Since the Hubble
Space Telescope was launched in 1990, there have been many
observations of what are believed to be black holes, including the photograph
below of a suspected black hole in the heart of the galaxy NGC 6251.
But the subject of black holes began in theoretical physics, long before
there were any observations by astronomers.

A black hole unobscured by dust

The advent of Einstein's General Theory
of Relativity gave physicists a mathematical language for describing
the gravitational force in a manner consistent with the constant speed
of light. Most of what we believe we know about black holes has come from
abstract theoretical models in general relativity.
But in order to observe black holes in Nature
we need to know how those abstract theoretical models translate to a Universe
filled with other stuff.

Abstract theoretical black holes

In the abstract theoretical model of black
holes, a black hole is studied as if it were the only thing in the Universe.
Using that approximation, the math of general relativity becomes doable,
and we can make predictions about black hole behavior that are useful
in understanding the black holes we see. In addition, we learn a lot
of things about black holes mathematically that we may never get a chance
to witness directly through observation.
In general relativity, the paths of light can
be calculated for many different distributions of matter and energy
using equations call the geodesic equations. The geodesic
equations give us the paths that would be followed by freely-falling
test particles. For example, a baseball after being hit by
Sammy Sosa and before being caught by an eager fan would be a freely
falling particle, travelling on a geodesic path through spacetime.
Light travels on geodesics paths through spacetime.
When those geodesic paths cross the event horizon of
a black hole, they never come back out. Interestingly, in a Universe
where the energy density is never negative, this behavior of light leads
mathematically to two very crucial properties of black holes:

The surface area of the event horizon of a black
hole can only increase, never decrease. This also
means that although two black holes can join to make a bigger black
hole, one black hole can never split in two.

The pull of gravity at the event horizon is constant;
it has the same value everywhere on the event horizon.

Note that according to the first property, it
is impossible for black holes to decay and go away, because a black hole
cannot get smaller or split into smaller black holes. This is going to
be changed when we add quantum mechanics to the theory in the next section.

Observable astrophysical black holes

If a black hole traps all the light that crosses
the event horizon, then how can we ever hope to observe one?
In the abstract theoretical model of a black hole,
it sits alone forever in the Universe letting us do math on it. In the
Nature we observe, the Universe is filled with dust and gas in addition
to stars, planets and galaxies. When dust and gas fall into a black hole,
they can be sucked towards the event horizon so fast that the atoms are
ionized and release bright light that escapes without crossing the event
horizon.
So the way astronomers and astrophysicists detect
black holes in astronomical observations is to look for light from ionized
dust and gas being sucked into something so fast that it could only be
a black hole, not a normal gravitating massive object like a star.
However, this bright light can be hard to see,
because most black holes also attract giant clouds of interstellar dust
that hide many of their features, as shown on the previous page. The suspected
black hole shown in the photo above has a warped dust cloud around it,
so that the bright light from the ionized gas can be seen.