Negative Mass - in General Relativity

In General Relativity

In general relativity, negative mass is generalized to refer to any region of space in which for some observers the mass density is measured to be negative. This can occur due to negative mass, or could be a region of space in which the stress component of the Einstein stress-energy tensor is larger in magnitude than the mass density. All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory. (Various versions of the positive energy condition, weak energy condition, dominant energy condition, etc., are discussed in mathematical detail by Visser.)

Morris, Thorne and Yurtsever pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time. In this article, and subsequent work by others, they showed that negative matter could be used to stabilize a wormhole. Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by negative-mass loops of cosmic string. Stephen Hawking has proved that negative energy is a necessary condition for the creation of a closed timelike curve by manipulation of gravitational fields within a finite region of space; this proves, for example, that a finite Tipler cylinder cannot be used as a time machine.