On A Quasi-local Mass

Preprint English OPEN
Zhang, Xiao;

We modify previous quasi-local mass definition. The new definition provides expressions of the quasi-local energy, the quasi-local linear momentum and the quasi-local mass. And they are equal to the ADM expressions at spatial infinity. Moreover, the new quasi-local ener... View more
  • References (24)
    24 references, page 1 of 3

    [1] J.D. Brown and J.W. York, Quasilocal energy in general relativity, Mathematical aspects of classical field theory (Seattle, WA, 1991), 129-142, Contemp. Math., 132, Amer. Math. Soc., Providence, RI, 1992.

    [2] J.D. Brown and J.W. York, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D(3) 47, 1407-1419 (1993).

    [3] M.P. do Carmo, F.W. Warner, Rigidity and convexity of hypersurfaces in spheres, J. Diff. Geom. 4, 133-144 (1970).

    [4] A.J. Dougan and L.J. Mason, Quasilocal mass constructions with positive energy, Phys. Rev. Lett. 67, 2119-2122 (1991).

    [5] F. Guan, Y.Y. Li, The Weyl problem with nonnegative Gauss curvature, J. Diff. Geom., 39, 331-342 (1994).

    [6] J.X. Hong, C. Zuily, Isometric embedding of the 2-sphere with nonnegative curvature in R3, Math. Z., 219, 323-334 (1995).

    [7] J. Kijowski, A simple derivation of canonical structure and quasi-local Hamiltonians in general relativity, Gen. Relat. Grav. 29, 307-343 (1997).

    [8] C-C.M. Liu and S.T. Yau, Positivity of quasilocal mass, Phys. Rev. Lett. 90, 231102 (2003).

    [9] C-C.M. Liu and S.T. Yau, Positivity of quasilocal mass II, J. Amer. Math. Soc. 19, 181 (2006).

    [10] N.O´ Murchadha, L.B. Szabados, K.P. Tod, Comment on “Positivity of quasilocal mass”, Phys. Rev. Lett. 92, 259001 (2004).

  • Metrics
Share - Bookmark