In principle, does a system of gravitational charges exhibit equivalent behavior to a time-reversed system of like electric charges? (At a single instance in time?)
I am aware that the evolution of this system would not behave the same because orbits cannot manifest in a simple system of like charges due to reasons regarding entropy; Just because it is entropically desirable to evolve from the big-bang state to the current universal state, it is not entropically desirable to evolve from the current universal state to the big-bang state just because we reversed the flow of time. (I intend to reverse the flow of time so that the fields reverse but not the global increase of entropy, this is why I specify At a single instance in time?).
I would ask that SE users to consider that the argument of playing a tape backwards is an ill conceived method for generating an answer since it always admits an unnatural evolution of state of the system (One that would never play out if entropy was increasing, I only reverse time for the sake of reversing the fields). For example if I tape an ink drop falling in water and watch it in reverse, it becomes immediately become apparent to me that it is being played in reverse because the system evolves in a way which violates the second law of thermodynamics. Even though this is true, what I can say with confidence is that every electric field of every particle will reverse in sign and the same can be said about the gravitational field. That is the true purpose of the question.
With that being said, I specify "(At a single instance in time?)" because I am more concerned with this idea on a fundamental level (i.e. The physical properties of the fields).