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A Boundary Term for the Gravitational Action with Null Boundaries

Krishnamohan Parattu
(
- IUCAA, Pune
)
,
Sumanta Chakraborty
(
- IUCAA, Pune
)
,
Bibhas Ranjan Majhi
(
- IUCAA, Pune and
- Indian Inst. Tech., Guwahati
)
,
T. Padmanabhan
(
- IUCAA, Pune
)

Jan 5, 2015

28 pages

Published in:

Gen.Rel.Grav. 48 (2016) 7, 94

Published: Jun 16, 2016

e-Print:

1501.01053 [gr-qc]

DOI:

10.1007/s10714-016-2093-7

View in:

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Abstract: (Springer)

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 \sqrt{-g} \left( \Theta +\kappa \right)

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.

Note:

47 pages, no figures, title changed

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

References(40)

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