  An arbitrary local theory of a symmetric two-tensor field $H_{\mu \nu}$ in
Minkowski spacetime is considered, in which the equations of motion are
required to be compatible with a nonlinear length-fixing constraint $H_{\mu
\nu}^{2}=\pm M^{2}$ leading to spontaneous Lorentz invariance violation, SLIV
($M$ is the proposed scale for SLIV). Allowing the parameters in the Lagrangian
to be adjusted so as to be consistent with this constraint, the theory turns
out to correspond to linearized general relativity in the weak field
approximation, while some of the massless tensor Goldstone modes appearing
through SLIV are naturally collected in the physical graviton. In essence the
underlying diffeomophism invariance emerges as a necessary condition for the
tensor field $H_{\mu \nu}$ not to be superfluously restricted in degrees of
freedom, apart from the constraint due to which the true vacuum in the theory
is chosen by SLIV. The emergent theory appears essentially nonlinear, when
expressed in terms of the pure Goldstone tensor modes and contains a plethora
of new Lorentz and $CPT$ violating couplings. However, these couplings do not
lead to physical Lorentz violation once this tensor field gravity is properly
extended to conventional general relativity.
