TY - JOUR

T1 - A boundary term for the gravitational action with null boundaries

AU - Parattu, Krishnamohan

AU - Chakraborty, Sumanta

AU - Majhi, Bibhas Ranjan

AU - Padmanabhan, T.

N1 - Funding Information:
The research of TP is partially supported by J. C. Bose research Grant of DST, India. KP and SC are supported by the Shyama Prasad Mukherjee Fellowship from the Council of Scientific and Industrial Research (CSIR), India. KP would like to thank Kinjalk Lochan for discussions.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

KW - Boundary term

KW - Einstein–Hilbert action

KW - General relativity

KW - Gibbons–Hawking–York term

KW - Null surfaces

KW - Variational principle

UR - http://www.scopus.com/inward/record.url?scp=84976385029&partnerID=8YFLogxK

U2 - 10.1007/s10714-016-2093-7

DO - 10.1007/s10714-016-2093-7

M3 - Article

AN - SCOPUS:84976385029

VL - 48

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

SN - 0001-7701

IS - 7

M1 - 94

ER -