On dRGT massive gravity with degenerate reference metrics

Understand

In dRGT massive gravity, to get the equations of motion, the square root tensor is assumed to be invertible in the variation of the action.

• However, this condition can not be fulfilled when the reference metric is degenerate.
• This implies that the resulting equations of motion might be different from the case where the reference metric has full rank.
• In this paper, by generalizing the Moore-Penrose inverse to the symmetric tensor on Lorentz manifolds, we get the equations of motion of the theory with degenerate reference metric.