Transcript Black Holes and Relativity (Professor Powerpoint)

Black Holes
&
Relativity
Einstein and Relativity
• 1905 – Theory of Special Relativity
– Time dilation and length contraction
– Space and time are intertwined
– Matter and energy are equivalent
1916 – Theory of General Relativity

Describes the effects of gravity on spacetime
•What is “relative” in relativity?
–motion…all motion is relative
•The laws of nature are the same for everyone
–the speed of light (in a vacuum), c, is the
same for everyone
Relativity only needs to be dealt with at
speeds approaching the speed of light.
–Since we do not experience extreme speeds
& gravity, we have no common sense about
relativity
Objects moving relative to each other are in different
reference frames, like the plane and ground below
•A ball moves forward in a plane moving at 900 km/hr
Thought Experiments
I
I
You could also observe that you are moving away.
Thought Experiments
I
I
I’
Thought Experiments
Very High Speed
me
I
I
me
my point of view
•I
(a) An observer moving with the space ship
observes a light flash moving vertically
between the mirrors .
(b) A stationary observer observes the flash
moving along a diagonal path.
The longer distance taken by the light flash
in following the diagonal path must be
divided by a correspondingly longer time
interval to yield an unvarying value for the
speed of light.
As you go faster and faster time slows down.
•Time dilation formula:
t '  t 1  (v / c )
2
moving
rest
The effects on time can be ignored for small velocities, but
increase asymptotically as velocity approaches the speed of
light.
Length contraction
L '  L 1  (v / c )
2
As speed increases, length in the direction
of motion decreases. Lengths in the
perpendicular direction do not change.
Now, if a pair of scissors lies directly across your field of
view, it will appear at its maximum length. Rotating it
makes it appear shorter. This is depicted in the following
figure.
The degree of
foreshortening would
depend on the angle
that the pair of scissors is rotated.
Rotation here is 48 degrees, so that its length appears to
be two thirds what it was.
That's almost what happens with space and
time when things move. The object is
"rotated" out of one of the space dimensions
and into the time dimension.
If you were in space and a rocket ship moved
by you extremely rapidly (close to the speed
of light), it would appear shorter.
That's because the front of the ship has been
"rotated" into the future, and the rear of the
ship has been "rotated" into the past.
At any instant , you see the projection of the
rocket into the three dimensions of space .
MASS increase
•The faster an object moves, the more massive
it becomes.
rest mass
Moving mass

1  (v / c )
2
Toward a New Common Sense
Suppose I move by you at close to the speed of
light…you will see my time run slower, m
length contract, and my mass increase
But what do I see?… I am stationary; I see you
moving by at high speed in the opposite direction.
Since the laws of nature are the same for
everyone, I see your time run slower, your
length contract, and your mass increase
Inside my vehicle, I am not aware of any slow
down, every thing seem normal.
How can we test Relativity ?
In 1887, the Michelson-Morley experiment
used an interferometer to show that the speed of
light is not affected by the Earth’s motion
around the Sun.
•subatomic particles have been accelerated to
speeds of 0.9999 c and no matter how much
energy we put in, they never reach c, but their
masses increase.
•A + meson particle decays in 18 nsec when at
rest, but at high velocities, it lives longer,proving
time dilation
Consequences of
General Relativity
More Consequences of
General Relativity
Ticket to the Stars
• Although we can not travel faster than the
speed of light…
• special relativity will make the journey seem
shorter if we can travel close to the speed of
light
• Time moves more slowly for the space traveler.
• Space travelers can reach distant stars in their
lifetimes, but their friends and family will not
be there to greet them when they return home to
Earth.
•The End, relatively speaking
Black Holes
The End-States for Low and High Mass Stars
Initial Stellar Mass
Final Core Mass
Final State
1-8
0.5 - 1.4
White dwarf
8 - 30
1.4 - 3.0
Neutron Star
> 30
> 3.0
Black hole
Gravity as curved space
First, about Black Holes :
The sun will not become a black hole, it does
not have enough mass.
If the sun could become a black hole, it would
not change the orbit’s or the planets
Treat it like a snake, don’t get near it and
it won’t bother you.
