Is it possible we live in a white hole? Is it possible we live in a white hole? We live in a universe that is expanding at an accelerating rate – does this not seem similar to a white hole? Could a living organism interpret a black hole as a white hole? Say if it exists or interprets time as space or time as negative time – this could explain how a white hole comes into existence – since we know black holes exist and form naturally – possibly white holes exist merely as a matter of perspective.
My personal belief is that to understand white holes (since it doesn't appear that can be born naturally ) and how they could come about,  we need to incorporate an understanding of our existence into physics in some way, so that a white hole is essentially a black hole (which we know can form naturally) but viewed from a different perspective.
Obviously this question seems silly and is only my intuition - but I think (as a non-physics student) it's worth discussing as the Big Bang Theory (to me at least) doesn't really make sense to me as it doesn't explain why the universe is expanding in the first place. These "why" questions are important and are the foundation to really understanding something.
 A: Kruskal coordinates (in the context of extended black holes, or worm-holes) on a black hole geometry are defined, from the Schwarzschild coordinates ${\displaystyle (t,r,\theta ,\phi )}$, by replacing $t$ and $r$ by a new timelike coordinate ${\displaystyle T}$ and a new spacelike coordinate ${\displaystyle X}$:
$$T=\left(\frac{r}{2 G M}-1\right)^{1 / 2} e^{r / 4 G M} \sinh \left(\frac{t}{4 G M}\right)$$
$$ X=\left(\frac{r}{2 G M}-1\right)^{1 / 2} e^{r / 4 G M} \cosh \left(\frac{t}{4 G M}\right)$$
for the exterior region ${\displaystyle r>2GM}{\displaystyle r>2GM}$ outside the event horizon and:
$$ T=\left(1-\frac{r}{2 G M}\right)^{1 / 2} e^{r / 4 G M} \cosh \left(\frac{t}{4 G M}\right) $$
$$ X=\left(1-\frac{r}{2 G M}\right)^{1 / 2} e^{r / 4 G M} \sinh \left(\frac{t}{4 G M}\right)$$

The picture above shows the Kruskal diagram, illustrated for $2GM=1$. The quadrants are the black hole interior (II), the white hole interior (IV) and the two exterior regions (I and III). The dotted 45° lines, which separate these four regions, are the event horizons. The darker hyperbolas which bound the top and bottom of the diagram are the physical singularities. The paler hyperbolas represent contours of the Schwarzschild $r$ coordinate, and the straight lines through the origin represent contours of the Schwarzschild $t$ coordinate.
The two diagrams below serve to understand how the two coördinate systems, $(t,r,\theta ,\phi )$, and $(X,T)$ are related. When, for example, a spherical lightwave (for which $r$ is a constant at any time $t$) is traveling towards the black hole, then you can see these waves as the concentric circles in the first picture (where $(x,y)$ represent $(r,t)$ and the angle refers to a Lorenz transformation, which is not important here).


In the picture above you can see how the concentric waves travel in the Kruskal diagram. Observe that there is also a wave traveling in a downward direction. They travel backward in time towards the other black hole. Or forward in time from the other black hole. I.e., the other black hole represents a white hole. It seems as if the black and white hole have an infinite extent, but this is due to the coördinates. The waves end up at a point, the center of the concentric circles.
Maybe this gives you an idea.
There are no known physical circumstances that can lead to the existence of white holes. They are purely hypothetical (due to the math). Though Smolin says that they actually exist on the other side of black holes. The other side gives rise to other universes Smolin thinks some kind of a Natural selection "procedure" is happening. Likewise, he thinks that our big bang is similar to a white hole spitting out our universe, and as such there was a white hole geometry before the big bang. I'm not sure I understand this. Can time run backward?
To answer your question, it's very unsure if we live in a WH. Time runs back inside one. Of course, you can say that time runs backward in our universe or that we live on the other side of a black hole, as Smolin says, but there is no certainty.
A: A white hole is a feature of the Schwarzschild solution. This is the solution for a spherically symmetric (isotropic but not homogenous) vacuum spacetime where there is no gravitating mass outside of the singularities.
The universe we live in is not described by a vacuum spacetime and it is both isotropic and homogenous. So it is unambiguously not the same spacetime. Also, there is no past horizon for the Big Bang singularity.
