The Event Horizon
Photons always travel at light speed
but when travelling out of a gravitational field they lose energy. This
causes them to appear to be more red to
an external observer (see the adjacent right figure, which we discussed in Chapter 4).
The stronger the gravitational
field, the stronger the
gravitational
redshift.
The extreme case is a black hole, where photons from within a
certain radius
become infinitely redshifted and thus
invisible to an external observer. Indeed, light in the vicinity of such
strong gravitational fields exhibits a whole set of quite strange behaviors.
The simplest kind of black hole is one that is spherically symmetric and carries no
electrical charge or angular momentum. One often terms this a
Schwarzschild black hole, in honor of Karl Schwarzschild who first obtained
the spherical black hole solution to Einstein's equations (see the right panel).
When Even Light Isn't Fast Enough
The event horizon (also termed the Schwarzschild radius)
is the point outside the black hole where the gravitational
attraction becomes so strong that the escape velocity
equals the speed of
light. Since no object can exceed the speed
of light, this means that nothing, not even light, could escape the black hole
once it is inside the black hole's event horizon. The
following table lists some escape velocities and the corresponding Schwarzschild
radius for several objects.
|
Escape Velocities and Schwarzschild Radii
|
| Object |
Mass
(Solar) |
Radius (km) |
Escape Velocity (km/s) |
Schwarzschild Radius |
| Earth |
0.00000300 |
6,378 |
11.2 |
9.0 mm
|
| Sun |
1.0 |
696,000 |
615 |
3.0 km
|
| White Dwarf |
0.8 |
10,000 |
4,600 |
2.4 km
|
| Neutron Star |
2 |
12 |
130,000 |
5.9 km
|
|
|
|
|
|
Becoming a Black Hole
All objects have the potential to become black holes. We just have to
compress their mass into a small enough volume.
For example, the Schwarzschild radius for a mass the size of the Earth is 9 millimeters
(about the width of the fingernail on your little finger). But Earth
actually has a radius of
more than 6300 kilometers and its escape velocity is just
11.2 km/s, well below the speed of light. Therefore, the Earth isn't a black hole.
But
if we could supply enough pressure to shrink the Earth to a radius of
9 millimeters, it would
collapse to a black hole with an escape velocity greater than the speed of light.
Compressing the Sun
into a Black Hole
|
Radius
(Solar Units) |
Escape Velocity
(km/s)
|
| 1.0 |
6.2 x 102
|
| 0.1 |
1.9 x 103
|
| 0.01 |
6.2 x 103
|
| 0.001 |
1.9 x 104
|
| 0.0001 |
6.2 x 104
|
| 0.00001 |
1.9 x 105
|
| 0.000001 |
6.2 x 105
|
|
|
|
|
|
Example: The Sun
Likewise, if the mass of the Sun were compressed into a radius of 3 kilometers
it would become a black hole. We illustrate turning the Sun into a black hole by
imagining compressing its radius in successive factors of 10
in the adjacent left table.
The escape velocity of the Sun is
almost 620 km/s, but if we shrank the radius of the Sun to 10 percent of its present value
the escape velocity would increase to almost 2000 km/s.
As we continued to decrease the radius
of the Sun (but keeping the same mass), the escape velocity would continue to rise.
When the
radius reached
0.00001 of its present value the escape velocity would be
190,000 km/s, about 2/3 of the speed of
light. Another decrease of the radius by a factor of
10 would cause the escape velocity to greatly exceed the speed
of light and the Sun would become a black hole.
Of course we don't have the technology to compress the Earth or the Sun into
a real black hole, so this is a theoretical exercise. But Nature seems capable of
compressing star-size and higher masses into black holes in the present Universe, and
may have compressed objects as small as protons into black holes in the incredible
densities of the big bang.
Making a Pretzel of Spacetime
A more
fundamental way of viewing the event horizon
is that in a black hole the gravitational field
is so intense that it bends space and time around itself so that inside the
event horizon there are literally no paths in space and time that lead to the
outside of the black hole. No matter what direction you went, you would find
that your path led back to the center of the black hole.
We shall discuss such paths in space and time further a little later.