Main Question or Discussion Point
Since black holes takes matter to a singularity, theoretically could there be a hole that does the opposite? As in push everything away like negative pressure.
Not really. A white hole has attractive gravity, not repulsive gravity. See below.A white hole, which does exactly what you proposed
No. A black hole, and its time reverse, a white hole, are both vacuum solutions; there is zero pressure everywhere (and also zero energy density). The white hole has things coming out of it and decelerating as they rise away. The black hole has things falling into it and accelerating as they fall. Gravity is attractive in both cases.could there be a hole that does the opposite? As in push everything away like negative pressure.