A few black hole questions:
Since Hawking Radiation causes a black hole to lose a set amount of mass per unit time as a function of radius, wouldn’t that information be sufficient to determine the distribution of matter/energy within the black hole?
With regards to the space time curvature is that basically the time coordinate is changing as a function of radius?
So if we look at each layer of the black hole sort of like an onion, how is it that stuff with a different time coordinate interacts?
Currently accepted theories say Hawking radiation is thermal, that is, complete random. It carries no information and bears no relationship to whatever “ingredients” went in to creating the black hole. Black holes still have no hair, even taking Hawking radiation into account.
More fundamental to your first and last questions, there is no “inside” to a black hole. Perhaps you’re referring to the event horizon?
–Mark
If x grams of matter are to be emitted from the black hole at time t wouldn’t it be accurate to say that there is x grams of matter at a particular radius from the center of the black hole that corresponds to time t?
No, not at all. Hawking radiation isn’t particles inside the hole somehow escaping through the event horizon. It’s (roughly speaking) caused by virtual particle pairs spontaneously forming near, but outside, the horizon. Then one particle of the pair escapes and the other falls in and is lost. Particle pairs are forming like this everywhere all the time, but normally they almost immediately recombine and the individual particles are never seen. The black hole’s gravity is able to separate the pair of virtual particles and cause them to become “real” particles.
–Mark
Well does the energy come from the center of surface of the black hole?
The energy comes from the mass of the black hole; that’s why the hole shrinks over time. Basically the particle that falls in has negative energy, which reduces the mass of the hole and allows the escaping particle to have positive energy.
–Mark
Under the standard models (which are really all we can go by, since observation is impossible), there is no place where a black hole has any mass. Any bounded volume that does not enclose the singularity contains no mass. Any bounded volume that does enclose the singularity contains the entire mass of the hole, but the singularity itself is “no place”: It corresponds to a point that is not a part of the spacetime.
I thought the idea of a true singularity was falling out of favor? Hmmm. These are the times I wish my math background was a bit better. I have to go by some primitive reasoning.
The idea came to me what would an evaporating black hole in an otherwise empty universe look like over time. And it seems a real singularity that held everything so to speak wouldn’t be able to evaporate. And since the rate of evaporation was a function of size it seems like you would be able to calculate the future change in size at any instant which would enable you to calculate the change in mass.
So the idea that if between year 0 and year 1 of evaporation if the black hole lost 1kg the idea that 1kg existed in the portion of the black hole that evaporated is incorrect? Even if each subsequent year or interval of time has a calculable mass that will be lost?
Frankly this reminds me of talk about particle/wave duality for electrons. Who cares? Someday if we can’t find a more convenient way, we’ll make artificial black holes so we can convert matter completely to energy. Even if the black hole “has no mass” or some other bullshit it’ll clearly have a certain amount of mass that went into making it, it’ll emit a certain amount of energy per unit time that will destroy the mass equivalent of that energy, and so on. You can probably also charge black holes by feeding them an imbalance of electrons or protons. Guess these “massless, uncharged” objects…will be moved around in your spacecraft’s engine core like they have a mass and a charge.
Many people aren’t happy with a singularity but we don’t have any good alternative theories at this point. But for practical purposes, it looks and quacks very much like a singularity. It’s certainly NOT the case that any of the mass of the black hole is spread out over a macroscopic region.
I think you may be thinking of “mass” as “a quantity of matter”, which doesn’t work well in this case. The black hole has a mass, which decreases over time due to Hawking radiation. If 1 kg of radiation is emitted, the hole’s mass decreases by 1 kg. But it’s not correct to think that a kilogram of particles was previously sitting inside the event horizon and now they’re outside.
–Mark
I think Chronos may have expressed himself unclearly. Black holes definitely do have mass; it’s one of the only three intrinsic properties that black holes do have, the other two being (electric) charge and angular momentum.
–Mark
Why is that? Can you elaborate on the rationale for it, please?
I am puzzled about the statement if for no other reason that it was my understanding that given a large enough black hole (i.e. large radius of event horizon), you could be inside of it without noticing much, if any, in the way of unusual phenomena. Those occurred only as you got nearer to the singularity. If I am right about that, then it would seem to imply that you could have a volume that doesn’t include the singularity (for example, the volume occupied by the “you” of my hypothetical above.
Have I embarrassed myself? Again?
Let’s try a thought experiment. Suppose we drop a lump of matter with significantly large mass towards a black hole. We can measure the distribution of the infalling mass by observing the spacetime deviations it causes.
What happens when it crosses the event horizon? Well, we can’t ever observe it crossing. Instead we see its gravitational effects slowly fade. (Similar to how a radiating body becomes red shifted.) Eventually, we’ll no longer be able to measure it at all, beyond the mass added to the black hole.
I expect this transition to be smooth, so I’m not sure what the boundary between the distribution of mass of irrevocably infalling matter and the singularity’s distribution is.
Strictly speaking, you’re right: There can of course be mass concentrations in the vicinity of a black hole, and there can even be mass concentrations within the horizon… for a very short time. But those mass concentrations will disappear in a time corresponding to the time it takes light to cross the hole, leaving behind the vacuum part of the hole
Ah, so it depends on the frame of reference (whether you’re looking in or are already in)?