Astronomy 162: Professor Barbara Ryden

``The gates of hell are open night and day;

Smooth the descent, and easy is the way:

But to return, and view the cheerful skies,

In this the task and mighty labor lies.''

- Virgil, The Aeneid, Book VI

[John Dryden translation]

- A collapsing stellar core with M > 3 M
_{sun}will become a**black hole**. - If anything enters the
**event horizon**of a black hole, it cannot escape again. - Near a black hole, spacetime is severely distorted.

An object with infinite density is distressing to think about (it was bad enough contemplating a neutron star with a density of 400 million tons per cubic centimeter!) Fortunately for the sanity of astronomers, it is impossible to see a singularity, because its escape speed is too high.

The escape speed V at a distance R from a mass M is given
by the formula:

V = ( 2 G M / R )^{1/2} ,

where G is Newton's gravitational constant.
For instance, at the surface of the Sun (whose mass
is 2 x 10^{30} kilograms), you are at a
distance R = 700,000 kilometers from the
Sun's center. The escape speed from the
Sun's surface can be computed to be V = 620 kilometers/second.
At R = 1 AU = 150,000,000 kilometers from
the Sun's center, the escape speed from the
Sun is only V = 42 kilometers/second. The
farther you get from a massive object, the
lower the escape speed is.

At a very great distance from a singularity of mass M, the escape
speed is tiny. As you approach the singularity, however, and
R steadily decreases, the escape speed V becomes higher and
higher. At a critical radius, known as the **Schwarzschild
radius**, the escape speed becomes equal to the
speed of light.

The numerical value of the Schwarzschild radius, R_{s},
is given by the equation:

where G is Newton's gravitational constant, and c is the
speed of light. In practical units,

R_{s} = 3 kilometers ( M / 1 M_{sun} )

In other words, a singularity with a mass equal to that
of the Sun will have a Schwarzschild radius of only 3 kilometers.
The Schwarzschild radius is directly proportional to the
mass of a singularity.

A **black hole** is defined as ANY object which
is smaller than its Schwarzschild radius. For instance,
take an astronomy professor with a mass of M = 70 kilograms.
Squeeze her down to a sphere with radius R = 10^{-25}
meters, and she will be a black hole.

In theory, a black hole can have any mass; take an object
of any size and squeeze it down to its Schwarzschild radius -
instant black hole. The collapse
of massive stars is merely a convenient means of making
black holes with masses of M = 3-10 M_{sun} and
Schwarzschild radii of R_{s} = 9-30 kilometers.

A black hole can be thought of as a Cosmic Lobster Trap; objects can enter the event horizon easily enough, but nothing (not even light) can come out. Here in the outside universe, we have no information whatsoever about what is going on inside an event horizon. We presume that once a dense stellar core is compressed into a black hole, it goes on to become a singularity; that is what the laws of physics predict. However, we have no way of confirming this prediction by observation from outside the event horizon. If you entered the event horizon, you would be able to discover whether there's a singularity inside. However, you wouldn't be able to communicate your results to anyone outside the event horizon. Information cannot travel from inside an event horizon to outside an event horizon.

In cheap science fiction stories, black holes are sometimes
described as if they are ``cosmic vacuum cleaners'', sucking
up everything in their path with the malevolent force of
their gravity. Black holes are much more benign than that.
Black holes are inescapable **only**
if you venture inside the
event horizon. The event horizon of a black hole which forms
from a collapsing star is quite small - only 10 miles or so
in radius.

- Clocks closer to the event horizon run more slowly.
- Photons originating near the event horizon are strongly redshifted.
- Photons passing near the event horizon are strongly deflected.

Suppose you are orbiting a black hole at a safe distance (well outside the event horizon). Unwilling to make the one-way trip inside the event horizon yourself, you drop a warthog - snout first - toward the black hole, after tying a to the warthog's tail. As the warthog drops toward the event horizon, what happens? Well, as frequently happens in life, what you see depends on where you are.

- The beacon flashes more slowly.
- The beacon becomes redder (even shifting to radio wavelengths).
- The beacon becomes dimmer.

- The beacon flashes at a constant rate.
- The beacon's color is the same.
- The beacon is of constant brightness.

Unfortunately, as the warthog approaches the singularity, it will be ripped apart by incredibly strong tidal forces. The gravitational pull on its snout will be much stronger than the pull on its rump, and it will be shredded. (The ASPCA would definitely not approve of this experiment...)

Still curious? Try this page of Frequently Asked Questions about black holes.

For cheap visual thrills, try a Virtual Trip to a Black Hole, demonstrating some of the bizarre relativistic effects that take place close to black holes.

Prof. Barbara Ryden (ryden@astronomy.ohio-state.edu)

Updated: 2003 Feb 12

Copyright © 2003, Barbara Ryden