14 ms·

If you think about it carefully you’ll realise that a human being’s body would span a breadth of radii and therefore the parts closer to the singularity would n

by qubex 3y ago

If you think about it carefully you’ll realise that a human being’s body would span a breadth of radii and therefore the parts closer to the singularity would not be able to send signals or matter to the parts that are further out, and that this would impede circulation and signal propagation.

raattgift 3y ago
Ok, on the way to thinking about it carefully I'll ask you to look at all the little pockets one can hide a puny human in on a (r, \theta, K) or plane contour graphset of the Kretschmann scalar for a large general black hole (BH). Unfortunately scalar invariants plots don't really offer anyone much intuition about the detailed fate of an astronaut jumping in, and anyway it's more fun to think about Taub-NUT BHs because nobody repeats slogans about those on hackernews. Now, one of the things one can think about carefully is the dynamics of extended bodies in general curved spacetime. Extended body dynamics is already a problem in gravity-free special relativity (e.g. Bell's spaceship paradox). I'd treat it slightly differently when gravity is important enough. The centre of momentum of a human obeys the universality of free fall; a quick bungee jump proves this pretty well. However, the internal components stuck to the skeleton do not individually free-fall (otherwise the end of the falling part of a bungee jump would go pretty badly) because they experience internal contact forces (cf. body forces like Newton's gravity). An infalling human is not a cloud of fine dust, or a big gassy star: there are intermolecular forces in play even in the wet flowy bits of the anatomy, and while far from outright rigidity, a puny human's microscopic bits zip around on accelerated curves rather than the free-falling geodesics of a pre-dustified (atomized? turned into a fine spray with particle sizes much much smaller than the size of a red blood cell) human. It's also why you aren't a microscopically thin puddle on the floor right now, and indeed why there is a floor to be on (or "mountains" on the surface of a neutron star or why a neutron star/BH (NS-BH) collision like GW200115 is different from a BH-BH collision, especially with a stiff equation of state). The mechanisms of support against freefall for every microscopic part of the anatomy in turn must be encoded in the stress-energy tensor rather than some notion of ultraspecific background curvature; consequently local T_munu != 0 suddenly becomes quasilocally relevant since it determines the curvature. For test particles, we don't care, we keep T_munu = 0. For puny humans the temptation is to do the same, but realistically we circle back to a statement like "nobody's developed a justifiable intuition for this" (although you can certainly look at a multiplicity of numerical results). Inside general black holes (following Lluis Bel) the gradient of the electrogravitic tensor is probably the killer; that's what captures the stretching up-to-down (cf the rope in the Bell's spaceship) and what also encodes inwards squeezing in the perpendicular directions. Essentially, you are liable to be resemble a radially-squeezed tube of toothpaste with the flowier bits spraying out the bottom when there is a local failure of your tissues' binding energies to decouple tissue-components from converging geodesics (roughly, the contact forces that slosh momentum into the spatial diagonal of the stress-energy tensor eventually fail to prevent it sloshing right back out) or kinda like if a bit of gas near the inner surface of a balloon were to become sharp as you really stretch the filled baloon along one axis (i.e., making it prolate)). One might then spend remaining moments of consciousness wondering if there are conditions in which free-falling distant starlight (null geodesics[*]) passing through the bloody mist (now on timelike geodesics[*]) could produce a rainbow for some intact massive object further below. In short, "think about it carefully" is the sort of thing one might do for a PhD thesis (demonstrating that you can actually do research) rather than a brief hackernews comment (which rarely demonstrates any such thing). [*] downside, interior solution of the geodesic equation depends on the entire history of the BH. And using Kerr as a starting point is fraught. David Madore (an engaging mathematician) put it pretty well when he wrote this years ago <http://www.madore.org/~david/math/kerr.html#course.real_black_holes http://www.madore.org/~david/math/kerr.html#course.real_blac...>. There are pretty visualizations there, but if you get extended-body/black-hole-interior trajectory intuitions out of them, send a postcard back to this thread. Oh, in addition to his agreeable couple paragraphs of objectsions, the space outside an astrophysical black hole isn't empty (otherwise how is there anyone to jump in?), and the spacetime there isn't even asymptotically flat. So now, for a black hole huge enough not to destroy you while you're still outside it, you get to think about: coupling with the host galaxy (does the shell theorem have an analogy there?); the cluster, whose metric may be quite inhomogeneous; and the cosmological constant; and justify whether those contributions are marginal or irrelevant in grinding out accessible trajectories. Maybe start with Schwarzschild-de Sitter as an approximation of the galaxy cluster all smooshed into a ginormous black hole in the far future, and take Schwarzschild->Vaidya (relic cmb) and then to spinning Vaiyda-de Sitter, extra credit for contrasting with AdS solutions since those thermalize but have off the shelf computer program implementations. Along the way you can re-calculate what happens to a human being dropped towards each iteration's central mass. Extra extra credit for considering binary black holes at various mass ratios: can we go beyond a gross qualititative guess like, "infaller dies faster in smaller of the pair"?

