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arXiv · 1501.01053

A Boundary Term for the Gravitational Action with Null Boundaries

Krishnamohan Parattu·Sumanta Chakraborty·Bibhas Ranjan Majhi·T. Padmanabhan
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Abstract

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 $2 \sqrt{-g} \left( Θ+κ\right)$ 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.

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Krishnamohan Parattu, Sumanta Chakraborty, Bibhas Ranjan Majhi, T. Padmanabhan. 2016-08-01. A Boundary Term for the Gravitational Action with Null Boundaries. https://doi.org/10.1007/s10714-016-2093-7

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