Today a friend of mine posed me a paradox involving black-holes, one that I couldn't solve.

Suppose we have planet, with a density such that it is almost to the point of turning into a black hole, armed with a powerful laser on the surface (kind of like Star War's Death Star) capable of shooting down any star ship. Now I, on a really fast spaceship (for the sake of discussion let's say around 10% of the speed of light) approach this planet.

Now, because of relativistic effects, from my point of view the planet will shrink, keeping mass constant, therefore increasing its density and finally turning in a black hole. Because of that the laser will never be able to escape the planet, and I'll be fine.

Instead, from the planet's point of view, nothing as really changed, only a puny space-ship is flying into its direction, the laser will shoot and take me down.

How is this possible?

  • 6
    $\begingroup$ Possible duplicate of Can a black hole form due to Lorentz contraction? $\endgroup$
    – ACuriousMind
    Jan 8 '16 at 16:18
  • 1
    $\begingroup$ Because the density is not the thing that matters. The thing that matters is the energy-momentum tensor. This tensor remains invariant. $\endgroup$
    – Apoorv
    Jan 8 '16 at 16:29
  • $\begingroup$ Notice though that it is possible to outrun a laser, even though you are at rest when it is shot towards you and you never reach light speed. en.wikipedia.org/wiki/Event_horizon#/media/…" You just need to keep accelerating. Incidentally, a constantly accelerating observer, will indeed observe an event horizon in many ways similar to that of a black hole, with Hawking temperature and all. Read more about $\endgroup$
    – Andrea
    Jan 18 '16 at 15:49