Infinite Curvature of Spacetime Singularity

I will make a pedagogical point regarding the visual representation of spacetime singularities (Black Holes). In popularized science articles and books the Black Holes are sometimes represented as follows:

This visual representation is misleading because the spacetime curvature in a singularity is infinite but in this representation the curvature at the singularity is almost zero. During the approach to the singularity the curvature of spacetime will increase not decrease.

Spacetime is a composite of 3 spatial dimensions and 1 temporal dimension. It is impossible to visualize the “infinite curvature” of a 2-dimensional surface. The visualization of the “infinite negative curvature” of  4-dimensional spacetime is totally beyond our mental capabilities. We cannot visualize perhaps but we can still think about the spacetime singularities in abstract terms.

An understanding of the spacetime singularity in terms of its event horizon is currently attempted by physicists.


  • Zero volume, infinite density.
  • Laws of physics are no longer valid.
  • Light emitted from beyond the event horizon (Schwarzschild radius) cannot escape the singularity.
  • There is an escape mechanism from the event horizon, however, related to quantum effects. This process is known as Hawking radiation or simply as Black Hole evaporation.
  • Objects sent towards an event horizon never appear to cross it from the sender observer’s point of view
  • To the sender the clocks on the spaceship sent towards an event horizon appear to slow down and finally stop at the event horizon
  • The General Relativity theory is inadequate to describe the spacetime singularity. We need a theory of quantum gravity for a better understanding of the event horizons.
  • “What is beyond the event horizon?” is a legitimate question for physics.
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