Surface gravity requires a metric and a time normalization

In the supplied Em03-A source, the Schwarzschild metric and normalized exterior Killing time are inputs to its surface-gravity calculation, giving $\kappa =1/(4GM)$ in the stated units CheungEm03A. Record record:correspondence supplies neither that metric nor the identification of its Killing generator with $L_0$.

Moreover, if a Killing generator $\xi$ satisfies

on its horizon, then ${\xi }^{\prime }=a\xi$, $a>0$, satisfies

Surface gravity therefore also depends on the generator normalization. A chiral mode bound cannot fix that absent identification.

The Em03 exterior-source records keep radiated energy, switching work, backreaction, and a mass-loss equation separate CheungEm03FG. A work ledger is not a gravitational mass-loss law.