What if an object had enough speed that from another perspective it was enough to form a blackhole?

Question

Suppose a baseball is traveling through a vaccum towards another object extremely fast. If it's travelling fast enough then shouldn't its kinetic energy give it enough mass that the observer thinks it should collapse into a black hole and evaporate as Hawking radiation? How can this be reconciled with the perspective of a second object at rest with the baseball, which would have no reason to see a black hole?

Answer 1

You start from a common and stubborn misconception: that objects acquire mass at high, relativistic speeds.

In reality it is the object's momentum $p$ that is relativistic:

$$p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}},$$

where $m$ is mass, $v$ is velocity and $c$ is the speed of light.

See relativistic mass.

So your relativistic object could never acquire the mass needed to form a black hole.