Lastly, I am not the writer of the message, I am
only the carrier of the message. I’ll tell you what I
know. Astronomers do not agree on everything
about B.H.
This photo of a Black
Hole was taken by
Master H at Oxford
College of Emory
University.
or does it?
If the core of a star collapses with more than
3 solar masses, no known force can stop the
collapse, not electron, or neutron
degeneracy.
The star collapses to
a radius of zero, a
point called the
Singularity.
The Singularity has
infinite density and
gravity.
The Schwarzschild Black Hole
Simplest black holes, static (non-rotating) mass.
The Schwarzschild radius defines the Event
Horizon, the boundary at which the escape
velocity is the speed of light
photon sphere : 1.5
times bigger than
the Schwarzschild
radius is where light
orbits the BH
•At the center the is
the singularity
What we “see” as the black hole, is the
distance from the singularity where the
escape speed is faster than c, the speed
of light. This distance is the
Schwarzschild radius, or event horizon.
The core of the star
is compressed into
a single point – the
singularity, with zero
size and infinite
density.
We have no way of finding out what’s
happening inside the “Event horizon”
Schwarzschild Radius (kilometers)
~ 3 x mass of star (solar masses)
The singularity is a region of space-time
in which gravitational forces are so
strong that the Laws of Physics , break
down there.
What if you got inside the Event Horizon
?
Tidal
forces destroy anything falling inward
The tidal forces
of the BH would
begin to stretch anything
falling in.
A person watching you getting closer and closer to event
horizon sees you move more and more slowly because the
light from you takes longer and longer to reach the
observer.
The light is stretched out and as you cross the horizon
your image will hover at the horizon and never reach the
observer.
You will actually become invisible way before that
because the longer wavelength will change to infrared
and to radio etc.
What the observer inside a probe falling
into a mass black hole see?
Someone on the probe observes something
different. They see the probe cross the
event horizon an continue falling toward
the black hole’s singularity.
•The probe falling into the black hole
experiences huge gravitational tides which
stretch vertically and compress horizontally.
The probe would be pulled apart disintegrate
as it falls inward.
What happens at the singularity?
When our volunteer finally reaches the
singularity, what what happen
Stephen Hawking believes that his body
would be infinitely crushed and become part
of the black hole, turned into energy.
Other theorists suggest that instead, our
volunteer might pass into another universe,
that a black hole is just one end of a
connector tube called a wormhole.
Time slows down as you get closer to a BH. So if
you got close to, but outside the Event Horizon,
and then escape suing your powerful retro rockets,
you will have aged much less than a person
waiting for you in a spacecraft far from the BH.
General relativity demands that singularities arise
under two circumstances
First, a singularity must form during the creation
of a black hole.
Second, an expanding universe like ours must
have begun as a singularity.
General Relativity predicts Wormholes for Kerr
Black Holes, but Astrophysicists are skeptical.
•Could a black hole somehow be connected to another
part of spacetime, or some other universe?
Kerr Rotating Black Hole
The singularity is
smeared out to form
a ring around the
center of the hole.
Surrounding the Event
Horizon is a sphere of
space time called the
Ergosphere, where
nothing can remain at
rest.
If an object is moving fast enough, it can
enter the Ergosphere and fly out again.
If the object stops it must fall into the Black
Hole.
Here space-time is being pulled around
the rotating black hole and this is called
inertial frame dragging.
Relativity forbids material objects from
traveling faster than light, but allows
regions of space-time to move faster than
light.
“BLACK HOLES HAVE NO HAIR”,
or this is all we can know about a BH.
•No-hair theorem: All traces of the
matter that formed a BH disappear
except for:
MASS
ANGULAR MOMENTUM
CHARGE
Charge is probably neutral
–Jacob Bekenstein (a Princeton graduate
student in 1972, stated that if a black hole has
entropy it also must have a temperature.
–Hawking (1972): If the Black Hole is a black
body at non-zero temperature, it must obeys
the laws of thermodynamics and radiate
energy.
If nothing can escape from a black hole ;
how can it radiate?
