if singularities can be observed from the rest of spacetime, causality may break down

Question

if singularities can be observed from the rest of space-time, causality may break down, and physics may lose its predictive power,i don't understand how it will happen?we don't have any idea what will happen at singularity.so we should not observe them.

Answer 1

Physics is based on the idea that behaviour is deterministic. That means we can take some system, write down the equations of motion that describe it, and we then know how that system is going to behave for the rest of time. Concepts like conservation of energy and momentum are deeply tied into this idea.

But if you write down the equation of motion for an object falling into a black hole, then once the object reaches the singularity the equations cannot predict what will happen next. This contradicts the basic assumptions upon which all of physics is built.

For the usual type of black holes the equations of motion actually predict that the infalling falling object takes an infinite time to reach the event horizon, and therefore never crosses it. So for us observers outside the black hole there is no problem since for us the object never reaches the singularity and our equations do work for an infinite time into the future. The problem with a naked singularity is that external observers would be able to observe the infalling object reach the singularity in a finite time. Beyond that time we would have no way to predict what happens next, which is a fundamental violation of all we hold sacred.