And that’s just it, TAMOP. General relativity clearly isn’t the only thing going on in the Universe. Many of the singularity theorems clearly do not apply in real-world cases due to known physics like atomic and nuclear degeneracy pressure. I think it’s the bigger leap of faith to assume there isn’t any other type at a smaller scale/higher energy than to assume the singularity theorem rigorously holds to all orders, but we’re talking about unexplored territory here.
The event horizon, however, isn’t nearly so dependent on those types of degeneracy.
Interesting, I’m vaguely aware that LQG has something different to say about black holes? I’m suprised the event horizon is much more durable than the singualrity, on the other hand perhaps I shouldn’t be due to the diffreren kind of limits that the event horizon and singualrity live in.
Hey, don’t worry about it, my brother still insists that I refer to him as a “dual board certified thoracic and endo-vascular surgeon” instead of just my brother the doctor.
First, “where relativistic effects become very noticeable” depends on what experiment you’re using to try to notice them. Relativistic effects are always present, at any distance from a mass, and at any speed. Second, the spaghettification isn’t inherently a relativistic effect: You’d get that in Newtonian mechanics, too. In fact, the tides are due to the Moon and Sun spaghettifying Earth’s oceans.
Quoth ethansiegel:
No, atomic and nuclear degeneracy pressure do not cause any problems whatsoever for the singularity theorems. Those are insufficient to prevent collapse anywhere above the Chandrasekhar limit, and even if you found some way to strengthen them (building a star out of lighter particles than protons and neutrons, say), you’ll still have some upper limit, which conditions inside a black hole would exceed. If there’s any physical phenomenon which can prevent the formation of a singularity, it’d have to be quantum gravitational in nature.
Chronos, I owe you an apology for my looseness with atomic and nuclear degeneracy pressure. You’re right that, for masses below a certain limit, there’s nothing wrong with forming a singularity.
However, your last statement isn’t strictly true. Even inside the event horizon of a black hole, if you violate the strong/dominant energy condition (which, for instance, scalar fields can do), you do not necessarily form a singularity. And, much like inflation, it can happen well below the scale of quantum gravity.
I think it’s important to keep an open mind when we’re extrapolating upwards 16 orders of magnitude in energy from anything that’s been well-studied.
You’re thinking of something like a Schwarzschild-deSitter black hole? I’m not an expert on those, but I have a friend who is. I’ll see if I can ask him about it.
As for “well below the scale of quantum gravity”, it’s worth pointing out that we don’t even know what the scale of quantum gravity is. The Plank scale is a plausible educated guess, but there are also plausible models that put it down all the way in the TeV range (hence all the speculation about the LHC producing black holes).
Fair enough. I wasn’t thinking about S-dS (which I haven’t looked at seriously since year 3 of grad school), I was thinking about the interior particles collapsing to a beyond-the-SM-state involving fundamental scalars with non-zero VEVs. Usually S-dS is used to describe spacetimes that are approximately Schwarzschild close to the source of the point mass and asymptotically de Sitter far away, but I do not know what it means for the interior of the event horizon.
But you’re right, in many extra-dimensions scenarios (which I don’t like personally, but aren’t any more ruled out than many of the speculative physics ideas I’m bringing up), the quantum gravity scale can be as low as TeV range. (Hell, I can’t complain too much; my 2nd scientific paper was about gravity in extra dimensions!)
In any case (back to the OP), I think it’s fair to say that there may not be a singularity at the center of every black hole, but we have no way of extracting that information once it passes beyond the event horizon.