Spaghettification: Geometrical & Mathematical Description

[zvwner]

TL;DR Summary

Looking for geometrical description / mathematical approach to describe Spaghettification to a given body

Looking for geometrical description / mathematical approach to describe Spaghettification to a given body.
Is there a specific paper (maybe computer simulations) that can serve me to understand in detail the phenomena?

 

[pervect]

There's a detailed treatment in MTW, for the Schwarzschld metric. But you'll need some familiarity with the Riemann tensor and its interpretation. to follow it It's an A-level approach (graduate level), I supect it's too high but don't see a level on this thread or have any insight.

The interior metric of an actual black hole will be differen than Schwarzschild.. Kip Thorne has a description of what he thinks will happen in one of his books, "Black holes and timewarps".

 

[Halc]

Does it need to be a singularity like a black hole? Saturn's rings are the result of spaghettification of some moon that dropped its orbit within the Roche limit. Of course I can't help you find a simulation of the formation of those rings. The mathematics involved is still quite complex, but probably less so than that of a black hole.

 

[PAllen]

Note, for a small BH, spaghetificaction happens well outside the event horizon, while for a supermassive BH it happens only well inside the horizon.

 

[PeterDonis]

Saturn's rings are the result of spaghettification of some moon that dropped its orbit within the Roche limit.

Not really. "Spaghettification" is not just a general term for "any effect of tidal gravity". It's a more specific term that describes what happens when tidal gravity increases without bound as some limit, such as the singularity inside a black hole, is approached.

Some authors use "spaghettification" in an even more specific sense, to mean, not just tidal gravity increasing without bound, but increasingly chaotic oscillations of tidal gravity, of the sort that occur in a BKL singularity.