Can length contraction cause an object to exceed black hole density?

[2.71828]

Hello Forum,

This is my first post :)

Einstein's special relativity finds that length is contracted if the observer is moving at high speeds. Now, assume there is a mass at rest in space that is below critical density of a black hole. If an observer were traveling at high speeds past this mass, the object will contract; therefore, placing the object above critical density. Are the existence of black holes relativistic?

 

[pervect]

Yes. In GR, mass, or density, alone does not generate gravity. Gravity is generated by the stress-energy tensor, which is a fully relativistic object. The density is a component of the stress-energy tensor, but its only one component. So while the density term does increase, other terms appear and the net result is that you don't wind up with a black hole.

It may (or may not) be interesting to note that the energy density at a point (T_00 of the stress-energy tensor) increases by a factor of gamma^2 due to a "boost" (a relativistic velocity transformation), because the stress-energy tensor measure energy, and not only do you have a smaller volume after the boost, but the smaller volume contains more energy due to the motion of the particles contained within. Here gamma is 1/sqrt(1-v^2/c^2), the usual relativistic term.

 

[2.71828]

Yes. In GR, mass, or density, alone does not generate gravity. Gravity is generated by the stress-energy tensor, which is a fully relativistic object.

Thanks Pervect. Looks like I got some reading to do on GR. I'm really enjoying this forum website :)