@Terrapin Station It seems an oddly parochial prejudice. What other celestial entities don't you believe in? I get the impression you doubt black holes merely because they're not directly visible.

"Spacetime curvature" isn't a real thing, because space/time aren't anything like substances. "Spacetime curvature" is at best a manner of speaking to account for observational data re existents.

It is your apparent attachment to "substance" that would be scientifically anachronistic here.

Solving equations has nothing to do with positing real ontological entities. — Terrapin Station

That is a thoughtless and irrelevant retort. The question that started this line of discussion was whether black holes were "invented" in order to accommodate some observations that, as you said, did not fit existing gravitational models. That is exactly backwards. The observations that we now attribute to black holes fit our gravitational models like a glove.

That they're consistent with GR doesn't make them a prediction of GR. We invented them so that they'd be consistent with GR, otherwise we'd need to retool our gravitational theory. — Terrapin Station

Not so.
Relativity was/is falsifiable, but has since been verified on several occasions.
It is used in GPS today.
Black holes are predictions of relativity, and has not been falsified per se.
That said, relativity's domain of applicability doesn't quite include the micro-domain of quantum mechanics, so there's not really any telling what may happen in a super-dense super-high-temperature black hole, where relativity suggests a singularity.

Tests of special relativity (Wikipedia article)
Tests of general relativity (Wikipedia article)

It follows from this lawful relation (i.e. Einstein's field equations) that whenever a spherical distribution of mass achieves a density such that it is contained within its Schwarzschild radius, then the escape velocity at the surface attains the speed of light. — Pierre-Normand

So the Schwarzchild principle does not follow directly from GR then, it follows from the assumption of a "spherical distribution of mas" in conjunction with GR. Such a spherical symmetry is just an ideal, like a perfect circle, there is no such thing in reality.

So the equations did exactly that - obliged us to posit ontologically real outcomes (of which black holes are one of many now empirically supported examples). — apokrisis

Are you claiming that a description which is based in the assumption of an ideal spherical symmetry is ontologically real? You are just committing the very same error as Aristotle when he assumed perfect, eternal, circular motions for the orbits of the planets. Such perfect circles are not ontologically real.

, no, a black hole tends towards a spheroid when using the Schwarzschild radius.
If it's not a "perfect sphere", then it's just some other shape, that can be modeled sufficiently accurately with the Schwarzschild radius for these purposes.

From wikipedia, it is based in the assumption of a speherical symmetry. But this simply assumes the traditional Newtonian representation of gravity, as a point particle at the gravitational centre of the massive object. I don't believe that such a symmetry has any basis in reality, it's just a theoretical convenience. So there is no reason to believe that the phenomena known as black holes are really similar to the theoretical black holes.

Another flat earther. — apokrisis

Not a flat earther, but a perfect circle denier. The ancient astronomers who wanted to replace the flat earth principles with perfect circles were just as wrong as the flat earthers. They described the sun, planets and moon as orbiting the earth, in perfect circles. The true reality was apprehended only through the realization that the so-called circles were not really circles. Dropping the idea of circles forced them have to figure out what was really the case.

Not a flat earther, but a perfect circle denier. — Metaphysician Undercover

You latched on to a phrase in a way that shows you don't understand the physical argument. Relativity would model the gravitational curvature as perfectly spherical, yet the definition is still asymptotic - the approach to a limit.

So Kerr models the ideal final state in a way then allows the calculation of actual physical histories. We can start to talk about real black holes in terms of their more lumpy and haphazard story of getting crushed down in practice towards the simple ideal.

Just check out the variety of modelled "imperfections" that in practice would break the perfect symmetry the description of the absolute limit describes....

The Kerr geometry exhibits many noteworthy features: the maximal analytic extension includes a sequence of asymptotically flat exterior regions, each associated with an ergosphere, stationary limit surfaces, event horizons, Cauchy horizons, closed timelike curves, and a ring-shaped curvature singularity. The geodesic equation can be solved exactly in closed form. In addition to two Killing vector fields (corresponding to time translation and axisymmetry), the Kerr geometry admits a remarkable Killing tensor. There is a pair of principal null congruences (one ingoing and one outgoing). The Weyl tensor is algebraically special, in fact it has Petrov type D. The global structure is known. Topologically, the homotopy type of the Kerr spacetime can be simply characterized as a line with circles attached at each integer point.

