A boundary term for the gravitational action with null boundaries

作者：Parattu Krishnamohan^*; Chakraborty Sumanta; Majhi Bibhas Ranjan; Padmanabhan T

来源：General Relativity and Gravitation, 2016, 48(7): 94.

DOI：10.1007/s10714-016-2093-7

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

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 root-g (Theta + kappa) 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.

• 出版日期2016-7