Chapter 24 Black Holes

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Chapter 24Black Holes

• Black Holes are out of sight!

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Black Holes

• Created when core of star is greater than about 5
  M ?
• Called black because gravity is so strong that
  even light can not escape.
• The idea of a black hole is a very strange one.
• To understand them we have to discard some
  commonsense ideas that we have about space
  time.

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Newtonian Worldview

• According to Newton
• Space is perfectly uniform and fills the universe
  like a rigid frame.
• Distance between two points is the same no matter
  who measures it.
• Time passes at an unchanging rate.
• Time elapsed between two events (eg two
  lightning strikes) is the same irrespective of
  whos measuring.

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Special Theory of Relativity

• Einsteins special theory of relativity is
  based on two basic principles
• Your description of physical reality is the same
  regardless of the constant velocity at which you
  are moving.
• If you are moving in a train at say 100km/h, then
  the length of your arm, and the time interval
  between the ticks of your watch are the same as
  if your train was moving in any other direction
  at any other speed (or not moving at all).

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Special Theory of Relativity

• Regardless of your speed or the direction of
  motion, you always measure the speed of light to
  be the same.
• Suppose you are traveling in a space ship at a
  speed of 99 of the speed of light towards a
  flashlight. You will measure the speed of the
  photons approaching you to be c, the same as an
  observer on a stationary space ship would observe
  it.
• This conflicts with Newtonian view, where the
  speeds should add up.

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Special Theory of Relativity
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Special Theory of Relativity
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Special Theory of Relativity

• Therefore, speed behaves differently in
  relativity than we are familiar with.
• Since speed involves both space(distance) and
  time, they two behave strangely.
• According to relativity, space and time seem to
  be intertwined, and are not two unrelated
  entities as described by Newton.
• In relativity we regard the 3 space dimensions
  and time as a single four dimensional entity
  called spacetime.

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Special Theory of Relativity

• Einstein made several predictions based on these
  two principles.
• Length contraction the length of an object that
  you measure depends on how the object is moving.
• The faster the object moves the shorter its
  length in the direction of motion.
• Therefore, a railroad car moving past a
  stationary observer at the railway station will
  look shorter to the observer than if it were at
  rest.

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Special Theory of Relativity
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Special Theory of Relativity

• However, if you were inside the train and
  measure its length, it will be the same length as
  measured from the ground when the train is at
  rest.
• The degree of shortening or length contraction
  depends on the relative speeds between the
  observer and the object being measured.
• Although, we cannot see such a shortening in
  ordinary moving objects (airplanes), it has been
  observed in fast traveling subatomic particles.

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Special Theory of Relativity

• Time dilation A clock moving past you runs more
  slowly than a clock that is at rest.
• Suppose you have two identical clocks, one place
  in a jet, and the other kept on the ground. When
  the jet landed the clock on it showed that it has
  less time elapsed than the one on the ground.
• However, for the passengers on the jet, time
  flowed at the normal pace, the clock ticked at
  the regular rate, their hearts beat at the same
  rate, etc.
• Compared to the people on the ground you have
  aged less.

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Special Theory of Relativity

• Relativity does not imply that nothing is
  absolute and every thing is relative
• speed of light in a vacuum and the laws of
  physics are absolute irrespective of how things
  are moving.
• These effects are real, and are not illusions.
• Einsteins special theory of relativity also
  predicts another relationship ? E mc2 .

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Special Theory of Relativity

• According the theory of relativity nothing in
  this universe can travel faster than the speed of
  light in a vacuum ? c 3.0 ? 108 m/s or
  186,000miles/sec

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General Theory of Relativity

• Newtons Theory of gravity was based on the
  premise that space time are absolute.
• Not satisfied with this picture, Einstein argued
• Gravity causes objects to accelerate (move)
• Moving objects affects the length of meter rulers
  and the tick of a clock that are moving with the
  object.
• Gravity must affect the shape of space flow of
  time
• Using a simple thought experiment Einstein showed
  that gravity must affect the shape of space and
  the flow of time.

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General Theory of Relativity
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General Theory of Relativity

• Einstein showed that there is no way to
  distinguish between an apple falling to the floor
  on Earth and the apparent motion of an apple
  inside an elevator accelerating up in a remote
  region of the universe(far from the gravitational
  influences of Earth and other objects)
• Equivalence principle in a small volume of
  space, the downward pull of gravity can be
  accurately and completely duplicated by an upward
  acceleration of the observer.

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General Theory of Relativity

• Einstein built his theory around the observation
  that acceleration due to gravity cannot be
  distinguished from acceleration due to any other
  force - The equivalence principle.
• The effects of special relativity that apply
  when objects are accelerated to near the speed of
  light - space being compressed, clocks slowing
  down - must also apply to objects moving in
  intense gravitational fields - near massive
  objects.
• Gravity (massive objects) distorts space and
  time, causing space to become curved and time to
  slow down.

