Black Holes: Do They Really Exist?

1
Black Holes Do They Really Exist?
We cannot see black holes directly, so we have
to look for indirect evidencesWhat would you
look for to find a stellar-mass black hole, like
those formed after the death of high mass stars?
To look for black holes formed by the death of
high-mass stars, we look for binary systems that
allows us to determine the mass of the objects.
If we can find an object with mass exceeding 3 M?
, but is neither a regular star, nor a neutron
star, then we can argue that it may well be a
black hole.
2
Can We Tell if it is a Black Hole?
If our X-ray telescope have high-enough
resolution and can resolve the structure around
neutron stars and (stellar-mass) black holes,
then these are what we might be able to
seeIllustration of the X-ray emissions from the
accretion disks around black hole and neutron
starbut this is beyond our current capability!
http//antwrp.gsfc.nasa.gov/apod/ap010119.html
3
Black Hole at the Center of the Milky Way Galaxy!
Similar to the method used to measure the mass
of the unseen companion in Cygnus binary system,
we can observe the orbits (period of size of the
orbits) of stars near the center of the galaxy to
measure the mass of the galactic center
4
Is it a Black Hole?

• How do we know the concentration of masses at the
  center of our galaxy is a blackhole or not?
• The mass at the center of the galaxy is estimated
  to be about 3 million M?. However, possessing a
  high mass does not make you qualify for a black
  hole
• You need to pack this mass into a space smaller
  than the Schwarzchild radius of that mass

If the black hole at the center of the Milky
Galaxy is about 3 million solar masses, then its
size must be smaller than 3 million km, or 10
light seconds. This is only a tiny spot near
Sagittarius A in the picture on the left, about
1/200,000 of the length of the scale-bar in the
picture
You can watch the recent NOVA program about the
black hole at the center of the Milkyway Galaxy
at http//www.pbs.org/wgbh/nova/blackhole/program.
html
5
Gamma Ray Bursts

• Gamma Ray Bursts are high energy radiations
  from cosmological sources discovered
  accidentally in the 1960s by military satellites
  designed to monitor nuclear weapon tests on
  Earth.
• The are found to be distributed uniformly in
  space, and not correlated to the strong X-ray
  sources that are more concentrated in our own
  galaxy.
• Because of the tremendous distances of these
  objects, the energy released by the GRBs exceeds
  the luminosity of millions of galaxies like our
  own Milky Way.

• It is still not clear today what are causing
  these high energy events
• At least some of the GRBs seem to come from
  unusally powerful supernovae. But we dont know
  how the Gamma Ray are produced.
• Collision of neutron stars?

6
Einsteins Special and General Theory of
Relativity

• Einsteins Special and General Theory of
  Relativity are one of the most important
  development of Science in the 20th centurythese
  theories fundamentally changed our perception of
  space and time.
• The Special Theory of Relativity deals with the
  law of motion without the influence of gravity.
• Newtons law of motion is correct only when the
  speed of motions are low compared to the speed of
  light.
• Special Relativity gives us the correct
  description of the law of motion for all speed
  range, even when it is close to the speed of
  light.
• The General Theory of Relativity includes the
  effect of gravity and acceleration.
• Equivalence Principle the effect of gravity and
  the effects of acceleration are identical.

7

• Development of Special Theory of Relativity

8
Special Theory of Relativity

• The basis of Special Relativity is two
  concepts in physics
• All physical laws are the same in the inertia
  frames (The laws of nature are the same for every
  one, Page 331 of Text book).
• For two persons moving with respect to each other
  with constant speed, they must observe the same
  physical laws.
• All motion are relative. We cannot distinguish
  who is in motion and who is at rest..
• Inertia Frames A coordinate system in which
  Newtons first and second law of motion are
  valid.
• The speed of light is constant for all inertia
  observers (The speed of light is the same for
  every one, Page 331, Text Book).
• The speed of light we would measure from the
  light emitted by a moving source is the same as
  that from a source at rest!
• However, the color of light emitted from the
  moving source will change with the speed of the
  source (with respect to the observer).

