When a high speed neutrino just misses an old neutron star, why isn't it trapped?

Question

Suppose a neutrino is seen travelling so fast that its Lorentz gamma factor is 100,000. It races past an old, no longer active neutron star, narrowly missing it. As far as the neutrino is concerned, it is the NEUTRON STAR that is moving at extreme speed, & its mass is 100,000 times larger than 2 solar masses. Therefore, from the speeding neutrino's perspective, the neutron star should appear to be a black hole definitely large enough to trap the neutrino.

So how come the speeding neutrino continues its travel right past the old stellar remnant?

Is there an agreed name for this question or paradox?

Answer 1

Have a look at Can a black hole form due to Lorentz contraction?

This isn't exactly the same as your question, but the answer is the same. It's popularly believed that the mass is the only thing that determines whether a black hole will form or not, but this isn't true. Einstein's equation relates the curvature to a quantity called the stress-energy tensor:

$$G_{\alpha\beta} = 8\pi T_{\alpha\beta}$$

where $G_{\alpha\beta}$ is the Einstein tensor that describes the curvature and $T_{\alpha\beta}$ is the stress-energy tensor. The mass contributes only one component (out of ten) to the tensor. In the rest frame of the neutron star the mass is the dominant component, but when you boost the neutron star the other components are non-zero and they balance out any relativistic change in the mass.

See in particular Ron Maimon's comment to my previous answer for more info about the other components of the stress-energy tensor.

Answer 2

See answers to my question If two ultra-relativistic billiard balls just miss, will they still form a black hole? for a closely related situation with a different answer. This raises the question whether the combination of neutron star and neutrino in the center of mass has enough total mass (energy) inside the "hoop" to form a black hole.

Answer 3

The laws which govern the "increasing of mass" due to moving are not just the same as simply increasing of $m$ by adding material. Namely, the moving mass never turns into black hole if it is not black hole when still.