ATOMS, STARS, AND GALAXIES 155
predicted a century before. The
French astronomer Pierre-Simon
Laplace had theorized corps
obscures, objects so dense that the
velocity required to escape their
gravity exceeded the speed of light.
The modern definition of black
holes is similar: objects in space
with such enormous gravity nothing
can escape them, not even light.
Event horizon
The Schwarzschild solution can
be used to calculate the size of
a black hole for a given mass. To
create a black hole, mass must be
compressed into a volume with a
smaller radius than that predicted
by the Schwarzschild solution. An
object so dense that its radius is
smaller than the Schwarzschild
radius for its mass will warp
spacetime to such an extent
that its gravitational pull will be
impossible to resist—it will create
a black hole. Any mass or light that
comes closer than the Schwarzschild
radius is doomed to be pulled into
the black hole. The points in space
that surround a black hole at a
distance of the Schwarzschild
radius form its “event horizon,”
so-called because it is impossible to
observe the events that take place
beyond it. Nothing comes out of a
black hole—no mass, no light, and
no information about what is inside.
The Schwarzschild solution
allows astronomers to estimate
the masses of actual black holes,
although it is not possible to be
exact because black holes rotate and
carry an electric charge, and these
factors are not accounted for by the
mathematics. If the sun became a
black hole, its event horizon would
be 2 miles (3 km) from the center.
A black hole with Earth’s mass
would have a^1 ⁄ 3 -in (9-mm) radius.
However, it is not possible to make
black holes from bodies this small;
it is thought that black holes form
from collapsed stars that are at
least three solar masses. ■See also: Gravitational disturbances 92–93 ■ The theory of relativity 146–53 ■
The life cycles of stars 178 ■ Hawking radiation 255 ■ The heart of the Milky Way 297
Karl Schwarzschild
Karl Schwarzschild’s
prodigious mathematical
abilities were obvious from
an early age. By the age of
16, he had published his first
scientific paper concerning
the mechanics of binary orbits,
and by 28, he was a professor
at the University of Göttingen
in Lower Saxony.
Schwarzschild made
contributions to the most
significant sciences of the age:
rad ioac tiv ity, atom ic theor y,
and spectroscopy. In 1914,
he joined up to fight in World
War I, but still found time for
mathematics. In late 1915,
he sent Albert Einstein some
early calculations, saying:
“As you see, the war treated
me kindly enough, in spite
of the heavy gunfire, to allow
me to get away from it all and
take this walk in the land of
your ideas.” The following
year, Schwarzschild presented
the full solution that bears
his name. He developed an
autoimmune disease while
serving on the Russian Front
and died in May 1916.Key work1916 On the Gravitational
Field of a Mass Point after
Einstein’s TheoryIt is theorized that beyond the
event horizon, at the center of the
black hole, lies a singularity—a
point of infinite gravity and infinite
density. However, it is impossible to
obtain information from beyond an
event horizon. In this diagram, one
of the three dimensions of space has
been removed to aid visualization.
Schwarzschild
radiusEvent horizonBlack holeSingularityWarping spacetime