Almost nobody actually believes the singularity is real, it’s just what the math tells us – it’s where the math of GR breaks down, and a better theory of gravity would be needed to resolve it.
I’ve never heard a black hole described as a manifold, but then again I’m not sure exactly what a manifold is.
exhaust manifold on combustion engine takes raw cylinder exhaust gases in pipes that all come down and combine into a single larger pipe that connects to the input of a catalytic converter.
the plenum in your attic is a manifold. One big duct runs from your air handler into a box with several ducts coming from it, delivering air to each of the vents. the ducts and the plenum form a manifold.
In literature, it means ‘many and various’.
In mathematics, “a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analog of this in three or more dimensions”
In Kantian philosophy, “the sum of the particulars furnished by sense before they have been unified by the synthesis of the understanding”
Origins: Old English manigfeald ; current noun senses date from the mid 19th century.
All from the wikipedia
They all have some descriptive relevance, but the one that really counts for us is the math one, suggesting the closed surface.
It wouldn’t surprise me though if it still worked; there are many examples of topologically closed surfaces that can still be traversed, if in unexpected ways. I’m thinking of another manifold, the klein bottle, and of course the mobieus strip.
Also Idk what you are talking about nobody believing there’s an actual singularity; I don’t know what else you think is happening, or of what use the mathematics might be if it doesn’t approach some degree of accuracy as concerns the physical character of the phenomena
We know that GR predicts some things extremely well, and QM some things extremely well, but they fundamentally disagree. Both CANNOT be entirely correct, and black holes is the most notable case where one or both break down. (See the “black hole information paradox”.)
Almost nobody actually believes the singularity is real, it’s just what the math tells us – it’s where the math of GR breaks down, and a better theory of gravity would be needed to resolve it.
I’ve never heard a black hole described as a manifold, but then again I’m not sure exactly what a manifold is.
@exscape
@readbeanicecream
A couple examples of manifolds:
exhaust manifold on combustion engine takes raw cylinder exhaust gases in pipes that all come down and combine into a single larger pipe that connects to the input of a catalytic converter.
the plenum in your attic is a manifold. One big duct runs from your air handler into a box with several ducts coming from it, delivering air to each of the vents. the ducts and the plenum form a manifold.
In literature, it means ‘many and various’.
In mathematics, “a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analog of this in three or more dimensions”
In Kantian philosophy, “the sum of the particulars furnished by sense before they have been unified by the synthesis of the understanding”
Origins: Old English manigfeald ; current noun senses date from the mid 19th century.
All from the wikipedia
They all have some descriptive relevance, but the one that really counts for us is the math one, suggesting the closed surface.
It wouldn’t surprise me though if it still worked; there are many examples of topologically closed surfaces that can still be traversed, if in unexpected ways. I’m thinking of another manifold, the klein bottle, and of course the mobieus strip.
@exscape
@readbeanicecream
Also Idk what you are talking about nobody believing there’s an actual singularity; I don’t know what else you think is happening, or of what use the mathematics might be if it doesn’t approach some degree of accuracy as concerns the physical character of the phenomena
Here’s some reading about black holes singularities and whether they’re real or not:
https://www.pbs.org/wgbh/nova/article/are-singularities-real/
https://en.wikipedia.org/wiki/Gravitational_singularity#Interpretation
We know that GR predicts some things extremely well, and QM some things extremely well, but they fundamentally disagree. Both CANNOT be entirely correct, and black holes is the most notable case where one or both break down. (See the “black hole information paradox”.)