# Does the mass of a collapsing star change?

Does a star, when collapsing into a neutron star, or even a black hole, pick up any significant relativistic mass due to its rapid collapse rate?

This is an old question, but I'd like to answer it anyway.

Does a star, when collapsing into a neutron star, or even a black hole, pick up any significant relativistic mass due to its rapid collapse rate?

No. Conservation of energy applies. When you drop a 100000kg asteroid from some high elevation above the Earth, some of the asteroid's gravitational potential energy, which is mass-energy, is converted into kinetic energy. The mass-equivalence of the system does not increase as the asteroid falls. Instead the asteroid's rest mass reduces as the relativistic mass associated with its kinetic energy increases*.

When the asteroid hits the Earth (BOOM!) some of the kinetic energy will get dissipated and radiated out into space, and then you're left with a mass deficit. The mass of the system is then less than it was. See Wikipedia: "This missing mass may be lost during the process of binding as energy in the form of heat or light, with the removed energy corresponding to the removed mass through Einstein's equation E = mc²".

The same applies to a collapsing star. There is no "pick up" of relativistic mass. Conservation of energy applies. But some of this energy is typically radiated away, so you're left with a reduced mass.

The same also applies to a brick. When you drop a brick, gravity converts some of its rest mass into kinetic energy. This gets dissipated, and you're left with a mass deficit. Then when you lift the brick you do work on it. You add energy to it, thereby increasing its mass. Then you're back where you started.

The same also applies to an electron.

* this also applies to the Earth, but to a much lesser extent, so we tend to forget about it.

The bulk motion of the gas would contribute to the relativistic mass-energy of the compact object.

White dwarfs are not produced by collapse, so there is nothing to comment on here.

Neutron stars are produced by collapse. Most of the kinetic energy is lost in the form of neutrinos, the rest would be thermalised within the neutron star, increasing the kinetic energy of its constituent particles (which become partially relativistic) and that energy does contribute to the gravitational mass.

When a black hole forms then all the mass-energy that goes into its formation contributes to its gravitational mass.

• And yeah I meant neutron star, not white dwarf (I study Mathematics, not Astronomy). – change_picture Apr 15 '16 at 5:37