Geometric mean of bimetric spacetimes

Abstract We use the geometric mean to parametrize metrics in Hassan–Rosen ghost-free bimetric theory and pose initial-value problem. The of two positive definite symmetric matrices is a well-established mathematical notion which can be under certain conditions extended quadratic forms having Lorentzian signature, say g f . In such case, null cone metric h middle cones appearing as average spacetime. parametrization based on ensures reality square root interaction potential. Subsequently, we derive standard n + 1 decomposition frame adapted state problem, that is, evolution equations, constraints, preservation constraints equation.