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# Advances in Theoretical and Mathematical Physics

## Volume 22 (2018)

### Number 1

### Quasi-local energy with respect to a static spacetime

Pages: 1 – 23

DOI: http://dx.doi.org/10.4310/ATMP.2018.v22.n1.a1

#### Authors

#### Abstract

This article considers the quasi-local energy in reference to a general static spacetime. We follow the approach developed by the authors in [7, 9, 19, 20] and define the quasi-local energy as a difference of surface Hamiltonians, which are derived from the Einstein–Hilbert action. The new quasi-local energy provides an effective gauge independent measurement of how far a spacetime deviates away from the reference static spacetime on a finitely extended region.

P.-N. Chen is supported by NSF grant DMS-1308164, M.-T. Wang is supported by NSF grant DMS-1405152, Y.-K. Wang is supported by MOTS in Taiwan grant 105-2115-M-006-016-MY2, and S.-T. Yau is supported by NSF grants PHY-0714648 and DMS-1308244.