A few questions about white holes

Question

White holes are seen in the maximally extended Schwarzschild solution, they are a region from the past that appear in the theory of eternal black holes, where the singularity exists in both infinite future and infinite past. Since time flows "looking" to the future, light rays can escape from the horizon into the universe and can never return. (ignoring the fact that it would take a infinite time)

However, I still have these questions about white holes:

1. The wikipedia article says that objects falling towards a white hole would never actually reach it's event horizon, but in the case of a eternal black hole, the white hole event horizon becomes a black hole event horizon at the future, and that any objects would eventually reach it. So that means that white holes doesn't only happen on eternal black holes? Is it possible to have a white hole in the future or a "pure" white hole?
2. How would anything escape the white hole, since it has positive mass and attracts matter? How can it's event horizon be a point of no entering?
3. If time is reversed, wouldn't the gravity wave information travelling at the speed of light be reversed as well, making it repel matter?
4. Is it absurd to say that a white hole would push matter into the past?

Thanks for reading, have a nice day.

Answer 1

1)
Light cones in the conformal diagram are at 45°. That means that an object occurring in the past in region "Universe" and moving towards region "White hole" will never cross the past event horizon, labelled "Antihorizon" in the diagram. A light ray will not either.

However in regions $r < r_s$, where $r_s$ is the Schwarzschild radius, the Schwarzschild geometry is dynamic and a spacelike hypersurface which extends from region "Universe" to region "Parallel universe" is not static. As this spacelike hypersurface is pushed forward in time (positive vertical axis of the diagram), it enters region "Black hole" and its geometry begins to change. The two asymptotically flat universes begin disconnected, each one containing a singularity at $r = 0$. As they evolve in time, their singularities join each other and form a nonsingular bridge (Einstein-Rosen bridge). The bridge enlarges until it reaches a maximum radius at the throat of $r = r_s$ and then contracts and pinches off, leaving the two universes disconnected and containing singularities at $r = 0$ once again.

An eternal black hole is a singularity in time.

2)
An object in region "White hole" follows a path within a light cone and directed forward in time (positive vertical axis of the diagram), hence it can only escape.

3)
As gravitational waves move at the speed of light, they follow a null path, that is at 45° and directed forward in time (positive vertical axis of the diagram).

4)
A white hole is a singularity in the past, out of which things appear to spring. In the diagram the time direction is the positive vertical axis.