https://doi.org/10.1140/epjc/s10052-016-3979-y
Regular Article - Theoretical Physics
Variational principle for gravity with null and non-null boundaries: a unified boundary counter-term
IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune, 411 007, India
* e-mail: sumantac.physics@gmail.com
** e-mail: sumanta@iucaa.in
Received:
17
November
2015
Accepted:
19
February
2016
Published online:
8
March
2016
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 propose a counter-term that can be used to eliminate variations of the “off-the-surface” derivatives of the metric on any boundary, regardless of its spacelike, timelike or null nature.
© The Author(s), 2016
