One argument for why we can never accelerate a spaceship to the speed of light is that it would take infinite energy to accomplish.
On the other hand, a black hole is said to contain an infinitely dense region of spacetime with zero volume at the center.
Why is the first argument considered an instant refutation of light-speed or faster travel (and it is persuasive to me), but the evident impossibility of infinite density in zero volume is not considered an instant refutation of the theory behind black holes?
Note, please, I am asking a question, not making an assertion. I am hoping for an accessible explanation from within the mainstream of physics.
On the other hand, a black hole is said to contain an infinitely dense region of spacetime with zero volume at the center.
Why is the first argument considered an instant refutation of light-speed or faster travel (and it is persuasive to me), but the evident impossibility of infinite density in zero volume is not considered an instant refutation of the theory behind black holes?
Note, please, I am asking a question, not making an assertion. I am hoping for an accessible explanation from within the mainstream of physics.