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The top answer to this question asserts that only rest mass curves spacetime. My poor understanding of the EFEs & special relativity is that $T_{\mu\nu}$ doesn't care about what whether energy density includes by rest mass or relativistic mass.

The linked author says that "relativistic mass is not "real" mass. The gravity of an object travelling at relativistic speeds does not increase, because its mass does not increase" and goes on to talk some stuff about frames of reference that I think is probably irrelevant.

I always thought that a black hole does not form because you reach a certain rest mass energy, it forms because a region of space reaches a certain energy density... and that accelerating a mass to a sufficiently high velocity that the region of space it occupies achieves this energy density would form a black hole.

In short, I think that guy's totally wrong. Are they? Why or why not?

Qmechanic
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neph
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2 Answers2

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The Oh My God particle was a cosmic ray...perhaps a proton...that struck Earth with about 50 joules of kinetic energy. In its own frame, it was a perfectly ordinary proton at rest, and it is Earth that had a Lorentz factor of 3.2e11, which would be enough "relativistic mass" to make a black hole 18 light seconds across. Notably, we're all still here.

Energy and mass are equivalent, but kinetic energy is frame dependent, and has no physical meaning in isolation. It only means something in relation to some larger system. So no, just moving fast is not enough to form a black hole.

Christopher James Huff
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Let me discuss this question in terms of the principle of equivalence.

Thought experiment:
A chamber, with walls that reflect light perfectly. That is, light that has entered that chamber is never absorbed by the walls; the light persists in that chamber just as a gas would persist in that chamber.

The energy of the light in that chamber contributes to the inertial mass of the assembly.

Next we consider a thought experiment where the chamber is in free fall. We compare the free fall of a chamber that is holding a significant amount of light energy to the motion of an empty chamber.

According to the principle of equivalence the free fall of the chamber-with-light-energy will be indistinguishable from the free fall of the empty chamber. It follows logically that if the principle of equivalence holds good the chamber-with-light-energy must have a larger gravitational mass than the empty chamber, matching the ratio of inertial masses of the two chambers.

Next we consider a thought experiment where the chamber is a housing for a setup for flywheel energy storage

We have that the spinning flywheel will have a larger inertial mass than a non-spinning flywheel, in accordance with the difference in accumulated kinetic energy. The kinetic energy of a spinning flywheel is confined to a finite volume of space. That is: the kinetic energy of a spinning flywheel has a definable energy density.

(Of course, in an actual setup this additional inertial mass is too small to be actually measured. An actual flywheel will disintegrate long before it reaches relativistic velocity.)

A celestial counterpart of a spinning flywheel is a spinning neutron star. Some neutron stars have an extremely large rate of spin.

The logic of the principle of equivalence implies that the kinetic energy of the neutron star spin must be contributing to the gravitational mass of that neutron star.

Cleonis
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