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Speed of Light
The speed of light, commonly denoted by c, was
experimentally measured to be 2,999,792,458
meter/sec. In the 19th century, it was thought
that like sound wave must be transmitted through
a medium, light must be transmitted by a
yet-unknown medium called ether. Ether was
thought to permeates the universe. Knowing
Earths relative motion with respect to the ether
was important for our understanding of our place
in the universe. In 1887, Michelson and Morley at
Case Western University performed a measurement
to determine the flow of ether as the Earth moves
in space. A talented baseball pitcher can
throw the ball with speed approaching 100 miles
per hour. If the pitcher throws the ball at you
from a car traveling at a speed of 100 mph toward
(or away from) you, you would measure the speed
of the baseball to be 200 mph (or 0 mph). Like
the baseball thrown toward you by a pitcher
standing on the car driving toward you, the speed
of light in the ether should be different
depending on how fast the Earth is moving in the
ether. Michelson and Morleys measured speed
of light in the direction perpendicular and
parallel to the direction of Earths motion in
space. Their experiment showed that the speed of
light is the same independent of the direction it
travels.
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The Constancy of the Speed of Light

• Michelson and Morleys results on the speed of
  light were completely against our intuition and
  every-day experience about relative motion.
  Either
• the measurement was wrong, or
• the rules concerning how physical laws should
  change (or not change, invariant) when viewed by
  two observers moving with constant speed with
  respect to each other (called a transformation
  from one reference frame to another) are
  different for light and matter,
• our understanding of the law of physics was
  wrong
• Einstein postulated that the speed of light is
  independent of the motion of its source. He
  search for a new transformation rule that apply
  to both matter and light, and developed The
  Theory of Special Relativity, which forced us to
  rethink our idea about space and time. It was a
  revolutionary idea when it was first introduced,
  and faced very strong resistance for many years.
  However, it was accepted gradually only after
  experimental verification of its predictions were
  provided.
• Today, the constancy of the speed of light (that
  the speed of light is constant regardless of the
  relative motion between the light source and the
  observer) is accepted as one of the Laws of
  Physics, like the universal law of gravity that
  says there is a gravitational field associated
  with every object with mass.

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Important Results of Special Relativity

• Some important results of special relativity
• Time Dilation
• Length Contraction
• Increase of Mass
• Relativistic Red Shift
• Equivalence of Mass and Energy E mc2

Note that the effects of special relativity are
significant only when the speed of the object
under study is very high, close to the speed of
light! The speed of motion we experience daily,
or we are familiar with, such as the speed of
cars, airplane, or even rockets and spaceship
traveling to the Moon, are too slow compared with
the speed of light, and the special relativistic
effect of these motion are very small and cannot
be measured easily.
12
Space Travel A Trip to Alpha Centauri
(Chapter 18, Section 5)
Alpha Centauri, the closest star to the Sun, is
about 4.5 light years away. Assuming we have the
technology to build a spaceship that can travel
at a speed of 86 that of the speed of light, or
about 150,000 times faster than the spaceship we
used to go to the Moon in the 1970s, and that
Alpha Centauri is not moving with respect to
Earth. Then, after launch, the mission control
will have to wait for 9.7 years to hear the
report from the astronauts on the spaceship that
they have just arrived to a planet orbiting Alpha
Centauri, because it takes the spaceship 5.2
years (4.5/0.86 ) to travel to Alpha Centauri,
and another 4.5 years for the report sent from
Alpha Centauri (traveling at speed of light!) to
travel back to the Earth. However, the astronauts
reported that the trip wasnt too bad after all,
because it only took them 2.5 years to get there,
according to the clock in their spaceship
This is the result of Time dilation and Length
Contraction in Special Theory of Relativity
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Time Dilation

Moving clock runs slower! Given two identical
clocks, if one were traveling with a constant
speed v with respect to the other, then the
traveling clock would run slower.
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Time Dilation

• You can see the moving clock slows down only
  when the speed of the moving clock (with respect
  to you) is very high
• For v 1,000 miles per hour (supersonic jets)
• v/c 0.000001, t 0.999999999 t0. The effect
  is not appreciable at all!
• For v0.86c, t 2.0 t0, or the traveling clock
  runs 2 times slower than the clock at rest with
  respect to you!

