# Help with showing the existance of the Schwarzschild singularity at r=0.

• blp
In summary, the conversation discusses the Schwarzschild metric and its properties, particularly the singularity at r=0. The metric can be written in a form that clearly shows the singularity, and there is a pair of pos and neg singularities at this point. This was initially interpreted as an Einstein-Rosen bridge, but the mathematical derivation of the singularities is still unclear. Kruskal or Penrose diagrams may be used to analyze the spacetime. However, the physicality of these singularities is debated.
blp
According to Wikipedia, if the metric was vacuum, spherically symmetric and static the Schwarzschild metric may be written in the form:
ds^2=((1-2GM/(c^2r))^-1)*dr^2+r^2*(dtheta^2+sin(theta)^2*dphi^2)-c^2*(1-2GM/(c^2r))*dt^2
I need someone to help me to derive an expression from the Schwarzschild metric that is a function of r that can be graphed, that clearly shows the singularity at r=0. Actually, their is apparently a pair of pos and neg singularities there. Is that true? Is that because there is a square root taken during it's derivation? Thanks.

Surely

$$1- \frac{2GM}{c^2r}$$ clearly diverges when r = 0. And its inverse diverges when

$$1 = \frac{2GM}{c^2r}$$.

Sorry, I should have been clearer. Obviously ds^2 diverges at r=0, but I want some way of graphing a 2D spacetime clearly curving towards infinity in the z axis direction as r approaches 0.

Also concerning the pair of pos and neg singularities at r=0. I remember reading somewhere that shortly after Schwarzschild came up with the black hole solution to GR that Einstein and Rosen noticed the above pair of singularities and interpreted them as being the two ends of a wormhole and called it a Einstein-Rosen bridge. If that is true, I'm curious how the singularities were mathematically derived. Does anyone know?

I think space-times are analysed with Kruskal or Penrose diagrams. If you want to take an equatorial slice, then rewrite the metric in cartesian coordinates. I can't say any more than that, not having studied the singularites because I don't think they can be physical. But that's just an opinion.

Thanks! I'm going to re post this with a different title to see if someone else might know about this.

## 1. What is the Schwarzschild singularity at r=0?

The Schwarzschild singularity at r=0 is a mathematical point of infinite density and gravitational pull at the center of a black hole, predicted by Albert Einstein's theory of general relativity. It marks the breakdown of the laws of physics and our current understanding of space and time.

## 2. How can we show the existence of the Schwarzschild singularity at r=0?

To show the existence of the Schwarzschild singularity at r=0, we must use mathematical equations derived from general relativity to describe the curvature of spacetime around a black hole. These equations predict that as we approach the center of a black hole, the curvature becomes infinite, indicating the presence of a singularity.

## 3. Why is it difficult to prove the existence of the Schwarzschild singularity at r=0?

It is difficult to prove the existence of the Schwarzschild singularity at r=0 because it is a theoretical concept that cannot be directly observed or measured. Additionally, our current understanding of physics breaks down at the singularity, making it challenging to study and verify.

## 4. Are there any alternative theories to explain the Schwarzschild singularity at r=0?

Yes, there are alternative theories such as quantum gravity that aim to explain the singularity at r=0 in a different way. These theories propose that the singularity may not be a point of infinite density, but rather a region of extreme energy and curvature.

## 5. What implications does the existence of the Schwarzschild singularity at r=0 have on our understanding of the universe?

The existence of the Schwarzschild singularity at r=0 has significant implications for our understanding of the universe. It challenges our current understanding of space and time and highlights the limitations of our current theories. It also raises questions about the ultimate fate of black holes and the possibility of other singularities in the universe.

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