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General Theory of Relativity

• According to Einsteins General Theory of
  Relativity, gravity is caused by the curvature
  of spacetime
• Far away from Earth (or any other source of
  gravity) spacetime is flat.
• Near the massive objects (Earth) spacetime is
  warped - clocks slow down space gets curved.
• Apple falls to the ground because that is the
  natural trajectory the apple can follow due to
  the space being curved near Earth.

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General Theory of Relativity
Gravitational curvature of spacetime The massive
object resides at the bottom of the gravitational
well
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General Theory of Relativity

• Imagine a stretched bed sheet
• If you place a ping pong ball on one side of this
  flat bed sheet it will not move in any preferred
  direction
• However, now if you first place a heavy stone at
  the center of the bed sheet then place the ping
  pong ball at a corner it will move towards the
  gravitational well at the center - because the
  bed sheet now is curved and the ball is simply
  following its natural trajectory in this curved
  space.
• This is a useful analogy to help you understand
  Einsteins gravity - general theory of relativity!

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General Theory of Relativity

• This explains why the acceleration due to gravity
  that an object(apple, cannon ball, etc.) will
  experience is independent of its mass.
• The curvature of space has the same effect on all
  objects.
• General theory of relativity has profound
  consequences for the way we think about the
  universe and these have been put to a variety of
  vigorous tests - and the theory has passed with
  flying colors.

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General Theory of Relativity

• Gravitational redshift
• In his famous equation E mc2 Einstein showed
  that radiation has an equivalent mass, and
  therefore light must respond to gravity, just
  like particles do.
• Photons leaving a massive objects suffer
  gravitational redshift, caused by the photons
  loosing energy as they climb out of the
  gravitational well.

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General Theory of Relativity

• The Gravitational Slowing of time
• According to GTR, near a massive object (Earth)
  time is warped.
• Clocks nearer to the Earths surface ticks more
  slowly than clocks at a higher elevations.

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The gravitational slowing of time and
gravitational redshift
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General Theory of Relativity
The gravitational bending of light Light bends
near a massive object because space near the
object is curved and light follows its natural
trajectory
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General Theory of Relativity
The precession of Mercurys orbit
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GTR predicts Black Holes

• Newtons theories are only valid when you study
  objects having low speeds (compared to speed of
  light) and weak gravity.
• The most bizarre prediction of GTR is that of the
  final outcome of a dying star with mass greater
  than about 3M?.
• Nothing can resist the gravitational collapse of
  such a star.
• GTR predicts that such a star will collapse to a
  point!! - all that mass that once was a star
  collapse to a point??? -

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Black Holes

• We can understand the nature of a black hole in
  terms of escape velocity.
• Escape velocity of Earth, i.e. the speed that a
  rocket should gain in order to escape Earth
  gravity is 11 km/s. Sun 600 km/s.
• Near a black hole the gravity is so strong that
  the escape velocity exceeds the speed of light -
  300,000 km/s.
• Since nothing can travel faster than light,
  nothing escapes the gravitational pull of such an
  object - not even light.

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Black Holes
The formation of a black hole
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Black Holes
The formation of a black hole
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Black Holes

• Photons emitted by a normal star is only
  slightly affected by the stars gravity.
• However, as a star keeps collapsing and
  compressing to enormous densities, the surface
  gravity of the shrinking sphere increases
  dramatically - and this increases the curvature
  of the surrounding region.
• Until, the star collapses beyond a certain size,
  the space around it curves so much that it closes
  on itself.

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Black Holes

• Photons flying out of such an object becomes so
  redshifted they loose all the energy and cease to
  exist.
• An object from which neither matter nor radiation
  can escape is called a Black Hole.
• Near a black hole the spacetime is highly curved,
  it is as if a hole has been punctured in
  spacetime (the fabric of the universe)
• In other words the gravitational well is
  infinitely deep!

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Black Holes

• Surrounding a black hole there is an imaginary
  sphere, where the escape velocity is just equal
  to the speed of light. This surface is referred
  to as the Event Horizon.
• Beyond this surface nothing is visible.
• The distance from the center of the black hole to
  the event horizon is called the Schwarzschild
  radius (RSch).
• All the mass that once was a star has now been
  crushed to a single point at the center, known a
  the singularity.

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The structure of a black hole
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The spacetime structure of a black hole
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Black Holes

• Once an object crosses the event horizon, it is
  gone for ever.
• Bizarre things happen inside a black hole
• Far from a black hole you have the freedom to
  move about in space but have no control over the
  flow of time.
• Inside a black hole however, gravity distorts
  space time. You loose your freedom to move in
  space but gain the ability to affect the passage
  of time!
• At the singularity space time are jumbled up -
  they do not exist as two separate entities.

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Black Holes

• Therefore, the singularities at the center of a
  black hole do not obey laws of physics.
• However, the random unpredictable thing that
  happen inside a black hole is shielded from the
  rest of the universe by the event horizon, since
  no information can pass beyond this surface.
• In the words of the british mathematician Roger
  Penrose Nature abhors naked singularities
• In other words, every singularity must be
  completely surrounded by an event horizon.

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Black Holes

• If you were unfortunate enough to fall into a
  black hole, you will be stretched like a
  spaghetti due to the immense tidal forces.
• However, suppose you were able to send a space
  probe into a black hole and it survives the
  descent, then from the safety of an orbiting
  space ship, you will observe that the clock on
  the probe will slow down and eventually stop upon
  reaching the event horizon.
• In other words, you will observe the space probe
  to slow down and it will take an infinite time to
  reach the event horizon.

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Falling into a black hole
As the probe reaches the event horizon, it is
distorted in to a long, thin shape, and a distant
observer sees the color of the probe change as
the light from the probe is redshifted. The
probe will appear to take an infinite amount of
time to fall in.
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Wormholes and Time Machines

• Einstein discovered that GTR predicts the
  possibility that black holes could connect our
  universe to another parallel universe via an
  Einstein-Rosen bridge.
• Such a bridge is called a worm hole.
• A worm hole also could be connected to another
  part of our own universe.
• However, theories suggest that these wormholes
  collapse as soon as they are formed.

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Wormholes and Time Machines

• Also, since traversing a wormhole means that you
  are emerging at a different spacetime domain
  than the one you started with, you could start at
  present time and emerge at a time in the past (or
  the future) - time travel!

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Wormholes and Time Machines
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Evaporation of Black Holes

• Quantum mechanics predict the concept of virtual
  pairs of particles.
• at every point in space pairs of particles and
  anti-particles are constantly being created and
  destroyed.
• Usually, this takes place during an extremely
  brief moment, that it does not affect the
  universe and cannot be detected and don't break
  laws of physics
• However, just outside the event horizon, if
  such a pair appears, one of them can be pulled
  into the black hole before they annihilate. The
  other member can escape to space.

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Evaporation of Black Holes
The net result is that some energy is taken from
the black hole. This decreases the mass of the
black hole according to E mc2. This was
predicted by Stephen Hawking and could provide a
way of detecting a black hole - Hawking Radiation
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Black Holes in Binary systems

• Black holes do not emit light, and therefore
  cannot be observed directly.
• However, their gravity is strong and would affect
  the orbits of close by objects
• Therefore, close binary systems provide us with
  the best way of detecting a Black Hole.

• Black Hole candidate Cygnus X-1 X-ray Source

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Black Holes in Binary systems

• Cygnus X-1 is a peculiar X- ray source with
  highly irregular X-ray pulses.
• The companion star of Cygnus X-1 is a 30M? B0
  supergiant, and from its orbit astronomers can
  estimate the unseen member is at least a 7M?
  object - a black hole?
• The material from the supergiant gradually
  spirals in towards the black hole, as it does
  friction heats up the gas. Very near the event
  horizon the temperatures reach extremely high
  levels and the hot gas emit X-rays.

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Black Holes in Binary systems

• The argument that Cygnus X-1 is a black hole is
  not airtight. Some critics have other possible
  explanations.
• Astronomers have found many other black hole
  candidates in binary systems

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Supermassive Black Holes in Galactic centers

• During the formation of galaxies, the gas at the
  galactic centers could compress due to its own
  gravity.
• If these regions get sufficiently dense, a black
  hole can form.
• Since, the amount of gas at the galactic centers
  are enormous compared to even the most massive
  stars, these black holes are referred to as
  Supermassive blackholes.
• A good example of such a black hole was
  photographed by the Hubble at the center of the
  M87 galaxy.

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Black Holes in Binary systems

• By measuring the speed of the material orbiting
  this tiny bright source of light at the center of
  M87, astronomers have calculated the mass of it
  to be three billion solar masses! Others like M87
  have been found.

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Primordial Black Holes

• In 1970s Stephan Hawking proposed the possibility
  that during the extremely hot and dense epoch of
  the universe just after the Bing Bang , local
  regions could have become dense enough to form
  black holes that have very small masses -
  Primordial Black holes
• These can have masses as large as Earths mass
  or smaller than a rain drop.
• However, to date we have not seen any evidence of
  these exotic objects.