  We prove in this paper that the Schwarzschild famiily of black holes are
linearly stable as a family of solutions to the system of equations that result
from expressing the Einstein vacuum equations in a generalised wave gauge. In
particular we improve on our recent work \cite{Johnsonlinstabschwarzold} by
modifying the generalised wave gauge employed therein so as to establish
asymptotic flatness of the associated linearised system. The result thus
complements the seminal work \cite{DHRlinstabschwarz} of
Dafermos-Holzegel-Rodnianski in a similar vein as to how the work
\cite{LRstabmink} of Lindblad-Rodnianski complemented that of
Christodoulou-Klainerman \cite{CKstabmink} in establishing the nonlinear
stability of the Minkowski space.
  This paper is the content of the authors PhD thesis.