15
In Mission Control

• Because of time dilation, to people in mission
  control, the clock on the spaceship appears to
  run slower than the clock in mission control, and
  the astronaut aged slowerBut it takes the
  astronaut 5.2 years (Earth Clock time) to get to
  Alpha Centauri.

16
Length Contraction

• A standard ruler would appear shorter measured by
  an observer traveling with speed v with respect
  to this ruler (This is also referred to as the
  Lorenz Contraction, first derived by Lorenz,
  before Einstein).
• Assuming that the distance between the Earth and
  Alpha Centauri is not changing, then we can
  consider this distance as a ruler
• For the astronaut, the Earth and Alpha Centauri
  are moving at a speed of 0.86 c with respect to
  their spaceship. Therefore, the distance between
  Earth and Alpha Centauri is only 2.25 light
  years.

17
For the Astronauts
Although the clock in the spaceship would appear
to run perfectly normal to the astronaut, the
distance between the Earth and Alpha Centauri is
shorter because of the effect of length
contraction. Therefore, it takes them only half
the time (compared to Earths point of view) to
get there.
18
Mass Increases
According to special relativity, the mass of an
object (as measured by a person at rest)
increases as its speed is increased. When it
achieves the speed of light, the mass of the
object becomes infinitely large. Newtons
second law of motion says that the acceleration
of an object times its mass is equal to the force
applied. F m ? a or, Thus, with an
infinite mass, a 0. In other words, as the
speed of a mass approaches that of the speed of
light, its mass approaches infinity, and we
cannot accelerate it any further, no matter how
hard we try
Therefore, nothing can move faster than the speed
of light!
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The Twin Paradox
If you are convinced about the effect of time
dilation and length contraction, then think about
this Imagine we have a pair of twin, one man,
one woman. If the brother stays on Earth at
mission control, while the sister takes the trip
to Alpha Centauri, then when the trip is over and
the sister returns to the earth, she would be
younger than her twin brother because, according
to special relativity, her clock (the moving
clock) runs slower. But From the
perspective of the sister, her clock runs
perfectly normal. Her heart beat is still about
50 pulses per minute. It was her brother and the
Earth and Alpha Centauri that went for a trip
with a speed of 0.86c. It was the clock of her
brother thats running slow! What is wrong here?
20
The Twin Paradox The Resolution

• The resolution of the twin paradox comes from the
  realization that in the coordinates system of the
  brother, it was the sister who actually traveled!
  
• In her trip to Alpha Centauri and back, the
  sister went through a series of events
• Accelerate from rest (with respect to Earth) to
  0.86 c,
• Traveling at 0.86 c for 2.7 years
• Making the turn around, which can be achieved by
  many different methods, for example,
• Decelerates to a stop (with respect to
  Earth-Alpha Centauri system), then accelerate
  toward earth to 0.86 c again,
• Making the turn (changing direction,
  accelerating) at the speed of 0.86 c
• Traveling at 0.86 c for another 2.7 years
• Decelerates to a stop on Earth
• The sister went through many different inertia
  frames during the trip. Meanwhile, the brother
  remains stationary (with respect to Earth), and
  felt only a constant gravitational field all the
  time. The twin do not experience the same thing.
  So, the argument that the brother, the Earth, and
  Alpha Centauri went for a trip went for a trip
  equivalent to the trip the sister experienced is
  not valid.

