1

If we use the Lorentz equation for the length contraction, and the Schwarzschild equation for the lightlike sphere, we can calculate the velocity for the object to form a black hole:

$ \Delta x^{'}=\Delta x\,\sqrt{1-\dfrac{v^2}{c^2}}\,\, $ --> Lorentz formula

$ r_{\text{s}}=\dfrac{2Gm}{c^2}\,\, $ --> Schwarzchild formula

$ 2r_{\text{s}}=\Delta x^{'}\,\, $ --> to a sphere

$ 2\left(\dfrac{2Gm}{c^2}\right)=\Delta x\,\sqrt{1-\dfrac{v^2}{c^2}} $

$ v=c\,\sqrt{1-\left(\dfrac{4Gm}{\Delta xc^2}\right)^2} $

Is this correct? Is this the speed that the object, in the spherical case, would have to attain to become a black hole?

Sorry for my English and little knowledge of physics, I am a freshman student in a university in Brazil.

Qmechanic
  • 201,751
Eduardo Cezar
  • 19
  • So plug in some numbers. If you had something the mass of the Earth (5.972 × 10^24 kg) what speed would you need to get for it to turn into a black hole? Can this speed exist? – zeta-band Aug 15 '18 at 22:01
  • Would be a velocity really very close to the speed of light, in the case of Earth, but possible in principle. – Eduardo Cezar Aug 15 '18 at 22:15
  • 3
    Please don't post cell-phone pictures of equations. Mark up your questions using mathjax instead. Posting pictures doesn't work with search engines and doesn't work for blind people. –  Aug 15 '18 at 23:24
  • Your object's already traveling very close to $c$ in some reference frame. So why isn't it a black hole? – PM 2Ring Aug 16 '18 at 02:12

0 Answers0