss variation of the gravitational action
The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classicalExpand
A novel derivation of the boundary term for the action in Lanczos–Lovelock gravity
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 derivationExpand
Comments on joint terms in gravitational action
This paper compares three different methods of computing joint terms in the on-shell action of gravity, which are identifying the joint term by the variational principle in the Dirichlet boundaryExpand


Boundary Terms, Variational Principles and Higher Derivative Modified Gravity
We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models ofExpand
A short note on the boundary term for the Hilbert action
One way to make the variational principle based on the Einstein–Hilbert action well-defined (i.e. functionally differentiable) is to add a surface term involving the integral of the trace of theExpand
Action Integrals and Partition Functions in Quantum Gravity
One can evaluate the action for a gravitational field on a section of the complexified spacetime which avoids the singularities. In this manner we obtain finite, purely imaginary values for theExpand
Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm
If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study severalExpand
Surface Integrals and the Gravitational Action
The authors discuss the modifications needed to free the Einstein-Hilbert action of gravitation from all second derivatives of fields, and give explicitly the resulting action applicable to eitherExpand
The unconstrained dynamical degrees of freedom of the gravitational field are identi- fied with the conformally invariant three-geometries of spacelike hypersurfaces. New results concerning theExpand
Gravitation: Foundations and Frontiers
1. Special relativity 2. Scalar and electromagnetic fields in special relativity 3. Gravity and spacetime geometry: the inescapable connection 4. Metric tensor, geodesics and covariant derivative 5.Expand
Republication of: The dynamics of general relativity
This article—summarizing the authors’ then novel formulation of General Relativity—appeared as Chap. 7, pp. 227–264, in Gravitation: an introduction to current research, L. Witten, ed. (Wiley, NewExpand
General Relativity; an Einstein Centenary Survey
List of contributors Preface 1. An introductory survey S. W. Hawking and W. Israel 2. The confrontation between gravitation theory and experiment C. M. Will 3. Gravitational-radiation experiments D.Expand
A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics
Preface Notation and conventions 1. Fundamentals 2. Geodesic congruences 3. Hypersurfaces 4. Lagrangian and Hamiltonian formulation of general relativity 5. Black holes References Index.