21
General Theory of Relativity
The core of general relativity is the Principle
of Equivalence, which describes gravitation and
acceleration as different perspectives of the
same thing, and which was originally stated by
Einstein in 1907 as We shall therefore assume
the complete physical equivalence of a
gravitational field and the corresponding
acceleration of the reference frame. This
assumption extends the principle of relativity to
the case of uniformly accelerated motion of the
reference frame. In other words, he postulated
that no experiment can locally distinguish
between a uniform gravitational field and a
uniform acceleration. For example, a person in
a sealed elevator (and cannot see outside)
accelerating at 9.8 m/sec2 (the gravitational
acceleration on the surface of the Earth) cannot
tell if he is sitting on the surface of the
Earth, or if he is in a place far away from any
stars and planets but is been accelerated
22
Effects of Very Strong Gravity

• Some important results of General Relativity
  of relevance to Astronomy
• Gravitational Redshift
• A blue photon emitted from a star with a strong
  gravitational field would appear red after it
  reaches us at a distance away
• Gravitational Lensing Effect
• Distortion of spacetime causes the light to
  travel a different path
• This effect is be used to measure mass of
  distance galaxies.
• Gravitational Time Dilation
• Time appears to run slower in strong
  gravitational field to an observer located at a
  distance away in a weaker gravitational field.

23
Experimental Verification of Time Delay

• Hafele and Keating Experiment
• During October, 1971, four cesium atomic beam
  clocks were flown on regularly scheduled
  commercial jet flights around the world twice,
  once eastward and once westward, to test
  Einstein's theory of relativity with macroscopic
  clocks.
• From the actual flight paths of each trip, the
  theory predicted that the flying clocks, compared
  with reference clocks at the U.S. Naval
  Observatory, should have lost 40/-23 nanoseconds
  during the eastward trip. They should have gained
  275/-21 nanoseconds during the westward trip.
• The flying clocks lost 59/-10 nanoseconds during
  the eastward trip and gained 273/-7 nanosecond
  during the westward trip.
• These results provide an unambiguous empirical
  resolution of the famous clock "paradox" with
  macroscopic clocks.
• J.C. Hafele and R. E. Keating, Science 177, 166
  (1972)
• Nanosecond 1 billionths of a second!
• 275 nanosecond is about ¼ of a millionths of a
  second.

24
Effects of Very Strong Gravity

• Some important results of General Relativity
  of relevance to Astronomy
• Gravitational Redshift
• A blue photon emitted from a star with a strong
  gravitational field would appear red after it
  reaches us at a distance away
• Gravitational Distortion Spacetime
• Distortion of spacetime causes the light to
  travel a different path
• Gravitational Lensing Effect
• This effect is be used to measure mass of
  distance galaxies.
• Gravitational Time Dilation
• Time appears to run slower in strong
  gravitational field to an observer located at a
  distance away in a weaker gravitational field.

25
Gravitational Redshift
Explanation1 It takes energy to move away from
an object with strong gravity (e.g., going up
stair, sending a satellite into orbit, or sending
the astronauts to the Moon). The same can be said
about a photon trying to travel from the surface
of a star to a distant location where the
gravitational pull of that star is almost zero.
The photon need to spend energy to get to the
far-away destination. So, the photon has less
energy when it reaches its far-away destination.
A photon with lower energy means it has longer
wavelength, or, it appears redder.
The ball stopped going up zero kinetic energy
For photons, think in terms of energy. Zero
energy photon Infinitely long wavelength, DARK,
Cant see it.
The speed is decreased at higher height Lower
kinetic energy
Lower (than initial) energy photon Long
wavelength, appears REDDER
Throw a ball upward with initial velocity V High
kinetic energy
Initial energy of photon depending on the
wavelength
26
Gravitational Redshift Stretching of Spacetime
Explanation2 Gravity stretches the spacetime
continuum. The photons are stretches with it.
Zero gravity, flat spacetime
B
A
Strong gravity, curved spacetime
D
C
The distance between C and D is stretched longer
by gravity.
C
D
Black hole
Photons are stretched so much that it is no
longer detectable.
27
Effects of Very Strong Gravity

