# Generally covariant dynamical reduction models and the Hadamard condition. (arXiv:1708.09371v2 [gr-qc] UPDATED)

We provide general guidelines for generalizing dynamical reduction models to

curved spacetimes and propose a class of generally covariant relativistic

versions of the GRW model. We anticipate that the collapse operators of our

class of models may play a r\^ole in a yet-to-be-formulated theory of

semiclassical gravity with collapses. We show explicitly that the collapse

operators map a dense domain of states that are initially Hadamard to final

Hadamard states -- a property that we expect will be needed for the

construction of such a semiclassical theory. Finally, we provide a simple

example in which we explicitly compute the violations in energy-momentum due to

the state reduction process and conclude that this violation is of the order of

a parameter of the model -- supposed to be small.