A boundary term for the gravitational action with null boundaries

Krishnamohan Parattu, Sumanta Chakraborty, Bibhas Ranjan Majhi, T. Padmanabhan

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133 Scopus citations


Constructing a well-posed variational principle is a non-trivial issue in general relativity. For spacelike and timelike boundaries, one knows that the addition of the Gibbons–Hawking–York (GHY) counter-term will make the variational principle well-defined. This result, however, does not directly generalize to null boundaries on which the 3-metric becomes degenerate. In this work, we address the following question: What is the counter-term that may be added on a null boundary to make the variational principle well-defined? We propose the boundary integral of 2-g(Θ+κ) as an appropriate counter-term for a null boundary. We also conduct a preliminary analysis of the variations of the metric on the null boundary and conclude that isolating the degrees of freedom that may be fixed for a well-posed variational principle requires a deeper investigation.

Original languageEnglish
Article number94
JournalGeneral Relativity and Gravitation
Issue number7
StatePublished - 1 Jul 2016
Externally publishedYes


  • Boundary term
  • Einstein–Hilbert action
  • General relativity
  • Gibbons–Hawking–York term
  • Null surfaces
  • Variational principle


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