• Some important results of General Relativity
  of relevance to Astronomy
• Gravitational Redshift
• A blue photon emitted from a star with a strong
  gravitational field would appear red after it
  reaches us at a distance away
• Gravitational Distortion Spacetime
• Distortion of spacetime causes the light to
  travel a different path
• Gravitational Lensing Effect
• This effect is be used to measure mass of
  distance galaxies.
• Gravitational Time Dilation
• Time appears to run slower in strong
  gravitational field to an observer located at a
  distance away in a weaker gravitational field.

28
Gravitational Distortion of Spacetime

• In classical physics, the universe is
  composed of a three-dimensional space, and a one
  dimensional time. Space and time as separate and
  independent dimensions. The three-dimensional
  space moves in the time dimension.
• In Einsteins General Theory of Relativity, space
  and time are considered inseparableand gravity
  arises from the curvature of the spacetime
  continuum.
• Both light and matter follow the same path in
  spacetime
• Therefore, in region of very strong gravity, the
  distortion of spacetime is so great that the path
  of both light and matter curves back inside

29
Bending of Light Path Around Black Holes
At a distance of about 1.5 Rsch of a black hole,
spacetime is distorted so much that photons
emitted from the back of your head actually go
around the black hole and come back to you.
30
Experimental Verification of Gravitational
Distortion of Spacetime

• Even without a black hole, we can verify
  Einsteins prediction of the gravitational
  distortion of spacetime
• According to GR, the spacetime near a heavy
  object like the Sun is distorted, causing the
  position of stars passing near the edge of the
  Sun be shifted by 1.75 arcsecond
• This effect was experimentally verified by Sir
  Eddington in 1919 during an eclipse observation
  http//www.firstscience.com/site/articles/coles.as
  p

Light path of star without the Sun
Stars far away from the Sun are not affected
Star near the Sun would be affected
31
Eddingtons Eclipse Measurement of Gravitational
Bending of Light
Eddingtons results were not accepted universally
by the scientific community right awayThis is
actually quite normal in the scientific
community. However, the results were confirmed by
many other eclipse measurements later
The red line marks where the star should be
without the gravitational bending of space time
by the Sun.
32
Gravitational Lensing Effect
In general relativity, gravity causes the
distortion of spacetime. Light travels along
these distorted path. Thus, a large gravitational
object sometime behave like a lens. It can form
image or images of distant objects behind it for
us to see if the alignment happens to be right.
This galaxy is directly behind the cluster.
Gravitational lensing produces the multiple
copies of the same galaxy we see here.
If we know the distance to the galaxy being
imaged, then we can calculate the mass of the
cluster.
33
What Happens if Your Neighbor is a Black Hole?

• If there is a black hole in the solar
  neighborhood, will it pull everything the Sun,
  the planets, and the asteroids and coments in?
• No! as long as we stay outside of its event
  horizon, we are safe
• Recall that there are stable orbits around a
  gravitational objects
• From a distance, a black hole is not different
  from an ordinary star or planet

If you take a trip to the black hole
If you want to know what it is like inside the
black hole, the NOVA program has a simulation,
but I am not so sure about it http//www.pbs.org/
wgbh/nova/blackhole/program.html
34
Concluding Remarks about the General and Special
Theory of Relativity

• The predictions of special and general
  relativity have been verified by many
  experiments. Today, not only physicists worry
  about the effects of Special and General of
  Relativities (SR and GR). These effects are part
  of our daily life also. For example, the Global
  Positioning Satellites (GPS) needs to take into
  account GR and SR time dilation effects in order
  to keep correct time from onboard atomic clocks.