I’m sure there’s a flaw in the following argument, but I’d like to know what. In theory you can make a black hole just by crowding enough photons into a small enough space. But if you’re using photons of a wavelength substantially greater than the Schwarzschild radius of the black hole that would be produced, then don’t you run into the problem that it’s uncertain whether in fact enough photons are within the Schwarzschild radius to undergo gravitational collapse?
Realistically it’s not something that needs to be worried about as the uncertainty , however you have hit upon a problem of quantum gravity.
In general relativity the stress-energy tensor describes the distribution of mass, energy, etc in spacetime and its related in a very straightforward way to certain tensors that describe the gravitational field in the form of the curvature of spacetime.
The problem is when we add quantum physics to the mix what changes?
One way to do this is semiclassical gravity, in semiclassical gravity the gravitational field in the form curvature is treated pretty much the same as it is in general relativity, but the source of the field (i.e. the stress-energy tensor) is treated using quantum physics. This is done by replacing the stress-energy tensor in Einstein’s field equations with the expectation value of the stress-energy operator. This means that if in a given region of spacetime if the stress-energy tensor is uncertain then the gravitational field will governed by the weighted-average of all possible different stress-energy tensors. To take your black hole example, gravitational collapse will only occur if it occurs in the average all possible outcomes.
However we’re running into some problems straightaway. Though the expectation value might yield a black hole we could make a measurement of the stress-energy tensor and find it in a non-black hole or in other words it’s possible to gravitationally uncollapse a black hole by collapsing its wavefunction! And indeed as the expectation value needn’t even be value that is the possible outcome of a measurement in theory, it’s at least conceivable that there could exist situations in which a measurment of the black hole will always reverse gravitational collapse. Of course at this point we would probably point out we only get such silliness as we’ve stretched semiclassical gravity past its breaking point and that a full theory of quantum gravity would not only treat the source of the gravitational field using quantum physics, but would also use quantum physics to treat the field itself. However now we run into one of the biggest problems of quantum gravity: if the geometry or even topology of spacetime is subject to uncertainties then how can we even define anything on it as the spacetime itself is defined by its geometry? As of yet there still is no full theory of quantum gravity.
I think that in any situation where it’d be ambiguous as to whether a black hole formed, the resulting black hole (if any) would be one on the verge of final evaporation.
For suitably-compatible values of “ambiguous” and “verge”, of course.
Reading this sentence, it is clear that you and I have very different definitions of “straightforward” ![]()
The tensors themselves aren’t all that straightforward, by a layman’s standards, but the relationship between them is about as straightforward as it can get, being merely a direct proportionality: G = 8piT