Quantum Mechanics says that virtual particles can
appear and disappear in space.
Matter and energy Hawking Radiation theory
can interchange !
E  mc
2
3. If a virtual particle falls into a black hole, it will
have to take in energy from the black hole to become
a real particle and the black hole will lose energy
HOW FAST DO BHs EVAPORATE?
• Evaporation time proportional to
(mass)3
66
• For 1 solar mass BH: 1.5  10 yr
Smaller masses, evaporate faster.
•A 3 Msun black hole would require about
1063 years to completely evaporate.
•This is about 1053 times the present age
of the Universe.
TYPES of Black Holes
• Primordial – can be any size, including
very small – created in the Big Bang
• Stellar mass- black holes – must be at
least 3 Mo many examples are known
•Massive black holes – about 106 Mo – such
as in the center of the Milky Way – many
seen
•Supermassive black holes – about 109-10
Mo - located in Active Galactic Nuclei, often
accompanied by jets – many seen
New theories
The event horizon surrounds the BH and prevents us
from seeing the singularity. Could a BH exist without
an event horizon? This would be called a naked
singularity. This is a real possibility for some BH.
One group has proposed that if orbiting mass falls
into the BH in the direction of its spinning and speeds
up the BH, the results is this appears to disrupt the
BH enough to strip away the event horizon, exposing
the singularity.
Since swirling matter is falling into BH they may have
found the mechanism that allows naked singularities
to exist.
With out an event horizon, processes in the singularity
could impinge on the outside world. This might account
for unexplained high-energy phenomena that
astronomers have seen.
The Big Bang was a naked singularity, we think.
Astro-physicists are trying to combine Relativity
with Quantum Mechanics. Quantum Mechanics
forbids a singularity and so the singularity
would not be an infinite point but rather a highly
dense area and the Laws of Physics would still
hold. Instead of BH it might become a
“Quantum Star”.
HOW TO DETECT BLACK HOLES
We can’t see them directly.
inary system
where one star
has a core
mass > 3 solar
masses and
emitting high
energy X-rays.
1. B
X-ray binary (artist’s impression)
HOW TO DETECT BLACK HOLES
M87 disk
2.
Orbital motion of
stars or gas clouds
(supermassive holes)
HOW TO DETECT BLACK HOLES
3. Random
motions of
stars in galaxy’s
nucleus (supermassive
holes)
Gas almost never falls directly into a black hole
Too much “swirl” (angular momentum) …Funnels in
forming an Accretion disk
We “see” a black hole by
the mass falling into it
Signature of a Black Hole
Candidate For Black Hole
Example: Cygnus X-1
Binary Star w/ two
objects:
•M=30 Msun primary
(seen)
•M=7 Msun companion
–Too small, too X-ray bright, and too faint at visible
wavelengths to be a 7 M star.
–Far too massive to be a white dwarf or neutron star.
Evidence for BH
800 light years
A disk of dust
fuelling a massive
black hole in the
centre of a galaxy.
The speed of the
gas indicates that
the object at the
centre of the disk is
1.2 billion times
the mass of our
Sun.
Matter
falling into
a black
hole often
forms jets
Gravitational lensing
• How can a black
hole or a neutron
star act like a lens?
• The answer comes
from Albert
Einstein, who
proved in 1919 that
light follows in the
path of the bent
time and space
which is warped due
to the gravitational
force of a massive
object.
Gravitational
Lenses
• Gravitational Lens
are observed quite
frequently with the
Hubble Telescope.
•In many cases, the
amount of matter
needed to make the
gravitational lens is
much more than can
be accounted for by
the visible matter.
•There must be dark matter there as well.
Gravity Waves
According to general relativity, in a stellar collapse to a
black hole, the star loses its magnetic field. The field’s
energy radiates in the form of gravitational waves,
which are ripples in the very fabric of space time.These
waves are also created when neutron stars collide, or
even when they are in close orbits around each other.
Gravitational waves are incredibly tiny, and
astronomers around the world have begun building
detectors to measure these small changes. Once
detected , they will provide a new , and unique way
of observing the universe.