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Linearized gravity with matter time
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DOI：10.1088/0264-9381/33/10/105012.png)
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Abstract
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We study general relativity with pressureless dust in the canonical formulation, with the dust field chosen as a matter time gauge. The resulting theory has three physical degrees of freedom in the metric field. The linearized canonical theory reveals two graviton modes and a scalar mode. We find that the graviton modes remain Lorentz covariant despite the time gauge, and that the scalar mode is ultralocal. We also discuss a modification of the theory to include a parameter in the Hamiltonian that is analogous to that in Horava-Lifshitz models. In this case the scalar mode is no longer ultralocal and it acquires a propagation speed that is dependent on the deformation parameter.
Keywords:
canonical gravity
linearized theory
quantum gravity
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