 
Summary: A note on positive energy theorem for spaces
with asymptotic SUSY compactification
Xianzhe Dai
Mathematics, University of California Santa Barbara, Santa Barbara, California 93106
Received 22 November 2004; accepted 5 January 2005; published online 23 March 2005
We extend the higher dimensional positive mass theorem in Dai, X., Commun.
Math. Phys. 244, 335345 2004 to the Lorentzian setting. This includes the
original higher dimensional positive energy theorem whose spinor proof is given in
Witten, E., Commun. Math. Phys. 80, 381402 1981 and Parker, T., and
Taubes, C., Commun. Math. Phys. 84, 223238 1982 for dimension 4 and in
Zhang, X., J. Math. Phys. 40, 35403552 1999 for dimension 5. © 2005
American Institute of Physics. DOI: 10.1063/1.1862095
I. INTRODUCTION AND STATEMENT OF THE RESULT
In this note, we formulate and prove the Lorentzian version of the positive mass theorem in
Ref. 4. There we prove a positive mass theorem for spaces of any dimension which asymptotically
approach the product of a flat Euclidean space with a compact manifold which admits a nonzero
parallel spinor such as a CalabiYau manifold or any special honolomy manifold except the
quaternionic Kähler manifold . This is motivated by string theory, especially the recent work in
Ref. 7. The application of the positive mass theorem of Ref. 4 to the study of stability of Ricci flat
manifolds is discussed in Ref. 5.
