Abstract
We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtain Heisenberg ⊕ Virasoro algebra with a central charge proportional to the gravitational Chern-Simons term of TMG. We also discuss that the flux of the chiral massive gravitons appears as the (Bondi) news through the null surface.
Highlights
Degrees of freedom which only reside at the boundary and do not propagate into the bulk, the boundary degrees of freedom (BDoF)
We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG)
In gauge or gravity theories BDoF can be conveniently labelled through surface charges associated with a certain sector of gauge symmetries which preserves the boundary structure and rotate us in the solution phase space
Summary
We perform the null boundary symmetry analysis for an arbitrary null surface in TMG and construct the maximal boundary phase space. Our charge analysis involves three steps: (1) finding appropriate slicing of the phase space; (2) fixing the Y -ambiguity and (3) separating the integrable part of charge and identifying the flux These three steps should be worked through in accord with each other. Going through these steps and after a tedious and technical analysis, we find that the charge algebra for the generic NVCT case is a Heisenberg ⊕ Virasoro algebra where the central charge is the gravitational anomaly of the theory It is the same algebra (1.1) as for the VCT but with the modified bracket.. We study charges of axisymmetric TMG solutions, including the warped black holes [58], and show that they have a vanishing expansion aspect charge and fall in the same category as non-expanding backgrounds in the VCT class
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