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 - 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

SN - 0001-7701

VL - 48

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

IS - 7

M1 - 94

ER -