Tim Thompson
Muse
- Joined
- Dec 2, 2008
- Messages
- 969
A lot of people don't seem to like the idea of black holes. Understandable if you happen to run into one, but not if you simply wish to challenge the general validity of the idea. But whether you like the idea or not, it seems only reasonable that one should actually know what a black hole is before deciding, one way or the other. So I steal the following comment from the overcrowded "Lambda cosmology" thread to illustrate the point.
The word singularity is a term from mathematics and describes a point, or locus of points, where a given equation is undefined. The ratio 1/0, for instance, is not equal to infinity, but is rather undefined because you simply cannot do it, the arithmetic operation does not exist at all. However, the limit of the ratio 1/x as x approaches 0 is infinity. There is a distinct difference & important between the two ideas, which is left as an exercise for the reader to figure out. So we say that the equation 1/x = is singular if x=0.
The key is the singularity is a mathematical artifact and not a physical object. The singularity is not as such expected to exist, but rather to indicate that the singular equation needs to be replaced with one that is not singular, either from the same or a different theory, if one is to physically describe events at the singular points in spacetime (the points which are singular in one equation need not be singular in another; 1/x = y is singular if x=0, but x2=y is not singular for any non-infinite value of x).
Viewed from the outside, the singularity is hidden behind an event horizon so it cannot be seen. Once inside the event horizon, the geometry is such that all existing spacetime trajectories terminate at the singularity. What happens than is, of course, equally undefined.
So let us ask the question: Do black holes actually exist? How can we tell, by observation, one way or the other? The answer is to look for the event horizon. All compact astrophysical objects, except black holes, have a hard compact surface. Most of the objects that appear massive enough to be candidate black holes are accompanied by an accretion disk of infalling material which becomes extremely hot, and is easily visible to astronomers in X-rays. If the hot matter hits a hard surface, it will flare in a manner that indicates the presence of a hard surface. On the other hand, if the hot matter falls into a black hole it simply disappears with no appreciable fanfare. Hence, we should be able to observationally distinguish between the presence or absence of the unique event horizon of the black hole by its flaring behavior. We also know that any hard hot surface will emit thermal X-rays, whereas a black hole event horizon will have no detectable thermal emission. So we should be able to distinguish between a "normal" compact object (such as a neutron star or exotic quark star & etc.) and an event horizon by the presence or absence of a thermal component in X-rays.
These have been done and observations now positively indicates the presence of event horizons. See, for examples Paul, et al., 1998; Done & Gierliński, 2003; Narayan, 2003; McClintock, Narayan & Rybicki, 2004; Remillard, et al., 2006.
All of you who have your own alternative ideas in cosmology or relativity, and those of you who insist that black holes are just artifacts of some kind, and not physically real have a new problem. Observational evidence strongly supports the presence of event horizons, and only black holes are known to be associated with such things. So in order to argue that black holes are not physically real, you have to deal not only with the mathematics of general relativity (i.e., read Chandrasekhar's Mathematical Theory of Black Holes and prove he is wrong), but also with a small but growing mountain of observational evidence.
Black holes are physically real and they are not going away any time soon.
The "zero volume" and "infinite density" part applies only to the singularity itself, but the black hole is a considerably more complicated thing which enjoys a volume considerably larger than zero, and a density of finite value.A black hole has zero volume and infinite density, creating what is known as a singularity.
The word singularity is a term from mathematics and describes a point, or locus of points, where a given equation is undefined. The ratio 1/0, for instance, is not equal to infinity, but is rather undefined because you simply cannot do it, the arithmetic operation does not exist at all. However, the limit of the ratio 1/x as x approaches 0 is infinity. There is a distinct difference & important between the two ideas, which is left as an exercise for the reader to figure out. So we say that the equation 1/x = is singular if x=0.
The key is the singularity is a mathematical artifact and not a physical object. The singularity is not as such expected to exist, but rather to indicate that the singular equation needs to be replaced with one that is not singular, either from the same or a different theory, if one is to physically describe events at the singular points in spacetime (the points which are singular in one equation need not be singular in another; 1/x = y is singular if x=0, but x2=y is not singular for any non-infinite value of x).
Viewed from the outside, the singularity is hidden behind an event horizon so it cannot be seen. Once inside the event horizon, the geometry is such that all existing spacetime trajectories terminate at the singularity. What happens than is, of course, equally undefined.
So let us ask the question: Do black holes actually exist? How can we tell, by observation, one way or the other? The answer is to look for the event horizon. All compact astrophysical objects, except black holes, have a hard compact surface. Most of the objects that appear massive enough to be candidate black holes are accompanied by an accretion disk of infalling material which becomes extremely hot, and is easily visible to astronomers in X-rays. If the hot matter hits a hard surface, it will flare in a manner that indicates the presence of a hard surface. On the other hand, if the hot matter falls into a black hole it simply disappears with no appreciable fanfare. Hence, we should be able to observationally distinguish between the presence or absence of the unique event horizon of the black hole by its flaring behavior. We also know that any hard hot surface will emit thermal X-rays, whereas a black hole event horizon will have no detectable thermal emission. So we should be able to distinguish between a "normal" compact object (such as a neutron star or exotic quark star & etc.) and an event horizon by the presence or absence of a thermal component in X-rays.
These have been done and observations now positively indicates the presence of event horizons. See, for examples Paul, et al., 1998; Done & Gierliński, 2003; Narayan, 2003; McClintock, Narayan & Rybicki, 2004; Remillard, et al., 2006.
All of you who have your own alternative ideas in cosmology or relativity, and those of you who insist that black holes are just artifacts of some kind, and not physically real have a new problem. Observational evidence strongly supports the presence of event horizons, and only black holes are known to be associated with such things. So in order to argue that black holes are not physically real, you have to deal not only with the mathematics of general relativity (i.e., read Chandrasekhar's Mathematical Theory of Black Holes and prove he is wrong), but also with a small but growing mountain of observational evidence.
Black holes are physically real and they are not going away any time soon.