Transcript Black Holes: Do They Really Exist?

Black Holes: Do They Really Exist?
We cannot see black holes directly, so we have to look for indirect
evidences…What 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.
The Case of Cygnus X-1
Cygnus X-1 is a X-ray binary system with a bright star of 18 M⊙, and an
unseen (invisible in the visible) companion of about 10 M⊙. If the mass
estimate of the X-ray source is correct, than it certainly exceeds the upper mass
limit of neutron star (~ 3 M⊙), making it a prime stellar black hole candidate.
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 see…Illustration
of the X-ray emissions from
the accretion disks around
black hole and neutron
star…but this is beyond our
current capability!
http://antwrp.gsfc.nasa.gov/apod/ap010119.html
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…
http://www.eso.org/outreach/press-rel/pr-2002/pr-17-02.html
Star Orbiting Massive Milky Way Centre Approaches to
within 17 Light-Hours
An international team of astronomers [2], lead by researchers
at the Max-Planck Institute for Extraterrestrial Physics
(MPE), has directly observed an otherwise normal star
orbiting the supermassive black hole at the center of the
Milky Way Galaxy.
Ten years of painstaking measurements have been crowned
by a series of unique images obtained by the Adaptive Optics
(AO) NAOS-CONICA (NACO) instrument [3] on the 8.2-m
VLT YEPUN telescope at the ESO Paranal Observatory. It
turns out that earlier this year the star approached the central
Black Hole to within 17 light-hours - only three times the
distance between the Sun and planet Pluto - while traveling
at no less than 5000 km/sec….
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
ofofthat
mass…
If the black hole atradius
the center
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
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
don’t know how the Gamma
Ray are produced.
– Collision of neutron stars?
Einstein’s Special and General
Theory
of Relativity
Einstein’s Special and General Theory of Relativity are one of the most important
development of Science in the 20th century…these 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.
• Newton’s 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.
Development of Special Theory of Relativity
Special Theory of Relativity
The basis of Special Relativity is two concepts in physics:
1.
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 Newton’s first and second law of
motion are valid.
2.
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).
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 Earth’s 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 Morley’s measured speed of light in the direction perpendicular and
parallel to the direction of Earth’s motion in space. Their experiment showed that the
speed of light is the same independent of the direction it travels.
The Constancy of the Speed of
Light
Michelson and Morley’s results on the speed of light were completely against our intuition
and every-day experience about relative motion. Either
1. the measurement was wrong, or
2. 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,
3. 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.
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.
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 wasn’t 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…
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.
Imagine a ‘clock’
which works by
counting the time it
takes for light to travel
from a light source F
to a mirror and bounce
back to the receiver D
…
If this clock is traveling with a constant velocity u with
respect to an observer (the observer at rest), it would
appear to the observer at rest that the traveling clock is
running slower compared to his identical reference clock
at rest, because of the extra distance (L is larger than L0)
that light needs to travel according to the observer at
rest…
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…
t is the time
measured by the
traveling clock…
t
t0
v2
1 2
c
t0 is the time
measured by the
observer at rest.
v is the speed of the
moving clock.
• 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 v=0.86c, t ~ 2.0 t0, or the traveling clock runs 2 times slower than the
clock at rest with respect to you!
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 slower…But it takes the astronaut
5.2 years (Earth Clock time) to get to Alpha Centauri.
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.
v = 0.0
L0
Earth
Alpha Centauri
v = 0.86c
Alpha Centauri
Earth
L=L0 / 2
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 Earth’s point of view) to get there.
Length of ‘ruler’ that is
moving at a speed of v
v2
L L0 1  2
c
Length of stationary ‘ruler’
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.
Newton’s second law of motion says that the acceleration of an object
times its mass is equal to the force applied.
F=ma
or,
a
F
m
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!
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 that’s running slow!
What is wrong here?
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:
1. Accelerate from rest (with respect to Earth) to 0.86 c,
2. Traveling at 0.86 c for 2.7 years
3. 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
4. Traveling at 0.86 c for another 2.7 years…
5. 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.
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…
Effects of Very Strong Gravity
Some important results of General Relativity of relevance to Astronomy…
1.
2.
3.
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.
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.
Effects of Very Strong Gravity
Some important results of General Relativity of relevance to Astronomy…
1.
2.
3.
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.
Gravitational Redshift
Explanation#1
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
The speed is
decreased at higher
height: Lower
kinetic energy
Throw a ball
upward with initial
velocity V: High
kinetic energy
For photons, think
in terms of energy.
Zero energy photon:
Infinitely long
wavelength, DARK,
Can’t see it.
Lower (than initial)
energy photon:
Long wavelength,
appears REDDER
Initial energy of
photon depending on
the wavelength
Gravitational Redshift:
Stretching of Spacetime
Zero gravity, flat spacetime
B
A
Explanation#2
Gravity stretches the spacetime
continuum. The photons are
stretches with it.
Strong gravity, curved spacetime
C
D
C
The distance between C
and D is stretched
longer by gravity.
D
Black hole
Photons are stretched
so much that it is no
longer detectable.
Effects of Very Strong Gravity
Some important results of General Relativity of relevance to Astronomy…
1.
2.
2.
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.
Gravitational Distortion of
Spacetime
In classical physics, the universe is composed of a threedimensional space, and a one dimensional time. Space and time
as separate and independent dimensions. The three-dimensional
space moves in the time dimension.
•
In Einstein’s General Theory of Relativity, space and time are
considered inseparable…and 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…
Two dimensional model of the curvature of spacetime…
Without gravity
With gravity
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.
Experimental Verification of
Gravitational Distortion of Spacetime
Even without a black hole, we can verify Einstein’s 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.asp
Light path of star without the Sun
Light path of star with the Sun
Stars far away from the Sun are not affected…
Star near the Sun would be affected
Eddington’s Eclipse Measurement of
Gravitational Bending of Light
Eddington’s results were
not accepted universally
by the scientific
community right
away…This 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.
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.
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
If you take a trip
star or planet…
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/blackh
ole/program.html
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.