0

Say we built a cigar the mass of the sun out in deep space, with radius of 1 km, and length of a million miles. A spaceship flies by within a km at an immense speed. No problem, it will zoom down the length and never feel much of a gravitational pull (if it did, we could help it with a slippery trough to slide along).

But from the spaceship's perspective, the cigar is squished into just 2 km length by Lorentz contraction. That is, the alien sees an speherical object, mass of the sun, radius of 1 km. That's a non-spinning black hole in his reckoning. No way he can let it pass by him within 1 km, because he'd go through the event horizon and be trapped forever.

What's going on? Where's my mistake? Isn't the shape more dense than a black hole in his reference frame?

Ralph Berger
  • 480
  • 1
    @safesphere you should answer it, the comment could be deleted by whatever reason –  Jun 29 '22 at 03:31
  • @safesphere I have been looking on the net and have not found as logical/mathematically an answer as your comment implies – anna v Jun 29 '22 at 03:37
  • 1
    possible duplicate https://physics.stackexchange.com/q/3436/ – anna v Jun 29 '22 at 03:47
  • 1
    Does this answer your question? If a mass moves close to the speed of light, does it turn into a black hole? – John Rennie Jun 29 '22 at 04:13
  • @annav https://physics.stackexchange.com/q/28422 – safesphere Jun 29 '22 at 04:24
  • 2
    @safesphere your "The Schwarzschild radius is timelike and is measured in seconds." is not seen in the duplicates – anna v Jun 29 '22 at 07:15
  • @annav The Schwarzschild radius is the radial interval between the horizon and the origin. The fact that this interval is timelike trivially follows from the metric and is a common knowledge. The common misconception of measuring the Schwarzschild radius in meters comes from defining it as the reduced circumference of the horizon, which is spacelike (e.g. 3 km for the Sun), but this is just an artifact of the definition. The radial interval from the horizon to the origin is timelike and is measured in seconds. Just look at the metric: https://math.stackexchange.com/questions/2929400/ – safesphere Jun 29 '22 at 16:40
  • @safesphere thanks. common to the ones specializing in GR I guess – anna v Jun 29 '22 at 16:45

0 Answers0