A Tachyon Dust Metric in General Relativity

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Abstract
Special relativity allows the possibility of a class of particles, called tachyons, which travel with speeds greater than the speed of light in vacuum. These particles have spacelike 4-velocities. Since tachyons have energy and momentum, they will contribute to the gravitational field through the energy-momentum tensor. One question then is what types of solutions to the Einstein field equations will tachyons yield. We consider a metric which admits a four-parameter isometry group. When this metric is used in the field equations using a dust energy-momentum tensor, solutions exist only for spacelike 4-velocity of the dust. We interpret these as solutions for a tachyon dust. Exact solutions to the field equations are obtained.

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