Markus Hanke

What do you mean by this? Clearly, gravity across vacuum regions just as much as it does inside energy-momentum distributions.

Exactly.

Thanks I've a good bit of material to go through now, much of it pretty non-trivial, so I'll have to take it a step at a time. This is all new territory to me, as until quite recently I wasn't aware that such things as fractal and fractional calculus even existed.

Great, thanks :) Let us, for the time being, just say that I am curious as to what happens when you relax the notion of smoothness that underlies pretty much all our physical models. I’m also curious what would happen if dimensionality of space/time were allowed to vary with scale, even just minutely, and take on non-integer values in some regimes. I’ve also recently discovered the concept of the fractional (distinct from “fractal”) derivative, which naturally introduces a notion of non-locality into analysis, so I am curious as to that, too. I want to first learn what the literature says about these things, and, once I’m a little familiar with the tools of the trade, experiment a little myself, insofar as I am able to. I do have something particular in mind, and yes, it’s to do with spacetime, but I don’t know yet if that is viable even in principle, so I won’t go into it just yet. I’m sure I will have a lot of questions along the way!

Textbook recommendations, please I'm currently investigating an idea I've had, and in that context I need to familiarize myself with both local and non-local Fα-calculus ("fractal calculus") on fractal sets. I don't wish to go into the details of the project just yet, as right now it only exists in form of a very rough outline, and I need to to investigate first if it is in fact worthwhile pursuing at all (chances are it might not be). Suffice to say I need a mathematical toolset that generalizes ordinary multivariate calculus / differential geometry on smooth differentiable manifolds to fractal sets with non-integer Hausdorff dimensionality. So I'm looking for a text that introduces Fα calculus, including fractal derivatives and integrals, both of integer and fractional order (think Riemann-Liouville with fractal measure); a generalization of the usual differential operators (div, grad, curl,...) to fractal sets; differential equations on fractal sets; and ideally Dirichlet forms. I've got access to "Fractal Calculus and Its Applications" by Golmankhaneh, but I find it to be too technical for me as an interested amateur. I'm hoping perhaps someone here can recommend a text on the subject that is more accessible and builds intuition, rather than just listing definitions and lemmas? I've tried searching the Interwebz of course, but there appears to be surprisingly little literature on this particular subject - or perhaps I just didn't search for it right. Thanks in advance!

As measured by which clock?

I’m currently on a month-long long-distance hike in the Alps, and have been crossing the border between Germany and Austria multiple times along my route. I noticed that I can’t access the site in Austria - it gives the very problems described by others above -, but as soon as I’m on the German side and my phone connects to a German provider, all seems fine. Maybe just a coincidence, but it is strange.

All these things originate outside the event horizon. What they don’t mention is that adding torsion into our models of gravity has other consequences too - in particular, it modifies the Dirac equation, making it non-linear. We have not observed any of the associated effects that would arise from this.

The problem is mostly that there exist situations in nature where both gravity and quantum effects appear to be simultaneously non-negligible. Thus, it is reasonable to assume that there should exist some mathematical framework that can describe such situations in an internally self-consistent way. But you are right in that this framework taking the form of a single unified theory is largely an assumption based on what happened with the other fundamental interactions. Though I must say it is difficult to see what a possible alternative might look like.

I used to have this problem too, until I recently changed phones (the old one died after ~10 years), and thus upgraded to new versions of both OS and browser. Now the issue is gone completely. Looks like this is a local problem, not server-side.

Spacetime and its geometry are “there” not only in vacuum, but also in the interior of energy-momentum distributions. There is no situation where there is not spacetime, since there is nowhere one can not place rulers and clocks. I still don’t get what the “issue” here is…?

They are the current scientific consensus, and thus the best models we currently have. Take careful note of the word “currently”. Physics, like all sciences, is a process - as new data becomes available to us, the consensus may need to be updated, and occasionally radically reworked (“paradigm shift”, like from Newton to Einstein eg).

It depends what is meant by “precisely”. If you mean exactly, ie with no deviations at all, then I agree that this is probably not possible. In practice though it is often possible to minimize differences such that their effects on the evolution of the system are negligible, at least for some specified period of time.

How about the Vaidya class of black holes? These spacetimes are not asymptotically flat.

Nice way to visualise this +1