I Big Bang Singularity vs Black Hole Singularities

[Islam Hassan]

Is there a fundamental difference between the (speculative) understanding of a singularity arising from the creation of a black hole and the singularity which we think may have been at the origin of the Big Bang?

Noteably, would there be two basic theoretical types of singularities, gravitationally attractive and gravitationally repulse ones or would both be variants of one fundamental singularity?IH

 

[PeterDonis]

Is there a fundamental difference between the (speculative) understanding of a singularity arising from the creation of a black hole and the singularity which we think may have been at the origin of the Big Bang?

Yes. These singularities are associated with different spacetime geometries.

would there be two basic theoretical types of singularities, gravitationally attractive and gravitationally repulse ones

No, there are more--the key difference is the spacetime geometry that the singularity is associated with. "Gravitationally attractive" and "gravitationally repulsive" are just time reverses of each other; they're not different spacetime geometries.

 

[Islam Hassan]

Yes. These singularities are associated with different spacetime geometries.
No, there are more--the key difference is the spacetime geometry that the singularity is associated with. "Gravitationally attractive" and "gravitationally repulsive" are just time reverses of each other; they're not different spacetime geometries.

What then do we think would govern whether a singularity is theoretically attracting matter or expelling it? If by definition a singularity is infinitely dense, what is speculated to be the consideration underlying the incoming/outgoing ‘momenta’ which would either attract or expel matter (and radiation)?IH

 

[Ibix]

The first thing to realize is that the singularities almost certainly don't exist. General relativity is away of taking our observations of here-and-now and extrapolating them to other places and times. The singularities are evidence that GR stops being an accurate model of reality somewhere between places and times we can test and whatever is/was going on inside a black hole and at the beginning of the universe. So one possible answer to your questions is that they are mis-conceived - there are no singularities.

That said, GR does predict singularities, and they are different in some sense. The black hole one is a singularity in the time-time part of the metric while the big bang one is in the space-space part, so different things are going wrong with the maths in the two cases.

Edit: way too slow, I see.

 

[Islam Hassan]

The first thing to realize is that the singularities almost certainly don't exist. General relativity is away of taking our observations of here-and-now and extrapolating them to other places and times. The singularities are evidence that GR stops being an accurate model of reality somewhere between places and times we can test and whatever is/was going on inside a black hole and at the beginning of the universe. So one possible answer to your questions is that they are mis-conceived - there are no singularities.

That said, GR does predict singularities, and they are different in some sense. The black hole one is a singularity in the time-time part of the metric while the big bang one is in the space-space part, so different things are going wrong with the maths in the two cases.

Edit: way too slow, I see.

Thanks, I will try to dig into this time-time, space-space aspect...I think this is what may best explain the difference.

And I agree that there is a fair chance that singularities are mathematical...that physically something else may be happening...IH

 

[PeterDonis]

What then do we think would govern whether a singularity is theoretically attracting matter or expelling it?

"Attracting" or "repelling" aren't good categories to begin with. The initial singularity in FRW spacetime, for example, is not "repelling matter". And, as I've already noted, while a black hole singularity can be thought of as "attracting matter", its time reverse, a white hole singularity, can equally be thought of as "repelling matter", but in essence they are the same spacetime geometry, just time reversed. They're not different singularities.

The black hole one is a singularity in the time-time part of the metric while the big bang one is in the space-space part,

This is not correct. Which "part of the metric" becomes singular (if any--see below) depends on your choice of coordinates and is not an invariant classification of singularities. Also, even in standard Schwarzschild coordinates, both $g_{tt}$ and $g_{rr}$ are singular at $r = 0$. And in FRW coordinates, none of the metric coefficients in FRW spacetime are singular at $t = 0$; it's just that the scale factor $a(t)$ vanishes.

The key difference between a black hole singularity and the initial FRW singularity is that the former has a Weyl tensor that increases without bound and a zero Ricci tensor, while the latter has a vanishing Weyl tensor and a Ricci tensor that increases without bound. This is a difference in spacetime geometry, as I said.

 

[Islam Hassan]

Thanks PeterDonis for the clarification...much appreciated...IH

 

[rootone]

Singularities are not physical 'things'
They are a mathematical conundrum,
In extreme circumstances something must be happening which is unknown. beyond well understood and tested physics

 

[Ibix]

This is not correct. Which "part of the metric" becomes singular (if any--see below) depends on your choice of coordinates and is not an invariant classification of singularities. Also, even in standard Schwarzschild coordinates, both $g_{tt}$ and $g_{rr}$ are singular at $r = 0$. And in FRW coordinates, none of the metric coefficients in FRW spacetime are singular at $t = 0$; it's just that the scale factor $a(t)$ vanishes.

I take your point about using curvature invariants - I should have remembered it without prompting. But $g_{rr}$ is not singular at $r=0$, unless I'm missing something completely. $g_{rr}=(1-r_s/r)^{-1}=r/(r-r_s)$ which goes to zero.

 

[martinbn]

The Weyl curvature conjecture distinguishes initial and final singularities. Roughly initial ones should have vanishing Weyl curvature and final (cosmological or collapse to a black hole) should have divergent Weyl curvature.

