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

@article{Parattu2016VariationalPF, 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}, year={2016}, volume={76}, pages={1-5} }

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

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#### References

SHOWING 1-10 OF 13 REFERENCES

Boundary Terms, Variational Principles and Higher Derivative Modified Gravity

- Physics
- 2009

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 of… Expand

A short note on the boundary term for the Hilbert action

- Physics
- 2014

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 the… Expand

Action Integrals and Partition Functions in Quantum Gravity

- Physics
- 1977

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 the… Expand

Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm

- Physics
- 2013

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 several… Expand

Surface Integrals and the Gravitational Action

- Physics
- 1983

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 either… Expand

ROLE OF CONFORMAL THREE-GEOMETRY IN THE DYNAMICS OF GRAVITATION.

- Physics
- 1972

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 the… Expand

Gravitation: Foundations and Frontiers

- Physics
- 2010

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

- Physics
- 2004

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, New… Expand

General Relativity; an Einstein Centenary Survey

- Physics
- 1979

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

- Mathematics
- 2004

Preface Notation and conventions 1. Fundamentals 2. Geodesic congruences 3. Hypersurfaces 4. Lagrangian and Hamiltonian formulation of general relativity 5. Black holes References Index.