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Black Holes
Into the rabbit hole
Vesc = (2GM/R)1/2
Substituting in the speed of light for the escape velocity, and
the event horizon for the radius of the orbit, gives one,
Rscw = 2GM/C2
Dark Stars ~ first postulated in 1700’s. John Micheille and
Pierre Lafatte wondered what would happen if a star had a
gravitational pull that made the escape velocity faster than
that of light.
They knew that light had an extrordinaryally high, but not
instantaneous speed.
Schwarzschild Radius
Light cannot escape from a Black Hole if it comes from a
radius closer than the Schwarzschild Radius, RS to the
singularity:
Schwarzschild Radius
Schwarzschild Radius
Light cannot escape from a Black Hole if it comes from a
radius closer than the Schwarzschild Radius, RS to the
singularity:
Schwarzschild Radius
Where M = Mass of the Black Hole
A black hole with a mass of 1 Msun would have a
Schwarzschild Radius of RS=3 km.
Compare this with a typical 0.6 Msun White Dwarf, which
would have a radius of about 1 Rearth (6370km), and a 1.4
Msun neutron star, which would have a radius of about 10km.
A blackhole with the mass of Earth would be about the “size”
of a
a.Golf ball
b.Volley ball
c.Person
d.Gym
e.School
A blackhole with the mass of Sol would be about the “size” of
a
a.LSW Campus
b.UNL Campus
c.Lincoln
d.Nebraska
e.United States
The word “Black Hole” was first used in 1967 by John
Wheeler. Before that they were called “Frozen Stars”.
It was first used this way in 1967, because it took this long
for people to really understand Albert E’s equations, and the
implications.
A star more massive than about 18 Msun would leave behind
a post-supernova core this is larger than 2-3 Msun:
Neutron degeneracy pressure would fail and nothing can
stop its gravitational collapse.
Core would collapse into a singularity, and object with
* zero radius
* infinite density
RS is named for German physicist Karl
Schwarzschild who in 1916 was one of the
first people to explore the implications of
Einstein's then-new General Theory of
Relativity, the modern theory of Gravity.
RS defines the "Event Horizon" surrounding the black hole's
singularity:
* Events occurring inside RS are invisible to the outside
universe.
* Anything closer to the singularity than RS can never leave
the black hole
* The Event Horizon hides the singularity from the outside
universe.
The Event Horizon marks the "Point of No Return" for objects
falling
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/blkhol.html
Gravity around Black Holes
Far away from a black hole:
* Gravity is the same as that of star of the same mass.
Close to a black hole:
* R < 3 RS, there are no stable orbits - all matter gets
sucked in.
* At R = 1.5 RS, photons would orbit in a circle!
Journey to a Black Hole: A Thought Experiment
Two observers: Jack & Jill
Jack, in a spacesuit, is falling into a black hole. He is carrying a
low-power laser beacon that flashes a beam of blue light once a
second.
Jill is orbiting the black hole in a starship at a safe distance away in
a stable circular orbit. She watches Jack fall in by monitoring the
incoming flashes from his laser beacon.
He Said, She Said...
From Jack's point of view:
* He sees the ship getting further away.
* He flashes his blue laser at Jill once a second by his watch.
From Jill's point of view:
* Each laser flash take longer to arrive than the last
* Each laser flash become redder and fainter than the one before it.
Near the Event Horizon...
Jack Sees:
* His blue laser flash every second by his watch
* The outside world looks oddly distorted (positions of stars have
changed since he started).
Jill Sees:
* Jack's laser flashing about once every hour.
* The laser flashes are now shifted to radio wavelengths, and
* The flashes are getting fainter with each flash.
Moral:
The powerful gravity of a black hole warps space and time around it:
* Time appears to stand still at the event horizon as seen by a distant
observer.
* Time flows as it always does as seen by an infalling astronaut.
* Light emerging from near the black hole is Gravitationally Redshifted
to longer (red) wavelengths.
Pictures & movies by relativist Robert Nemiroff at the Michigan Technical
University.
Approaching the Black Hole
The first frame depicts the observer in empty space looking toward the constellation Orion. The three
stars in Orion's belt are visible to the right of the center of the screen. Sirius can be seen as the
brightest star in the sky below and to left of Orion's belt, and Betelgeuse is the reddish star just above
Orion's belt.
As the movie progresses the observer moves toward the black hole. An odd diffuse glow of light
appears in the center of the screen. Soon a black spot appears - the black hole itself. The black hole is
almost completely dark - light cannot escape from it. Black holes do release a slight bit of light as they
evaporate, as postulated by Hawking.
As the observer moves toward the black hole, the original star images appear pushed away from the
black hole This is because the starlight that originally reached you is now strongly attracted toward the
black hole and hence deflected away from you. Only starlight passing further from the black hole might
now be attracted toward the black hole so that it is deflected to your eye.
