Last year Prof. Ashoke Sen proved Soft Theorems for gravitons for generic theories of gravity. 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.

Last year Prof. Ashoke Sen proved Soft Theorems for gravitons for generic theories of gravity. 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.