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> But there's a postulate that only rest mass can make a black hole, and relativistic mass doesn't count. That's news to me. Could you provide a reference? "Re

> But there's a postulate that only rest mass can make a black hole, and relativistic mass doesn't count. That's news to me. Could you provide a reference? "Relativistic mass" is just rest mass + kinetic energy, and so yes, it should influence the energy-momentum tensor like everything else. > (Because otherwise you could travel fast and see inside the black hole.) How so?

btilly 3y ago
I explain it in https://news.ycombinator.com/item?id=37344926 https://news.ycombinator.com/item?id=37344926. Something can't become a black hole just because it is moving fast. If it is a black hole, it is a black hole in all reference frames. Including the one where it is just sitting there and the rest of the universe is going the other way.
- codethief 3y ago
  Of course the (non-)existence of a black hole is a coordinate-/observer-independent statement (unless we talk only about apparent horizons), but the full energy ("relativistic mass") of a moving object will still show up in the energy-momentum tensor as seen from an outside (non-moving) observer. For instance, if we take a hot gas, we absolutely have to account for its temperature & pressure (the kinetic energy & momentum of its constituents) in the energy-momentum tensor. To see that this is a necessity, even for a single particle moving at relativistic speeds, consider energy conservation: If you accelerate a particle, you have to expend energy and that energy needs to come from somewhere (say nuclear fission). As a consequence, this energy will already show up in the energy-momentum tensor before acceleration (in the fission case: as rest mass of your isotopes) and, by local energy-momentum conservation (= 4-divergence of the tensor being zero), it then must also show up in the tensor afterwards. Whether or not that energy can lead to a black hole is a different question. For a single massive object flying at relativistic speeds in an otherwise empty universe: Probably not, because one can simply transform that "relativistic mass" away by switching coordinates, as you say. For several objects moving relative to each other at high speeds, or even a single particle moving relative to the "rest of the universe", it's not so simple, though – you won't find a coordinate system in which all terms in the energy-momentum tensor are small (let alone zero) everywhere.

btilly 3y ago

I explain it in https://news.ycombinator.com/item?id=37344926 https://news.ycombinator.com/item?id=37344926. Something can't become a black hole just because it is moving fast. If it is a black hole, it is a black hole in all reference frames. Including the one where it is just sitting there and the rest of the universe is going the other way.

codethief 3y ago
Of course the (non-)existence of a black hole is a coordinate-/observer-independent statement (unless we talk only about apparent horizons), but the full energy ("relativistic mass") of a moving object will still show up in the energy-momentum tensor as seen from an outside (non-moving) observer. For instance, if we take a hot gas, we absolutely have to account for its temperature & pressure (the kinetic energy & momentum of its constituents) in the energy-momentum tensor. To see that this is a necessity, even for a single particle moving at relativistic speeds, consider energy conservation: If you accelerate a particle, you have to expend energy and that energy needs to come from somewhere (say nuclear fission). As a consequence, this energy will already show up in the energy-momentum tensor before acceleration (in the fission case: as rest mass of your isotopes) and, by local energy-momentum conservation (= 4-divergence of the tensor being zero), it then must also show up in the tensor afterwards. Whether or not that energy can lead to a black hole is a different question. For a single massive object flying at relativistic speeds in an otherwise empty universe: Probably not, because one can simply transform that "relativistic mass" away by switching coordinates, as you say. For several objects moving relative to each other at high speeds, or even a single particle moving relative to the "rest of the universe", it's not so simple, though – you won't find a coordinate system in which all terms in the energy-momentum tensor are small (let alone zero) everywhere.