Javier Lafuente-López
A viable spacetime is one that admits a complete timelike geodesic. It is shown that a causal diffeomorphism preserving the Ricci tensor between two spacetimes is necessarily a homothety, if one of them is viable.
This paper contains 9 sections, 14 theorems, 48 equations.
Theorem 1
The necessary and sufficient condition for a connection $\overline{\nabla}$ on $M$ to be conformal is that there exists a vector field $A\in\mathfrak{X}(M)$ such that: In particular, $A=(\mathrm{grad})_{g}\sigma$, if and only if $\nabla$ and $\overline{\nabla}$ are the Levi-Civita connections associated with $g$ and $\overline{g}=e^{2\sigma}g$ respectively.
