Advances in Theoretical and Mathematical Physics

Volume 25 (2021)

Number 1

Quasi-local mass near the singularity, the event horizon and the null infinity of black hole spacetimes

Pages: 101 – 128



Nishanth Gudapati (Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts, U.S.A.)

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


The behaviour of geometric quantities close to geometric pathologies of a spacetime is relevant to deduce the physical behaviour of the system. In this work, we compute the quasi-local mass quantities: the Hawking mass, the Brown–York mass and the Liu–Yau mass in the maximal extensions of the spherically symmetric solutions of the Einstein equations inside the black hole region, at the singularity, the event horizon, and the null infinity, in the limiting sense of a geometric flow.

N. Gudapati acknowledges the support of the Gordon and Betty Moore Foundation and the John Templeton Foundation through the Black Hole Initiative of Harvard University.

S.-T. Yau acknowledges the support from NSF Grant DMS-1607871.

Published 28 September 2021