Note that the Kerr geometry is unstable with regards to perturbations in the interior region. This instability means that although the Kerr metric is axis-symmetric, a black hole created through gravitational collapse may not be so.‹See TfD›[dubious – discuss] This instability also implies that many of the features of the Kerr geometry described above may not be present in such a black hole.‹See TfD›[dubious – discuss]

A surface on which light can orbit a black hole is called a photon sphere. The Kerr solution has infinitely many photon spheres, lying between an inner one and an outer one. In the nonrotating, Schwarzschild solution, with α=0, the inner and outer photon spheres degenerate, so that all the photons sphere occur at the same radius. The greater the spin of the black hole is, the farther from each other the inner and outer photon spheres move. A beam of light traveling in a direction opposite to the spin of the black hole will circularly orbit the hole at the outer photon sphere. A beam of light traveling in the same direction as the black hole's spin will circularly orbit at the inner photon sphere. Orbiting geodesics with some angular momentum perpendicular to the axis of rotation of the black hole will orbit on photon spheres between these two extremes. Because the space-time is rotating, such orbits exhibit a precession, since there is a shift in the {\displaystyle \phi \,} \phi \, variable after completing one period in the {\displaystyle \theta \,} \theta \, variable.

https://en.wikipedia.org/wiki/Kerr_metric

You latched on to a phrase in a way that shows you don't understand the physical argument. Relativity would model the gravitational curvature as perfectly spherical, yet the definition is still asymptotic - the approach to a limit. — apokrisis

Well, we differ in opinion clearly, because I think you will necessarily get a mistaken result if you start from the premise of the perfect symmetry, and work backward away from this, to describe something which is not a perfect symmetry. It's like starting from a false premise.

So I believe that what you describe in the Kerr geometry is very useful for determining the ways in which the real black holes may differ from the perfect symmetry which is derived from the theory. But the real black holes will never be properly understood unless we can establish premises for the reasons why it does not conform to a perfect symmetry, then represent it with theory which starts from those premises, rather than the premise of perfect symmetry. The latter being only useful for determining how the real black hole differs from the perfect symmetry. To determine the true nature of the real black holes would require further speculation, not being accessible through the principles of GR.

Well, we differ in opinion clearly, because I think you will necessarily get a mistaken result if you start from the premise of the perfect symmetry, and work backward away from this, to describe something which is not a perfect symmetry. It's like starting from a false premise. — Metaphysician Undercover

I suppose on the same principle you object to rulers that pretend to be straight, and clocks that pretend to be regular.

It is physically impossible that they are, so we must simply throw all rulers and clocks away.

I suppose on the same principle you object to rulers that pretend to be straight, and clocks that pretend to be regular. — apokrisis

As I said, it's very useful for determining the different ways in which the thing being measured varies from the standard of measurement, but the straight ruler wont tell you why the thing you are trying to measure is crooked. Nor will you get an accurate measurement of the crooked thing using the straight ruler. That's why we must devise other means for measurement. But first we must figure out why the straight ruler is not giving an accurate measurement.

I feel like responding to you is exactly like chucking information down a black hole. The maximum entropy condition applies. Understanding is bent until no light could ever escape the perfect orb of denial.

But first we must figure out why the straight ruler is not giving an accurate measurement. — Metaphysician Undercover

So you don't think GR might help with that? Or do you accept the calculation of geodesics - only not in the vicinity of a black hole for some reason?

the straight ruler wont tell you why the thing you are trying to measure is crooked — Metaphysician Undercover

Except GR is telling you why your (Newtonian) ruler has a limit to its crookedness. The metric might curve, but it it can't be more curved than the surface of a sphere. A sphere is absolutely crooked - crookedness gone to its equilibrium limit. Talk of things being rounder than a circle is unphysical craziness.

And GR also defines the opposing limit of non-Euclidean curvature in saying that rulers could be bent hyperbolically the other way. Kind of like a white hole. Or the "inside" of inflation. That again is a limit-based argument. You can't diverge any faster than at an exponential rate. Crookedness in both directions has its geometric limits.

So a straight ruler has to live in an actually flat world - perfectly poised for no particular reason between the hyperspheric and hyperbolic limits on curvature. Or else we accept it bends with its world due to the world's gravitational contents, but we have ways of factoring that energetic out of our measurements. We know how to make relativistic corrrections so we can treat the world as if it met our demands to just be flat ... and its material contents don't make a difference to that.

So you don't think GR might help with that? — apokrisis

No, I don't. That's the point. GR is coming at the real existing phenomenon which is called a blalk hole, with the Schwartzchild principle, which assumes a perfect symmetry. This is the straight ruler. The real existing black hole is not a perfect symmetry, so it is something which cannot be measured with the straight ruler. The straight ruler (GR with Schwartzchild principle) might be able to help us determine how the real black hole differs from the theoretical black hole, in a somewhat unreliable, speculative way, but it will not be able to tell us why the real black hole differs from the theoretical one. Therefore won't tell us the true nature of the real black hole. We need another theory for that, something which gives us the appropriate ruler.

Crikey. That's nothing like how Kerr explained it. He said his metric was a mathematical description of a flat space containing a spinning object. Those were the two parameters that finally popped out as the solution to an appropriate simplification of the general equations. But hey, what do these "experts" know, eh?

The straight ruler is your analogy. Don't you recognize it as your analogy?

