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AN EXACT SOLUTION TO
RELATIVITY PREDICTS
BLACK HOLES
CURVES IN SPACETIME
IN CONTEXT
KEY ASTRONOMER
Karl Schwarzschild
(1873–1916)
BEFORE
1799 Pierre-Simon Laplace
develops a theory about black
holes, which he calls “corps
obscures,” or “dark bodies.”
1915 Albert Einstein’s
general theory of relativity
shows that the force of
gravity is caused by a
warping of space and time.
AFTER
1931 Subrahmanyan
Chandrasekhar calculates
the mass of stellar cores
that become neutron stars
and black holes.
1979 Stephen Hawking
proposes that black holes do
actually emit radiation as a
result of quantum fluctuations.
1998 Andrea Ghez shows
that a supermassive black
hole sits at the center of
the Milky Way.
I
n 1916, German mathematician
Karl Schwarzschild managed
something that even Albert
Einstein had failed to do—he
provided a solution to the field
equations of general relativity
that could yield precise answers.
The Einstein field equations are a
complex set of formulae that link
space and time (or spacetime) with
the action of gravity. Schwarzschild’s
achievement, known as the
Schwarzschild solution, was to
solve the equations to show exactly
The Schwarzschild solution
is an exact solution to relativity
that predicts black holes.
The gravitational field
of a mass is a warping
of spacetime.
This warping can be
described mathematically
using the Schwarzschild
solution.
how spacetime curved in the
presence of mass. This solution
showed how the gravity of objects
like the sun and Earth was warping
spacetime in accordance with the
theories of relativity. A generation
later, Schwarzschild’s mathematics
were used to throw light on the
darkest of all objects, the black hole.
No escape
In the early days of relativity,
black holes were purely theoretical
objects, although they had been
Black holes are surrounded
by an event horizon, a boundary beyond
which nothing can be observed.