Carrollian minimal massive gravity and the fate of third-way consistency

Abstract

We construct the Carrollian limit of minimal massive gravity. The limit is singular for the algebra and regular for the Chern-Simons-like data. The one divergent bracket points along the null direction of the contracted bilinear form. The Lagrangian is therefore finite while the brackets are not. The contracted curvature still obeys a cubic closure condition, forced on shell rather than identically. The third-way coupling itself, however, is removable. For generic parameters an invertible redefinition of the auxiliary field and the boost connection takes it to Carrollian topologically massive gravity up to a boundary term. The same redefinition fails before the limit. We solve for an anti-de Sitter vacuum and a Carrollian black hole, whose rotation parameter leaves the frame and survives only in the boost connection. The degenerate vector flavor metric obstructs the standard charge formula, which we replace by a canonical one. The boundary charges, obtained in two independent ways, carry no trace of the deformation. A Dirac analysis gives nine first-class constraints and no local degrees of freedom on any background. The massive graviton is removed. The asymptotic symmetry algebra is bms_3, with central charges carried by the Einstein and Lorentz-Chern-Simons terms. The black hole has two sets of thermodynamic data, each with its own first law. One obeys the Bekenstein-Hawking area law, the other keeps the Chern-Simons entropy.