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

The European Physical Journal C

Krishnamohan Parattu¹  T. Padmanabhan¹  Sumanta Chakraborty¹ 

[1] IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007, Pune, India;

关键词: Boundary Term;    Normal Derivative;    Surface Gradient;    Spacetime Region;    Hilbert Action;   

DOI  :  10.1140/epjc/s10052-016-3979-y

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY