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```Black Holes
Michael Beattie
Life Cycle of a Star
• Formed when a large amount of gas (mostly
hydrogen) starts to collapse in on itself due
to is gravitational attraction
• Eventually, the gas will be so hot that
hydrogen atoms will coalesce to form
helium
• Eventually the star will run out of its
nuclear fuels
When a Star Runs Out of “Fuel”
• In 1928 Indian graduate student
Subrahmanyan Chandrasekhar worked out
how big a star could be and still support
itself against its own gravity
• The idea: a star can maintain itself at a
constant radius by a balance between the
attraction of gravity and the repulsion from
the Pauli exclusion principle
The Chandrasekhar Limit
• Mass of more than one and a half times the mass
of the sun
• White dwarf: radius of about 5000 kilometers,
density of 1 ton per cubic centimeter, supported by
exclusion principle repulsion between electrons in
its matter
• Neutron star: radius of about 10 kilometers,
density of 100 million tons per cubic centimeter,
supported by exclusion principle repulsion
between neutrons and protons in its matter
Beyond the Limit
• Chandrasekhar showed that the exclusion
principle could not halt the collapse of a star more
massive than the Chandrasekhar limit
• Robert Oppenheimer solved the main problem of
understanding what would happen to such a star
and his work was later extended by a number of
people
• As the star contracts more and more, the
gravitational field becomes increasingly stronger,
to the point where light can no longer escape
The Event Horizon
• Imagine an object with such an enormous
concentration of mass in such a small radius that
its escape velocity was greater than the velocity of
light. Then, since nothing can go faster than light,
nothing can escape the object's gravitational field
• Think of the event horizon as the place where the
escape velocity equals the velocity of light, a oneway membrane around the black hole where
anything can fall in, but nothing can come out
Size of a Black Hole
• There is no limit in principle to how much or how
little mass a black hole can have. Any amount of
mass at all can in principle be made to form a
black hole if you compress it to a high enough
density.
• The Schwarzschild radius (the radius of the
horizon) and the mass are directly proportional to
one another: if one black hole weighs ten times as
much as another, its radius is ten times as large.
Evidence of Black Holes
• John Mitchell pointed out that a black hole still
exerts a gravitational force on nearby objects
• Astronomers have observed systems in which one
visible star orbits around an unseen companion,
attracted to it by gravity
• Some of these systems, such as one called Cygnus
X-1, are also strong sources of X rays
```
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