Transcript Black Holes - Wayne State University Physics and Astronomy

Black Holes
&
Curved Spacetime
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Questions about Black Holes
What are black holes?
Do they really exist?
How do they form?
Will the Earth someday be
sucked into a black hole?
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Introduction to Black Holes
At the end of a massive star’s life, its outer layers
are blown off in a (Type II) supernova explosion
If the core remnant has a mass greater than 3
MSun, then not even the super-compressed
degenerate neutrons can support the core against
its own weight
Consequently, according to theories, gravity
overwhelms all other forces and crushes the core
until it is infinitely small
The resulting point-like object is a black hole
Only the most massive, very rare stars (with
initial masses greater than 40 MSun) will form
black holes when they die
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General Relativity
Under the extreme circumstances of a black
hole, Newton’s theory of gravity is inadequate
Newton’s theory works well in ordinary
situations (motions in everyday life, planetary
orbits, etc), but it fails when
gravity becomes extremely strong
large masses move very rapidly
light is affected by a huge mass
To understand what black holes are, we begin
with an introduction to Einstein’s theory of
general relativity
It improves on Newton’s theory of gravity
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The Equivalence Principle (1)
The equivalence principle says that life in a freely falling
laboratory is indistinguishable from, and hence equivalent
to, life with no gravity
No experiment can be done inside a sealed laboratory to
determine whether it is floating in space without gravity or
falling freely in a gravitational field
In other words, the two situations are
equivalent
In the absence of air friction, the boy
and girl on the right fall downward at
the same rate (their speeds increase
by the same amount each second),
and so does the ball if they aim it
straight at each other
Consequence of the equivalence
principle: if the three are isolated in a
box that is falling with them, no one
inside it will will be aware of any gravity
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The Equivalence Principle (2)
When a space shuttle is in
free-fall orbit around the
Earth, everything inside the
shuttle either stays put or
moves along a straight line
because gravity appears to
be absent inside the shuttle
To the astronauts inside it,
falling freely around the
Earth creates the same
effects as being far off in
space, remote from all
gravitational influences
In other words, the astronauts feel weightless in such orbit
Thus the effects of gravity can be compensated by the right
acceleration
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Here’s the Rub
If a laser beam is sent from the back of a shuttle to
the front,
in zero gravity the laser will hit the front center of the
shuttle
in free fall around the Earth the laser must also hit the
front center, according to the equivalence principle
but from the time the light left the rear wall until it reaches
the front the shuttle has moved!
Thus the equivalence principle would seem to imply
that light is bent by gravity!
Since light has no mass, this would contradict the
expectation that only objects with mass are influenced
by gravity
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Einstein’s Radical Idea
He suggested that the light curves down to meet the
front of the shuttle because the Earth’s gravity bends
the fabric of space and time
Any event in the universe can be pinpointed using the
three dimensions of space (where?) and the one
dimension of time (when?)
Einstein showed that
there is an intimate connection between space and time
we can build a correct picture of the physical world by
considering the two together, in what is called spacetime
According to his theory, called general relativity,
the presence of mass (gravity) curves or warps the
fabric of spacetime
the stronger the gravity (the larger the mass) is, the
more spacetime is curved or warped
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Gravity Bends Spacetime (1)
When an object (an electron, a space shuttle, or a
light beam) enters a region of spacetime distorted by
the presence of another object’s mass, the path of the
first object will be different from what it would have
been in the absence of the second’s mass
In summary, matter tells spacetime how to curve, and
the curvature of spacetime tells other matter how to
move
Three-dimensional analogy of spacetime:
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Gravity Bends Spacetime (2)
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Gravity Bends Light’s Path
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Tests of Einstein’s Theory of General Relativity (1)
Since Newton’s theory is inadequate when gravity is
very strong, Einstein’s theory can be tested where
Newton’s fails
The motion of Mercury about the Sun provides a
“laboratory” to test Einstein’s theory
Mercury’s orbit undergoes very slow, but detectable,
rotation in space
This rotation cannot be fully explained by Newton’s
theory
Einstein’s prediction
was remarkably
close to the data,
giving him much
confidence in his
theory
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Tests of Einstein’s Theory of General Relativity (2)
Einstein’s theory also predicts that starlight is deflected
when it passes near the Sun
If a star’s position is known when the Sun is not in the way,
then an observation of a shift in the star’s position when
the Sun is in the way will confirm the theory
Such an observation could be done during a total solar eclipse
so that much of the Sun’s bright light is blocked out
The confirmation was made first in 1919 by British
astronomers and later by others!