by qubex 3y ago

raattgift 3y ago

Ok, on the way to thinking about it carefully I'll ask you to look at all the little pockets one can hide a puny human in on a (r, \theta, K) or plane contour graphset of the Kretschmann scalar for a large general black hole (BH). Unfortunately scalar invariants plots don't really offer anyone much intuition about the detailed fate of an astronaut jumping in, and anyway it's more fun to think about Taub-NUT BHs because nobody repeats slogans about those on hackernews. Now, one of the things one can think about carefully is the dynamics of extended bodies in general curved spacetime. Extended body dynamics is already a problem in gravity-free special relativity (e.g. Bell's spaceship paradox). I'd treat it slightly differently when gravity is important enough. The centre of momentum of a human obeys the universality of free fall; a quick bungee jump proves this pretty well. However, the internal components stuck to the skeleton do not individually free-fall (otherwise the end of the falling part of a bungee jump would go pretty badly) because they experience internal contact forces (cf. body forces like Newton's gravity). An infalling human is not a cloud of fine dust, or a big gassy star: there are intermolecular forces in play even in the wet flowy bits of the anatomy, and while far from outright rigidity, a puny human's microscopic bits zip around on accelerated curves rather than the free-falling geodesics of a pre-dustified (atomized? turned into a fine spray with particle sizes much much smaller than the size of a red blood cell) human. It's also why you aren't a microscopically thin puddle on the floor right now, and indeed why there is a floor to be on (or "mountains" on the surface of a neutron star or why a neutron star/BH (NS-BH) collision like GW200115 is different from a BH-BH collision, especially with a stiff equation of state). The mechanisms of support against freefall for every microscopic part of the anatomy in turn must be encoded in the stress-energy tensor rather than some notion of ultraspecific background curvature; consequently local T_munu != 0 suddenly becomes quasilocally relevant since it determines the curvature. For test particles, we don't care, we keep T_munu = 0. For puny humans the temptation is to do the same, but realistically we circle back to a statement like "nobody's developed a justifiable intuition for this" (although you can certainly look at a multiplicity of numerical results). Inside general black holes (following Lluis Bel) the gradient of the electrogravitic tensor is probably the killer; that's what captures the stretching up-to-down (cf the rope in the Bell's spaceship) and what also encodes inwards squeezing in the perpendicular directions. Essentially, you are liable to be resemble a radially-squeezed tube of toothpaste with the flowier bits spraying out the bottom when there is a local failure of your tissues' binding energies to decouple tissue-components from converging geodesics (roughly, the contact forces that slosh momentum into the spatial diagonal of the stress-energy tensor eventually fail to prevent it sloshing right back out) or kinda like if a bit of gas near the inner surface of a balloon were to become sharp as you really stretch the filled baloon along one axis (i.e., making it prolate)). One might then spend remaining moments of consciousness wondering if there are conditions in which free-falling distant starlight (null geodesics[*]) passing through the bloody mist (now on timelike geodesics[*]) could produce a rainbow for some intact massive object further below. In short, "think about it carefully" is the sort of thing one might do for a PhD thesis (demonstrating that you can actually do research) rather than a brief hackernews comment (which rarely demonstrates any such thing). [*] downside, interior solution of the geodesic equation depends on the entire history of the BH. And using Kerr as a starting point is fraught. David Madore (an engaging mathematician) put it pretty well when he wrote this years ago <http://www.madore.org/~david/math/kerr.html#course.real_black_holes http://www.madore.org/~david/math/kerr.html#course.real_blac...>. There are pretty visualizations there, but if you get extended-body/black-hole-interior trajectory intuitions out of them, send a postcard back to this thread. Oh, in addition to his agreeable couple paragraphs of objectsions, the space outside an astrophysical black hole isn't empty (otherwise how is there anyone to jump in?), and the spacetime there isn't even asymptotically flat. So now, for a black hole huge enough not to destroy you while you're still outside it, you get to think about: coupling with the host galaxy (does the shell theorem have an analogy there?); the cluster, whose metric may be quite inhomogeneous; and the cosmological constant; and justify whether those contributions are marginal or irrelevant in grinding out accessible trajectories. Maybe start with Schwarzschild-de Sitter as an approximation of the galaxy cluster all smooshed into a ginormous black hole in the far future, and take Schwarzschild->Vaidya (relic cmb) and then to spinning Vaiyda-de Sitter, extra credit for contrasting with AdS solutions since those thermalize but have off the shelf computer program implementations. Along the way you can re-calculate what happens to a human being dropped towards each iteration's central mass. Extra extra credit for considering binary black holes at various mass ratios: can we go beyond a gross qualititative guess like, "infaller dies faster in smaller of the pair"?