> a black hole, but we have time backwards compared to the usual way we think of black holes
Observations of our universe are straightforwardly understood -- and predicted -- by laying matter fields on an expanding Robertson-Walker metric. The same observations are not at all easy to understand by laying matter fields on a time-reversed Oppenheimer-Snyder-like black hole metric.
The first thing you run into is that at the largest scales (i.e., where the solid angles subtended by galaxy clusters are small for observers like us) visible matter is arranged roughly isotropically and roughly homogeneously: we detect typical spiral galaxies (and more importantly various atomic line transitions associated with them, like the <https://en.wikipedia.org/wiki/Lyman-alpha_forest>) at all sorts of redshifts.
Your homework would be to generate lightlike geodesics that can reproduce these observations at any time in a black-hole-like metric. If you can do that at for a single spacelike slice of your black hole, you then would want to work on evolving that slice using e.g. the <https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...>.
Just scratching the surface of how you would go about doing that would be an interesting research project for a layperson. Among other things, you would end up learning a lot more about what's in your second paragraph, and likely develop an idea about how much work is involved in writing down even a simple "pet theory" of physical cosomology that accords with observational data. Or at least you'd have a better idea of what observational data there is that needs to be accounted for. You'd also confront all sorts of open questions about the interiors of black holes where there is significant matter; that would be timely given the recent preprint by Roy Kerr at <https://arxiv.org/abs/2312.00841>.
Ok.
> a black hole, but we have time backwards compared to the usual way we think of black holes
Observations of our universe are straightforwardly understood -- and predicted -- by laying matter fields on an expanding Robertson-Walker metric. The same observations are not at all easy to understand by laying matter fields on a time-reversed Oppenheimer-Snyder-like black hole metric.
The first thing you run into is that at the largest scales (i.e., where the solid angles subtended by galaxy clusters are small for observers like us) visible matter is arranged roughly isotropically and roughly homogeneously: we detect typical spiral galaxies (and more importantly various atomic line transitions associated with them, like the <https://en.wikipedia.org/wiki/Lyman-alpha_forest>) at all sorts of redshifts.
Your homework would be to generate lightlike geodesics that can reproduce these observations at any time in a black-hole-like metric. If you can do that at for a single spacelike slice of your black hole, you then would want to work on evolving that slice using e.g. the <https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...>.
Just scratching the surface of how you would go about doing that would be an interesting research project for a layperson. Among other things, you would end up learning a lot more about what's in your second paragraph, and likely develop an idea about how much work is involved in writing down even a simple "pet theory" of physical cosomology that accords with observational data. Or at least you'd have a better idea of what observational data there is that needs to be accounted for. You'd also confront all sorts of open questions about the interiors of black holes where there is significant matter; that would be timely given the recent preprint by Roy Kerr at <https://arxiv.org/abs/2312.00841>.