Quantum Black Holes
We do not yet have a consistent theory of quantum gravity, but there are some approximate
results about black holes suggesting that a complete theory of quantum gravity may have some
surprises in store for us. Let us discuss briefly two of those results.
Are Black Holes Really Black?
General relativity indicates that once a particle crosses the event horizon of a spherical
black hole it can never cross back over the event horizon and is forever trapped. Thus, a
black hole is truly black since nothing can come back out of it. However, approximate
solutions to the gravitational problem incorporating principles of quantum mechanics
suggest that this may not always be so. These results, first
published in 1974 by British cosmologist Stephen
Hawking (see the right panel),
indicate that because of quantum mechanical effects a black hole can actually
emit particles and eventually evaporate. The top right animation illustrates at a
qualitative level how this can happen. The Hawking result indicates that black holes are
not truly black!
The following table illustrates some calculated lifetimes for Hawking black holes of various
masses. Because these black holes emit particles, it is possible to define an effective
temperature
for them. This effective temperature is also listed in the table (expressed in energy units).
|
Properties of Hawking Black Holes
|
| Mass (kg) |
Mass (Solar) |
Lifetime (s) |
Lifetime (y) |
Temp
|
| 1.06 x 1013 |
5.3 x 10-18 |
4.7 x 1021 |
1.5 x 1014 |
1 MeV |
| 1.06 x 1011 |
5.3 x 10-20 |
4.7 x 1015 |
1.5 x 108 |
100 MeV |
| 1.06 x 1010 |
5.3 x 10-21 |
7.2 x 1011 |
2.3 x 104 |
1 GeV |
| 1.06 x 108 |
5.3 x 10-23 |
5.9 x 105 |
1.9 x 10-2 |
100 GeV |
| 1.06 x 107 |
5.3 x 10-24 |
5.3 x 102 |
1.7 x 10-5 |
1000 GeV |
| 1.06 x 105 |
5.3 x 10-26 |
5.1 x 10-4 |
1.6 x 10-11 |
100,000 GeV |
|
|
*Adapted from
Quantum Theory, Black Holes, and Inflation,
Ian Moss (Wiley)
|
Notice that even the most massive black hole in the table is 17 orders of magnitude less
massive than the Sun, and has a lifetime that is 10,000 times longer than the age of the
Universe. We conclude that
for stellar size black holes the Hawking effect is completely negligible.
On the other hand, the miniature black holes near the bottom of the table have
lifetimes of seconds or less before they would explode in a burst of particles and radiation.
Searches for such tiny black holes and their explosions as they emit particles
have proven negative so far.
Black Holes and Elementary Particles
An even more bizarre possibility is being suggested by recent work in m-brane and
superstring theory. Some results obtained there indicate a possible intimate
connection between black holes and elementary particles. In particular, there now exist
solutions to equations of m-brane theory that have the same properties as
particular kinds of black holes! This is truly astonishing! We normally think of black holes
as stellar-mass or greater objects having no connection to the microscopic
description of elementary particles, and of superstrings as a possible theory for the structure
of elementary particles having only an indirect bearing on the larger world. Is superstring
theory suggesting that in some sense
black holes and elementary particles may be one and the same?
A great deal of work must be done to clarify this issue. The black hole solutions
to superstring theory are highly abstract mathematical
constructions that have the general properties of black
holes but certainly do not have the specific features that we expect of normal black holes.
For example, they are charged, whereas we expect most black holes will not have an electrical
charge, and the solutions have been obtained in a hypothetical Universe having five spacetime
dimensions instead of our current four. Nevertheless, if this possible
connection between superstring theory and black holes survives further
scrutiny, it would rank among the most surprising
results in the history of science.