Answer 1:
Theoretically, a white hole does exists,
because it (together with its paired black
hole) is a solution of the Einstein's
equation for gravity. But to "find" a white
hole is difficult.
A white hole is connected with a black hole
through a "worm hole", or an
Einstein-Rosen bridge.
A brave adventurer has to enter a black hole
horizon, and if he survives all the extreme
conditions in that hell of twisted space-time, he
may exit through a white hole and claim success.
But, as Thorne carefully studied before,
the condition that permits an adventurer to
pass through the worm hole is almost
impossible. And, a less brave observer far
from the black hole, who plans to videotape what
happens to the adventurer, will never see him
enter the black hole, because of the "infinite
red shift" at the horizon of the black hole,
namely time is infinitely dilated at the black
hole horizon.
But if we do not want adventurers to risk their
lives, it is possible to observe some signature
of white hole through, say, gamma ray burst.
This was proposed about 10 years ago, but I am not
sure how firmly it is established now.
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Answer 2:
No - the big bang did not expand out into a
void. The big bang was a rapid expansion of
space itself, with all of the matter and energy
located in space being more-or-less carried along
for the ride.
Black holes are objects in the universe
where the gravity is so strong that light cannot
escape from them. Because gravity and the
movement of space are expressions of the same
phenomenon, this means that you can think of black
holes as sort of an inverse of the big bang, i.e.
the big bang is a sort of a white hole.
However, black holes are localized places
where space collapses back into a point. Black
holes are located at a specific place in space.
There is no center of the explosion that was the
big bang. The big bang was everywhere at once!
Apart from the big bang itself, we know of no
white holes in the universe. We also have no
plausible ways in which a white hole might be
created, since gravity is an attractive force, not
a repulsive force. You would also expect a white
hole to blow itself apart, for the same reason. We
do know about ways that black holes can form,
however. This is probably the reason why black
holes exist and white holes do not.
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