I suppose on the same principle you object to rulers that pretend to be straight, and clocks that pretend to be regular. — apokrisis

My claim was that we cannot derive the true nature of a real black hole through the means of the Schwartzchild principle because it approaches with the concept of a perfect symmetry, when the real black hole is not a perfect symmetry. You replied with the above quote about using straight rulers. And so I explained that I would object to using a straight ruler to measure a crooked object. That is what applying the Schwartzchild GR principle to a real black hole is analogous to, trying to measure a crooked object with a straight ruler. As much as the Kerr formulation may be an adaptation of the perfect symmetry in an attempt to measure the black hole, which is not a perfect symmetry, it is not the best approach. The right approach is to formulate a new theory which starts from a description of what a black hole really is.

Not so.
Relativity was/is falsifiable, but has since been verified on several occasions. — jorndoe

Verification is always provisional at best, and all it amounts to in this case is that the mathematics in question isn't clearly falsified by observation.

I explained that I would object to using a straight ruler to measure a crooked object. — Metaphysician Undercover

Is a crooked object one that is not straight in your view? If so, you have just defined it in contrast to straightness. You are claiming to have measured some degree of departure from the ideal.

But please, if you are measuring crookedness in some other fashion, explain away.

I have determined that the straight ruler is incapable of measuring the object which I desire to measure. If you want to call that "measured in some degree", then that's fine. I still need to find a better tool.

So how are you measuring crookedness? You have thrown away the notion of its converse - the ideal of the perfectly straight. What now? Talk me through your solution. What is this better tool that doesn't base itself on the ideal of the perfectly straight?

I haven't thrown away the ideal of the perfectly straight, I've determined that it is not useful in this situation. There are still many uses for those ideals. We use these ideals, such as geometrical principles, in construction and manufacturing, production. We build things according to these principles. But when we go to measure naturally existing things, we find that they do not naturlly exist according to these same ideals. We can artificially force naturally occurring elements to take the form of the ideal, as we do in manufacturing, but in their natural occurrence, they are not in the form of the ideal.

So you keep avoiding my question of how you would actually measure crookedness. Is there any way other than comparing it to what it is most directly not?

So you keep avoiding my question of how you would actually measure crookedness. Is there any way other than comparing it to what it is most directly not? — apokrisis

Well, as an example, I would take a string, and make it follow all the crooks of the crooked object, to get a better measurement.

OK. So after telling me how long something is - after all its crookedness has been flattened out - when are you going to tell me how crooked it is?

That's the hard part. That's what we need a different theory for. I hold the string to the ruler, so I just convert it to that straight ruler scale, but this does not really measure the item. That's why we need to refer to other scales. We can measure the volume by putting it in water and seeing how much water is displaced. We can weigh it, and figure the density. All these are different ways of measuring the item. I don't know how you would measure for crookedness, it depends on how you would define that. But what's your point?

My point remains the same. Crookedness is defined in terms of a departure from straightness.

Or the alternative is to be able to imagine "idealised crookedness" as the other pole of being from which actual being can then be measured. So now you would be measuring a reciprocal lack of crookedness (and thus an approach to the opposite ideal of absolute straightness).

This is simply how measuring the world works. We have to find some believable ideal and then measure the degree of deviation in terms of that. Then those ideals turn out to believable because they are self-defining by dichotomous logic. We see that reality is in fact bounded by its ideal extremes - and the bit in the middle we want to measure is now a position between the two bounds.

So talking about measuring crookedness by creating a crooked bit of string is not measuring anything. It doesn't give a number that reflects a position on some natural idea of a spectrum that is anchored by "fixed" bounds - or extremum principles, ideal limits.

Crookedness is defined in terms of a departure from straightness. — apokrisis

Sure, you can define crooked as not straight if you want. But there are all kinds of different ways that something can be crooked. It could be bent, twisted, curved, etc.. So "not-straight" tells us very little about the shape of the object, because "straight" is just one particular ideal which the object does not conform to. So we can proceed from the determination of not-straight, toward describing what the thing is really like, idea which it does conform to. Describing an object is saying what it is. And if necessary, we sometimes have to produce new idea which are based in the very existence of that object itself. Nevertheless, we describe an object by saying what it is, not what it is not. Proceeding toward understanding the object by saying what it is not, is very tedious, and it is much more efficient to describe what the object is.

This is simply how measuring the world works. — apokrisis

There is a lot more to understanding the world than measuring it. If the object doesn't conform to a particular ideal, and cannot be measured according to that ideal, then we do not gain an understanding of the object by saying it is not-X. We need to describe it, say what it is, in order to understand it. Describing an object is completely different from measuring it. And, I think it is necessary to have an accurate description before it is even possible to measure an object. The description allows us to determine which of our ideals will be useful in measurement, and develop other ideals if necessary.

Describing an object is completely different from measuring it. — Metaphysician Undercover

And so you change the subject yet again.

And so you change the subject yet again. — apokrisis

I thought I'd try to make some progress in this discussion. You seem to be bogged down in your infatuation with measurement.

Sure, you can define crooked as not straight if you want. But there are all kinds of different ways that something can be crooked. It could be bent, twisted, curved, etc. — Metaphysician Undercover

So now you have all these other description of crooked - bent, twisted, curved, etc. If something is not bent, what is it? If something is not twisted, what is it? If something is not curved, what is it?

Do you object violently to the description of "straight" for some reason?