Advances in Theoretical and Mathematical Physics

Volume 22 (2018)

Number 1

Quasi-local energy with respect to a static spacetime

Pages: 1 – 23



Po-Ning Chen (Department of Mathematics, University of California at Riverside)

Mu-Tao Wang (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Ye-Kai Wang (Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


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.

Published 7 September 2018