 

[Ibix]

The Weyl curvature conjecture distinguishes initial and final singularities. Roughly initial ones should have vanishing Weyl curvature and final (cosmological or collapse to a black hole) should have divergent Weyl curvature.

How does that work for something like a maximally extended Schwarzschild spacetime? Aren't the two singularities identical under time reversal? Or are you only talking about realistic spacetimes?

 

[PeterDonis]

The Weyl curvature conjecture distinguishes initial and final singularities.

This conjecture is a conjecture about what spacetime geometry will actually occur. It does not change the characteristics of any particular spacetime geometry.

How does that work for something like a maximally extended Schwarzschild spacetime?

It doesn't. Maximally extended Schwarzschild spacetime is a particular spacetime geometry; you can't change its geometry by making a conjecture. The conjecture is basically saying something like: singularities in the past like the white hole singularity in maximally extended Schwarzschild spacetime will never actually occur.

 

[PeterDonis]

$g_{rr}$ is not singular at $r=0$, unless I'm missing something completely. $g_{rr}=(1-r_s/r)^{-1}=r/(r-r_s)$ which goes to zero.

Yes, you're right, I was forgetting that you can rewrite $g_{rr}$ so the denominator is not singular at $r = 0$.

 

[Ibix]

It doesn't. Maximally extended Schwarzschild spacetime is a particular spacetime geometry; you can't change its geometry by making a conjecture. The conjecture is basically saying something like: singularities in the past like the white hole singularity in maximally extended Schwarzschild spacetime will never actually occur.

OK - that's what I thought @martinbn was saying, but wasn't sure I wasn't misunderstanding. Does this conjecture disfavour closed FLRW universes too? I thought the "big crunch" was basically a time-reversed big bang, presumably with zero Weyl and diverging Ricci curvatures.

 

[PeterDonis]

Does this conjecture disfavour closed FLRW universes too?

No. Those also have vanishing Weyl curvature at the initial singularity.

I thought the "big crunch" was basically a time-reversed big bang, presumably with zero Weyl and diverging Ricci curvatures.

In an idealized exact FRW geometry, this is true. But the kind of universe envisioned in the Weyl curvature conjecture is one which initially is like an idealized exact FRW solution, but over time evolves structure due to gravitational clumping around small variations in the matter distribution, so that if such a universe is closed, the "Big Crunch" singularity will basically be a lot of gravitationally clumped systems coming together, which will involve diverging Weyl curvature. In other words, such a universe is not time symmetric. Basically the Weyl curvature conjecture is an attempt to account for time asymmetry in universes like ours (since our actual universe resembles the one I just described in that it is much more gravitationally clumped now than it was just after the Big Bang--i.e., variations in density are much larger).

 

[Ibix]

the kind of universe envisioned in the Weyl curvature conjecture is one which initially is like an idealized exact FRW solution, but over time evolves structure due to gravitational clumping around small variations in the matter distribution, so that if such a universe is closed, the "Big Crunch" singularity will basically be a lot of gravitationally clumped systems coming together, which will involve diverging Weyl curvature. In other words, such a universe is not time symmetric. Basically the Weyl curvature conjecture is an attempt to account for time asymmetry in universes like ours (since our actual universe resembles the one I just described in that it is much more gravitationally clumped now than it was just after the Big Bang--i.e., variations in density are much larger).

This seems a bit have-your-cake-and-eat-it to me (I'm aware this is likely a problem with my understanding!). Don't you need the universe to be homogeneous on a large scale for an FLRW-type solution? So if you are saying that the universe eventually stops looking homogeneous then why are FLRW-type solutions relevant in that far future? Or, alternatively, if it always looks homogeneous on a large enough scale and all this Weyl curvature is just local noise then don't we still have Ricci curvature somewhere?

I see there are a couple of arxiv papers referenced in https://en.m.wikipedia.org/wiki/Weyl_curvature_hypothesis, so I shall do some reading. Any good introductory/overview type references gratefully accepted.

 

[PeterDonis]

this is likely a problem with my understanding!). Don't you need the universe to be homogeneous on a large scale for an FLRW-type solution?

Yes.

if you are saying that the universe eventually stops looking homogeneous

I'm not. Our universe is homogeneous on a large scale, but it has very large variations in density on smaller scales. The Earth is about 30 orders of magnitude denser than the average density of the universe as a whole; a neutron star is about 13 orders of magnitude denser still.

if it always looks homogeneous on a large enough scale and all this Weyl curvature is just local noise then don't we still have Ricci curvature somewhere?

Yes. What difference does that make? In a Big Crunch in a universe similar to ours but closed, both Weyl and Ricci curvature would increase without bound as the Big Crunch was approached. Whereas in an idealized exact FRW universe that was closed, Ricci curvature would increase without bound but Weyl curvature would vanish. There's no requirement that Ricci curvature have any fixed relationship to Weyl curvature.

 

[Islam Hassan]

What is the lower limit in terms to the limit of homogeneity? I recall a video from sixtysymbols refencing “the largest structure” in the universe which had very substantial extent:

IH