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Bending of Light
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Tests of Einstein’s Theory of General Relativity (3)
Einstein’s theory further predicts that the stronger the
gravity, the slower the pace of time
In 1959, a comparison of time measurements on the
ground and top floors of the physics building at
Harvard University showed that the clock on the
ground floor ran more slowly than the one on the top
floor confirming Einstein’s prediction
It was further confirmed in 1976 by the
measurements of time delays experienced by radio
signals sent by the Viking lander on Mars as they
passed near the Sun
The delays were
also caused by
the curving of
spacetime near
the Sun
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Summary of Black-Hole Formation
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Ultra-strong Gravity
As a massive star collapses, the gravity on its surface
increases and therefore, according to general relativity, the
spacetime around the star becomes more and more curved
In other words, the curvature of the spacetime increases
As a result, when the star has shrunk down to a sufficiently
small size (just a little larger than a black-hole), only light
beams sent out perpendicularly to its
surface could escape
Other light beams and objects sent
outward could no longer escape, following
paths that curve back to the surface
If the collapsing star shrinks just a little
more, nothing will be able to escape and
the star will become a black hole
Since not even light can escape, the object
appears black
The black hole’s size defines its event
horizon
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“Event Horizon”
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Escape Velocity: Rocket Analogy
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Escape Velocities
White dwarfs and neutron stars have huge
surface escape-velocities because they have
roughly the mass of the Sun packed into an
incredibly small volume
A solar-mass white dwarf has a radius of only
10,000 kilometers, and its surface escapevelocity is about 5,000 km/s
A 2-solar-mass neutron star would have a
radius of just 8 km, and its surface escapevelocity would be an incredible 250,000 km/s!
Real neutron stars have masses above 1.4
solar masses and smaller radii, and so their
escape velocities are even larger!
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Event Horizon
A black hole probably has no surface
Astronomers use the distance at which
the escape velocity equals the speed of
light for the size of the black hole
This distance defines a surface called the
event horizon because no messages (via
electromagnetic radiation or anything
else) of events happening within that
distance of the point mass can make it
to the outside
The region within the event horizon thus
appears black
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Schwarzschild Radius
Within the event horizon space is so curved
that any light emitted is bent back to the point
mass
Karl Schwarzschild was the physicist who
derived the first exact solution to Einstein’s
equations of general relativity
Schwarzschild found that the light rays within
a certain distance of the point mass would be
bent back to the point mass
This distance is the same as the radius of the
event horizon, and is sometimes called the
Schwarzschild radius
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What Would It Feel to Fall into a Black Hole?
Falling into a Black Hole (1)
According to theory, falling toward a black hole would
not be a pleasant experience…
Falling feet-first, your body would be scrunched
sideways and stretched along the length of your body
by the tidal forces of the black hole
Your body would look like a spaghetti noodle!
Stretching happens because your feet would be pulled
much more strongly than your head
Sideways scrunching happens because all points of
your body would be pulled toward the center of the
black hole
Your shoulders would be squeezed closer together as
you fell closer to the center of the black hole
Tidal stretching/squeezing of anything falling into a
black hole is conveniently forgotten in Hollywood
movies
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Falling into a Black Hole (2)
A friend watching you as you enter a black
hole would see your clock run slower and
slower (than his) as you approached the event
horizon
This is the effect of time dilation
Your friend would see you take an infinite
amount of time to cross the event horizon
Time would appear to him to stand still
However, in your reference frame your clock
would run forward normally and you would
reach the center very soon…
…a truly once-in-a-lifetime experience
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Falling into a Black Hole (3)
If you reported back the progress of
your journey into the black hole using
photons with very short wavelengths
(very high frequencies), your friend
would have to tune to progressively
longer wavelengths (lower frequencies)
as you approached the event horizon
This is the effect of gravitational redshift
Animation
Eventually, the photons would be
stretched to infinitely long wavelengths
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Detecting Black Holes (1)
Since, according to theory, black holes (their event
horizons) are only several miles across and completely
black, how do we go about finding them?
