Black Holes

1
Black Holes
Curved Spacetime
2
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?

3
Introduction to Black Holes

• At the end of a massive stars 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

4
General Relativity

• Under the extreme circumstances of a black hole,
  Newtons theory of gravity is inadequate
• Newtons 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 Einsteins theory of general
  relativity
• It improves on Newtons theory of gravity

5
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

6
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

7
Heres 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

8
Einsteins Radical Idea

• He suggested that the light curves down to meet
  the front of the shuttle because the Earths
  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

9
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 objects
  mass, the path of the first object will be
  different from what it would have been in the
  absence of the seconds 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

10
Gravity Bends Spacetime (2)
11
Gravity Bends Lights Path
12
Tests of Einsteins Theory of General Relativity
(1)

• Since Newtons theory is inadequate when gravity
  is very strong, Einsteins theory can be tested
  where Newtons fails
• The motion of Mercury about the Sun provides a
  laboratory to test Einsteins theory
• Mercurys orbit undergoes very slow, but
  detectable, rotation in space
• This rotation cannot be fully explained by
  Newtons theory
• Einsteins prediction
  was
  remarkably
  close to the
  data,
  giving him much
  
  confidence in his
  theory

13
Tests of Einsteins Theory of General Relativity
(2)

• Einsteins theory also predicts that starlight is
  deflected when it passes near the Sun
  
• If a stars position is known when the Sun is not
  in the way, then an observation of a shift in the
  stars 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 Suns bright
  light is blocked out
• The confirmation was made first in 1919 by
  British astronomers and later by others!

14
Bending of Light
15
Tests of Einsteins Theory of General Relativity
(3)

• Einsteins 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 Einsteins 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
  

16
Summary of Black-Hole Formation
17
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 holes size defines its event
  horizon

18
Event Horizon
19
Escape Velocity Rocket Analogy
20
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
  escape-velocity is about 5,000 km/s
• A 2-solar-mass neutron star would have a radius
  of just 8 km, and its surface escape-velocity
  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!

21
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

22
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 Einsteins 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

23
What Would It Feel to Fall into a Black Hole?
24
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

25
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

26
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

27
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,
  Keplers laws can be used to deduce the invisible
  objects mass
• If it is too big for a neutron star or a white
  dwarf, then it is likely a black hole!

28
Views of a Possible Black Hole
far away
up close
29
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

30
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

31
Accretion from a Binary Partner
32
X-Ray Emission
Visible Star
black hole
accretion disk
Gas pulled off
Gas temperature increases closer to BH. Gas near
BH emits x-rays.
Animation of black hole in binary star system
33
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
• Chandras 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

34
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

35
Some Black-Hole Candidates in Binary Star Systems
36
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 123616.1621513
• 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

37
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

38
Stellar Question

• What would happen to the Earths orbit if the Sun
  were suddenly replaced by a black hole with the
  same mass as the Sun?

39
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