For an object that has fallen into a black hole, does the event horizon they went thru look like a white hole? This question is not asking if the event horizon is white hole and a black hole, as the answers to the linked question explain why.
The question I am asking here is more like the following.  If a Spaceman were to enter a black hole, then look up, would they see something that looks like a white hole, but is not a white hole?
The basic effects disregarding the future and past lightcones are the same, nothing can go past the event horizon (from inside the blackhole) and nothing can go past the event horizon of a white hole(from the outside of a white hole).  Putting the properties of lightcones is the only thing that differentiates the two, the black hole event horizon has the effect that any object passing thru it, has its future light cone pointing to the singularity, where as for a white hole, an object would have its future lightcone  pointing away from the singularity.  Other than that would the two only "look the same"?
 A: It depends on whether you are talking about everything you would see from that position, looking in that direction, or what the event horizon would look like.
In the former case, the answer is "No." Looking at a white hole, you would be looking inwards and all you would "see" would be the past singularity, which in the case of a static eternal black hole would be completely dark. Falling into a black hole and looking outwards you would see stars and galaxies. Completely different.
If you are talking about the appearance of event horizons before and after you get to them, then they all look the same, and they all look like ordinary empty space. Before you get to it, you cannot see it. It is in the future. To ask what the event horizon of a black hole looks like from the outside is like asking what 'next Tuesday' looks like. After you cross over you can see it (if there is anything there to see), and it looks like any other bit of past spacetime. The event horizon of a white hole looks like a patch of empty space between you and the past singularity. The event horizon of a black hole from the inside looks like a patch of empty space between you and the stars and galaxies.
Event horizons as such are nothing exotic. In fact, you are passing through countless event horizons all the time. The one-way nature of an event horizon is simply the one-way nature of the past moving through the present into the future. Nothing can escape from the future into the past, nothing that happens in the future can affect the past. It is exactly the same thing, locally. It's just that around a black hole, spacetime is twisted round so the entire future of points on the horizon is directed into the hole.
It helps a lot, in understanding black holes, to study the Rindler wedge.

This is the reference frame of a uniformly accelerated observer, like an astronaut on a continuously firing rocket. From the astronaut's point of view, the acceleration feels like gravity - it's very similar to the experience of an observer hovering a fixed distance outside a black hole (or sat on the surface of a planet). As the accelerating astronaut looks back at their own rocket exhaust, they see it receding ever faster, red-shifting into the darkness as the last few milliseconds of light are stretched out forever. The astronaut's coordinates have two event horizons - no matter how far in the future she goes, she can never see any event that happens after the future event horizon, and no matter how far in the past you go, an observer on the past horizon can never see the astronaut. The past horizon behaves like a white hole, the future horizon like a black hole.
And yet, for a non-accelerated observer watching the rocket zoom past, this is simply flat, empty Minkowski space! There is no gravity. There are no event horizons beyond which they can never see. This is much like the experience of an observer in freefall, dropping towards a black hole. To them, the event horizons are just undistinguished patches of empty space. And the reason no signal can escape is simply that signals cannot travel through any point from the future into the past.
White holes (in the static/eternal case) look black. Event horizons all look like ordinary empty space. Looking out past the horizon you see stars and galaxies. In fact, the appearance is almost exactly the same as what you would see just outside the horizon!
