Last year Prof. Ashoke Sen proved [Soft Theorems for gravitons for generic theories of gravity][1]. The papers are exceptionally well-written and I think I understand most of it(partly due to the lecture series available online by himself) but there's a trivial thing that I'm stuck on. He says that the on-shell condition for a particle with polarisation $\epsilon_i(p_i)$ is $\epsilon^T.K = 0$. Here K is the kinetic energy operator (or the 2 point coupling matrix). I understand that I must be missing something trivial I just can't figure out what. I appreciate all the help I can get.


  [1]: https://arxiv.org/abs/1703.00024