Consider a neutron star with a mass close to that necessary to form a black hole. In a moving frame, it has additional kinetic energy, and its energy density should increase.
Why is it not possible that in a sufficiently fast-moving frame, it would exceed the threshold to form a black hole? For that matter, why can a similar argument not be used for elementary particles?
Why is it not possible that in a sufficiently fast-moving frame, it would exceed the threshold to form a black hole?
In general relativity (GR), the theory that predicts the existence of black holes, the source of gravity is not just the energy density. It is the entire stress energy tensor.
The energy density is the time-time component of this tensor, and has the usual attractive gravitational effects. However, momentum density is the time-space component of the stress energy tensor, and (although it is more complicated than this simple statement) it can be thought of as having a gravitational effect that cancels out some of the effect of the time-time component.
So, as you look at different frames you will see both an increased time-time component and an increased time-space component. The second largely cancels out the effect of the first. So a fast moving neutron star does not become a black hole.
Furthermore, the usual black hole solution assumes spherical symmetry. A fast moving star is no longer spherically symmetric, so that solution does not apply.
