The Positive Mass Theorem

Abstract

AbstractThe important positive mass theorem roughly says that—in contrast to Newtonian gravity theory—it is impossible to construct an object out of ordinary matter, i.e., matter with positive local energy density, whose total energy (including gravitational contributions) is negative. In this chapter we will give essentially E. Witten’s proof of the positive energy theorem, which makes crucial use of spinor fields. To be complete, we develop the necessary tools on spinors in GR in an appendix to this chapter. It is very remarkable that spinors have turned out to be so useful in simplifying the proof of an entirely classical property of GR. We add some remarks on the Penrose inequality, which can be regarded as a sharpening of the positive energy theorem for black holes.KeywordsBlack HoleApparent HorizonSpinor FieldSpacelike HypersurfacePositive Mass TheoremThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.