The discussion revolves around the role of the Lorentz factor in general relativity (GR), particularly its applicability in non-flat spacetimes and its relationship with the stress-energy tensor. Participants explore whether the Lorentz factor can be used in various contexts within GR, including fluid dynamics and gravitational time dilation.
Participants express differing views on the applicability of the Lorentz factor in general relativity. While some argue it is relevant in certain contexts, others maintain that it is rarely applicable in GR. The discussion remains unresolved regarding the extent to which the Lorentz factor can be utilized in non-flat spacetimes.
Participants reference various mathematical formulations and concepts, indicating that assumptions about local inertial frames and the nature of spacetime may influence the applicability of the Lorentz factor. There are also unresolved questions about notation and definitions related to the metric tensor.
Your intuition is right, it won't become a black hole. It seems that people associate high intensity gravitational fields with black holes and that isn't really the case. Its possible to have a naked singularity in which case the intensity of the gravitational field increases without bound and yet there is no event horizon associated with it. An infinitely long mass filament is just such an object.shalayka said:... The reason I'm wondering about this is because where two bodies undergoing rectilinear motion, passing each other at high velocity, it seems non-intuitive that they could appear as black holes to each other (if the rest+kinetic energy vs. body volume ratio were adequate).
Recall that a black hole is an object whose mass resides entirely within a partcular surface. In the rest frame of the object this surface is a sphere as measured whose radius is less than or equal to the Schwarzschild radius. If that is true in one frame of reference then its true in all frames of reference.shalayka said:... The reason I'm wondering about this is because where two bodies undergoing rectilinear motion, passing each other at high velocity, it seems non-intuitive that they could appear as black holes to each other (if the rest+kinetic energy vs. body volume ratio were adequate).