2

Suppose you have a neutron star that's as close as can be imagined to the required mass to become a black hole, perhaps just one proton mass away from this limit, when it collides with a dust grain from space.

Is the collapse instantaneous? Is the event horizon formed in the center and moves outward as more mass gets pulled in? Are there gravitational waves as a result of the sudden shift in the spacetime geometry?

Any details that are known about such an event would be greatly appreciated! Thank you

Edit: As requested I'm limiting my question to be more specific to what most interests me - Does the event horizon form at the center of the neutron star? Is there a specific "initial size" that grows?

Ofer Sadan
  • 121
  • Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. – Community Jun 21 '22 at 06:48
  • I will note that you probably mean "apparent horizon" and not "event horizon", as the event horizon is a topological feature whose development is very deeply intertwined with what will happen in the future, and event horizons can even form in flat regions of spacetime. – Zo the Relativist Jun 21 '22 at 14:55
  • The asymptotic horizon first forms where the gravitational potential (time dilation) is extremal, which is at the center. Then the spacelike radius of the horizon remains zero, but its circumference increases. Whether or not you call this "growing" depends. – safesphere Jun 22 '22 at 05:07
  • @safesphere How do you define the spacelike radius of the horizon? – JanG Feb 23 '24 at 07:36
  • @JanG It is given by the polar coordinate system used in the original paper by Schwarzschild: $r\equiv\sqrt{x^2+y^2+z^2}$ - This way, $r$ is spacelike and is zero at the horizon. Note that what is known today as “the Schwarzschild solution” is actually the solution by Droste. It defines radius as the reduced circumference. This approach depends on the metric, but is mathematically equivalent, if used carefully. So the spacelike part of $r$ is still zero at the horizon. It follows straight from the metic that the inner radial interval is timelike, so it adds nothing to the spacelike radius. – safesphere Feb 24 '24 at 03:07
  • @safesphere I think I understand now your comment. I have found the same view in Christian Corda paper A clarification on the debate on "the original Schwarzschild solution". – JanG Feb 24 '24 at 11:40
  • @JanG I’ve seen this paper, but didn’t study it deeply. At a glance, it makes a generally correct conclusion that the Schwarzschild and Droste solutions are mathematically equivalent through a coordinate transformation. In fact, Droste stated this during the presentation of his paper when he just learned of the existence of the Schwarzschild paper. However, there is one serious caveat. No mathematically valid coordinate transformation (differentiable with a differentiable inverse) can remove the horizon singularity. Therefore the physical evolution of matter through the horizon is impossible. – safesphere Feb 25 '24 at 05:59
  • 1
    @JanG The existence of the inner singular spacetime is an assumption. The inner solution only shows what it would have been, if it existed. Like that the sides of my one square meter coffee table would be minus one meter, if negative sides existed in reality, but they don’t. In a realistic collapse, the inner spacetime never forms, so there is nothing inside ever as far as the universe is concerned. And if you jump in, they say you can cross to some weird brief temporal sideway extension of spacetime located beyond the cosmological eternity. Even if unlikely true, this doesn’t affect anything. – safesphere Feb 25 '24 at 06:10
  • @safesphere You speak exactly my thoughts. I try to prove it mathematically for static spherically symmetric perfect fluid spheres, outgoing from the hypothesis that Einstein's theory does not break down at the star center when the pressure diverges by finite energy density there. – JanG Feb 25 '24 at 07:51
  • @safesphere By the way, your example with coffee table is exquisite. – JanG Feb 25 '24 at 08:42
  • @safesphere Brightest universe black hole discovered. Why only now? (…)The world's telescopes produce so much data that astronomers use sophisticated machine learning tools to sift through it all. Machine learning, by its nature, tends to find things that are similar to what has been found before.(…). The same bias can be found among physicist who learned GR. – JanG Feb 25 '24 at 08:59

0 Answers0