Einstein's laws solved the problem of objects moving near the speed of light but breakdown themselves when you come to black holes and the BBT.
I think the only real issue with black holes and singularities, in terms of relativity, is one of perspective. When trying to describe what is going on inside a singularity using relativity we get infinity; when trying with quantum theory we get infinity raised to infinity. We then say, there is a problem here, this can't be.
But I think the equations are working fine.
If we think about dimensions (not parallel universe type things, but length, width, height) and more specifically lesser dimensions we can see some interesting things that might explain what is going on with the infinity issue.
Think about the dimensional objects from 0 to 3.
0 dimensional is a point. No length width or height, it exists and can occupy a location, but seems to shrink into nothing as you try and approach it.
1 dimensional is a line. It can be thought of as the distance between two points. We typically say it has the single dimension of length.
2 dimensional is a plane. It can be though of as the distance between two separate lines. We typically say is has two dimensions of length and width.
3 Dimensional is a Volume, a cube, a sphere, cylinder, cone ect. It can be thought of as the distance between two separate planes. And has three dimensions, length, width, height.
OK, so, how many squares can you find in a cube? If you have rolled a lot of dice you might say 6. But if you start slicing the cube along any axis that is parallel or perpendicular to any edge of the cube you can create an infinite number of potential squares.
Same goes for finding the number of potential lines in a plane. You can think of a plane as an infinite number of lines that occupy the same "height".
And now for the line; How can you express a line in terms of only points, no lengths? Answer: ?
Going back to the singularity. It is the very definition of a point. So for us to try and express higher dimensional math in that space, it seems reasonable that all we are going to see is ?'s.
We get useful analyses of a dimensional entity when we use lesser dimensional entities to sub-divide it. Like using individual lines to create a grid on a plane; Using planes to slice volumes; or using points to establish a location on a line.
So if we want to unlock what is going on at the level of the singularity we need to find a dimensional component that is less than a point. If we think about the point as the distance between two things, we might be able to express the point in more detailed terms. But I haven't been able to think of anything that would work. Well more specifically I thought off nothing. A point can be thought of as the distance between two non-entities. This basically places the point or singularity at the cusp between existence and non existence.
So if we think about the big bang theory, the universe began with a singularity. And everything that has followed has relied on that initial separation, segregating our universe from the non-universe. Traditional math might still fail to adequately express such a thing, but I believe that the real issue is one of perspective.