Question

Is a Kruskal diagram a 2D flat space projection of Schwarzschild space-time diagram? If not, isn't it true that one could not draw one accurately on a paper?

BTW, I am not referring to Penrose Diagrams. What I mean is, if I try to draw a diagram with R and T axes, it won't fit on a 2D paper. Instead, I would need to bend it in a third dimension (for example, a Flams paraboloid is a Schwarzschild diagram with R and θ and is a 3d structure looking like a well). is my reasoning correct?

Answer 1

No, a Kruskal diagram is not a 2D flat space projection of a Schwarzschild space-time diagram. In a Schwarzschild space-time diagram, the two axes represent the radial distance (R) and the time (T). However, due to the curvature of space-time caused by the presence of mass, accurately representing a Schwarzschild diagram with R and T axes on a 2D paper would be challenging. Instead, a 3D representation, like a Flamm's paraboloid, is often used to visualize the Schwarzschild diagram.

Step-by-step explanation:

No, a Kruskal diagram is not a 2D flat space projection of a Schwarzschild space-time diagram. In a Schwarzschild space-time diagram, the two axes represent the radial distance (R) and the time (T). However, due to the curvature of space-time caused by the presence of mass, accurately representing a Schwarzschild diagram with R and T axes on a 2D paper would be challenging. Instead, a 3D representation, like a Flamm's paraboloid, is often used to visualize the Schwarzschild diagram. So, your reasoning is correct in that simply drawing a 2D diagram with R and T axes would not accurately represent the Schwarzschild space-time diagram.