I do not think that space-time flows, rather photons and other matter flow in space-time. If E=hn does -E=-hn ie. dE=hdn? For a black hole we can use Albert's photo-electric effect but reverse it (Sammy's electro-photic effect) and use anti-matter, then we should get photons going backwards in time ie. going back to the source and let the source be the black hole. This is a linear model like simple relativity, but we could also use GR for a gravitational model.