Black holes are predictions of Albert Einstein's theory of general relativity. There are many known solutions to the Einstein field equations which describe black holes, and they are also thought to be an inevitable part of the evolution of any star of a certain size. In particular, they occur in the Schwarzschild metric, one of the earliest and simplest solutions to Einstein's equations, found by Karl Schwarzschild in 1915. This solution describes the curvature of spacetime in the vicinity of a static and spherically symmetric object, where the metric is,
,
where is a standard element of solid angle.
According to general relativity, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius. (Indeed, Buchdahl's theorem in general relativity shows that in the case of a perfect fluid model of a compact object, the true lower limit is somewhat larger than the Schwarzschild radius.) Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the centre of the system. Because relativity forbids anything from traveling faster than light, anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the centre. A gravitational singularity, a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear black.
The Schwarzschild radius is given by
where G is the gravitational constant, m is the mass of the object, and c is the speed of light. For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters — about the size of a marble.
The mean density inside the Schwarzschild radius decreases as the mass of the black hole increases, so while an earth-mass black hole would have a density of 2 × 1030 kg/m3, a supermassive black hole of 109 solar masses has a density of around 20 kg/m3, less than water! The mean density is given by
Since the Earth has a mean radius of 6371 km, its volume would have to be reduced 4 × 1026 times to collapse into a black hole. For an object with the mass of the Sun, the Schwarzschild radius is approximately 3 km, much smaller than the Sun's current radius of about 696,000 km. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes.
The formula also implies that any object with a given mean density is a black hole if its radius is large enough. The same formula applies for white holes as well. For example, if the visible universe has a mean density equal to the critical density, then it is a white hole, since its singularity is in the past and not in the future as should be for a black hole.
More general black holes are also predicted by other solutions to Einstein's equations, such as the Kerr metric for a rotating black hole, which possesses a ring singularity. Then we have the Reissner-Nordström metric for charged black holes. Last the Kerr-Newman metric is for the case of a charged and rotating black hole.
There is also the Black Hole Entropy formula:
Where A is the area of the event horizon of the black hole, is Dirac's constant (the "reduced Planck constant"), k is the Boltzmann constant, G is the gravitational constant, c is the speed of light and S is the entropy.
A convenient length scale to measure black hole processes is the "gravitational radius", which is equal to
When expressed in terms of this length scale, many phenomena appear at integer radii. For example, the radius of a Schwarzschild black hole is two gravitational radii and the radius of a maximally rotating Kerr black hole is one gravitational radius. The location of the light circularization radius around a Schwarzschild black hole (where light may orbit the hole in an unstable circular orbit) is 3rG. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at 6rG for a Schwarzschild black hole.
Alternative models
Several alternative models, which behave like a black hole but avoid the singularity, have been proposed. But most researchers judge these concepts artificial, as they are more complicated but do not give near term observable differences from black holes (see Occam's razor). The most prominent alternative theory is the Gravastar.
In March 2005, physicist George Chapline at the Lawrence Livermore National Laboratory in California proposed that black holes do not exist, and that objects currently thought to be black holes are actually dark-energy stars. He draws this conclusion from some quantum mechanical analyses. Although his proposal currently has little support in the physics community, it was widely reported by the media.[23][24]
Among the alternate models are Magnetospheric eternally collapsing objects, clusters of elementary particles[25] (e.g., boson stars[26]), fermion balls,[27] self-gravitating, degenerate heavy neutrinos[28] and even clusters of very low mass (~0.04 solar mass) black holes.[25]
Finally, plasma cosmologists suggest that Bierkland currents provide an alternative explanation for the observed phenomenon. Plasmas transfer energy over great distances to smaller regions where it may be periodically or catastrophically released. Peratt explains the flickering of electromagnetic radiation: "The flickering of a light in Los Angeles does not mean that the supply source, a waterfall or hydroelectric dam in the Pacific Northwest, has abruptly changed dimensions or any other physical property. The flickering comes from electrical changes at the observed load or radiative source, such as the formation of instabilities or virtual anodes or cathodes in charged particle beams that are orders of magnitude smaller than the supply. Bizarre and interesting non-physical interpretations are obtained if the flickering light is interpreted by a distant observer to be both the source and supply." Plasma cosmology in this manner is a minority view not within mainstream science
2007-02-07 12:19:23
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answer #1
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answered by Anonymous
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The size of a black hole is related to its mass by the equation:
D = (GM) / c²
where D is the diameter of the event horizon, G is the gravitational constant, M is the mass, and c is the speed of light. A black hole the size of a dinner plate would weigh roughly 30 times the mass of the Earth, but 40 million times smaller than the diameter of the Earth. That means the gravitational pull in the vicinity of our black hole dinner guest will be 50,000,000,000,000,000 g's, so I think I would be making plans to be elsewhere.
Accleration near a black hole is also found by the relativistic formula:
a = (GM) / r²
or, using the formula for D, and setting 2r = D, 300,000,000 m/sec for c, and 9.8 m/sec² for g, we have 100,000,000,000,000,000 g's, which is roughly the same order as with the nonrelativistic derivation.
2007-02-07 11:34:00
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answer #2
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answered by Scythian1950 7
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all though the Chandrasekhar limit is valid...it is theoretically possible to make anything a black hole if u can squeeze it to a small enough size...for example, to make the Earth a black hole, one would have to squeeze it to the size of a marble...therefore it something was big enough and made about the size of a plate a "mini black hole" is possible....after the large object crosses the event horizon (point of no return)...it would be spaghetti (stretched to the width of spaghetti...obvious), thus anything in close range could be sucked in....
2007-02-07 12:48:28
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answer #3
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answered by Rafi 2
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