Indirect methods must be used!
Their presence may be detected from their effects on
surrounding material and stars
A binary-star system may have a black hole as one of
its members
The behavior of the visible companion may reveal
whether or not the other is a black hole
If sufficient data about the system is collected, Kepler’s
laws can be used to deduce the invisible object’s mass
If it is too big for a neutron star or a white dwarf, then it is
likely a black hole!
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Views of a Possible Black Hole
far away
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up close
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Detecting Black Holes (2)
Measuring the masses of all of the binary-star
systems in the Milky Way Galaxy would take
much too long a time
It is estimated that there are over a 100 billion
binary systems in the Galaxy!
Even if it took you just one second to somehow
measure a binary's total mass and subtract out
one star's mass, it would take you over 3,000
years to complete your survey
How could you quickly hone on the binary
systems that might have black holes?
Fortunately, black holes can advertise their
presence loud and clear with the X-ray
emission associated with them
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X-Ray Emission
A visible star in a binary system loses some of its gas
to its black-hole companion
The gas material forms an accretion disk as it spirals
onto the black hole
Gas particles in the disk rub against each other and
heat up from friction
As the particles whirl closer to the event horizon, the
friction can heat them to about 100 million kelvins,
which is hot enough for the emission of X-rays
Since X-ray sources in the Galaxy are rare, if you find
an X-ray source, then you know something strange is
happening with the object
If the unseen companion is very small, then the X-ray
brightness of the disk will be able to change rapidly
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Accretion from a Binary Partner
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X-Ray Emission
Visible Star
black hole
accretion
disk
Gas pulled off
Animation of black hole in binary star system
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Gas temperature
increases closer
to BH. Gas near
BH emits x-rays.
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Chandra X-Ray Observatory
It is one of NASA's great
observatories
launched by the space
shuttle Columbia on
July 23, 1999
It detects/images X-ray
sources that are billions
of LY away
Chandra’s mirrors are the
largest, most precisely shaped and aligned, and
smoothest mirrors ever constructed
It produces images 25 times sharper than the best
previous X-ray telescope
Chandra's improved sensitivity is making possible more
detailed studies of black holes, supernovae, and other
exotic objects
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Black-Hole Candidates
Several black-hole candidates have been
found
Examples include
Cygnus X-1 and V404 Cygni in the
constellation of Cygnus
LMC X-3 in the constellation Dorado
V616 Mon in the Monocerotis constellation
J1655-40 in Scorpius
and the closest, V4641 Sgr in Sagittarius, is
about 1600 light years away
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Some Black-Hole Candidates in Binary Star Systems
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Chandra's X-Ray Images of Black Holes
This movie is a sequence of X-ray images of
deep space taken by Chandra
The black holes are first marked, and then the
view zooms onto one pair of particularly close
black holes, known as SMG 123616.1+621513
Astronomers believe that these black holes
and their galaxies are orbiting each other and
will eventually merge
The movie ends by showing an animation of
this scenario
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Black Hole in Center of Milky Way
Astronomers believe that super-massive black-holes
may lie in the central regions of large galaxies
These regions may serve as “feeding grounds” for
black holes that form therein
A black hole can grow in
mass and size by “eating”
the surrounding matter,
such as dust, asteroids,
other stars, or even other
black holes
The central region of our
Galaxy is thought to harbor
a super-massive black-hole
with a mass of around 3.6
million MSun
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Stellar Question
What would happen to the Earth’s orbit
if the Sun were suddenly replaced by a
black hole with the same mass as the
Sun?
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Hollywood and Reality
Black holes are portrayed in TV and films as
cosmic vacuum cleaners, sucking up everything
around them
or as tunnels from one universe to another
Black holes are dangerous only if something gets
too close to them
Because all of their mass is compressed to a point,
it is possible to get very close where the gravity
gets very large
Objects far enough away will not sense anything
unusual
If the Sun were replaced by a black hole of the
same mass, the orbits of the planets would remain
unchanged
It would, however, be darker and colder
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