The Lorentz factor, denoted as γ, plays a limited role in general relativity (GR), primarily appearing in local inertial frames where the metric is flat. It is relevant when converting between different frames, such as in the derivation of the stress-energy tensor for fluids in non-flat spacetimes. The discussion highlights that both gravitational and kinematic time dilation contribute to relativistic effects, such as the precession of orbits, exemplified by Mercury's orbit around the Sun. The relationship between gravitational and kinematic time dilation is established through formulas involving the Schwarzschild metric and the average orbit radius.
PREREQUISITESPhysicists, graduate students in theoretical physics, and anyone interested in the interplay between special and general relativity, particularly in the context of time dilation and gravitational effects.
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).