Note also "new" dimmer images of stars become visible near the black hole. Here the strong gravity of
the black hole has pulled another image of stars around the far side toward your eye. Soon there are
two discernable images of everything in the sky. A secondary images of star can be identified with their
corresponding primary image by noting that they can be connected by drawing a straight line on the sky
through the center of the black hole and finding stars of like color.
As the computer generated animation continues, the observer stops just 42 kilometers from the black
hole. The universe looks like a very strange place from here.
Circling the Black Hole
The first frame shows a background sky highly distorted by the black hole
in the center. The gravity of the black hole is so great that it actually
deflects the background starlight. Large light bending effects cause the
background sky to appear to move in unusual ways as you circle the
black hole. Light paths are so curved that light can reach you from
anywhere on the sky - even from behind the black hole - no part of the
sky is eclipsed. Distant starlight has fallen to you and therefore appears
'blueshifted.'
The large light bending effects cause stars on the opposite side of the
black hole to become greatly magnified. Stars usually too dim to see
become visible. If you watch closely you can identify an invisible circular
ring around the black hole on either side of which stars counter-rotate.
This is an Einstein ring , and stars do not cross through it. Stars
approaching the exact opposite side of the black hole from you are seen
to have two bright images, one appearing just outside this Einstein ring,
and the other 180 degrees around the face of the black hole and just
inside this Einstein ring. Stars in this location appear to move with the
highest angular speed.
Approaching the Photon Sphere
As before, from this orientation, the black hole's enormous gravity bends light to
make two discernible images of the constellation Orion. You now descend to the
photon sphere. A photon sphere is a location where gravity is so strong that light
can travel in circles. Photons orbit the black hole at the distance of the photon
sphere. A photon could leave the back of your head, go once around the black
hole, and be seen by your eye - you can see the back of your head.
At the photon sphere, no light emitted outside can reach you from below - you
look into the vast emptiness of the black hole. The sky you once knew is now
behind you, compacted to occupy only half its original area.
Looking Up at the Photon Sphere
The first frame is dark as you peer into the black hole itself. You begin to look up
and stars come back into view. Now the stars are more blue than ever before as
starlight that has fallen into the black hole to reach you has become more energetic.
You may notice many dim stars just above the blackness - these are stars that are
greatly de-magnified by the enormous gravity. You may also notice that some stars
that you see in front of you - you expected to see behind you. Starlight from these
stars has been bent around the far side of the black hole.
No starlight can reach you from below - it could not escape the black hole's
enormous gravity. In other words, all light that crosses the photon sphere going in
can never go outward from the black hole.
Circling the Black Hole at the Photon Sphere
You currently sit at the black hole's photon sphere, where light can travel endlessly in
a circle due to the star's great gravitational pull. The apparent position of the photon
sphere is always easy to spot - it is the apparent dividing line between black hole
and sky.
As you circle the black hole the sky appears to move in strange ways. Here an
Einstein ring for background stars can be seen as an invisible line above the photon
sphere horizon. Stars approaching the exact other side of the black hole from you
appear to approach this line, are greatly magnified, and move with high angular
speeds. As one background star image is greatly magnified, so is another 180
degrees around the black hole - but with your current point of view you can see only
one at a time. Your spaceship's motion can cause a star image below this Einstein
ring to become very bright and shoot out of view - while a moment later the other
bright image of this same star zooms into view above the Einstein ring and fades.
You are not at the event horizon, which is still below you. Were you to travel to the
event horizon the sky would appear to scrunch up into a little dot opposite the black
hole. My computer programs cannot yet track you that far with much accuracy, and
so I cannot take you there today. Nobody really knows what it looks like inside a
black hole, on the other side of the event horizon.
Misconceptions about Black Holes
1.Cosmic Vacumn cleaners
2.Getting close to one will tear you apart
3.Can’t get into the event horozon
4.You can’t see a black hole
5.You can’t find a black hole
6.Black Holes will last forever
Stars traveling very fast
Average Sun moves 200-300 kilometers per second, stars
in middle of galaxy move 12,000 to 15,000 km/sec.
Stars traveling this fast have kinetic energy that has been
converted from GPE.
By calculating the mass of stars near the center of the
Universe, and using the formula force = mass x acceleration,
it has been found that the black hole in the center of our
galaxy has a mass of about
a.
b.
c.
d.
e.
1,000 Suns
10,000 Suns
100,000 Suns
1,000,000 Suns
4,000,000 Suns
All of this mass is in an area of about the size of our Solar
System, so the ONLY thing it could be would be…..
Vacuum Polarization May Stop Black Hole From Ever
Forming, And A Dark Star Forms Instead. Appears
The Same From Distance, But NO Set Even Horizon
MASS
Repulsive Force
Effective Cloud of
Negative Mass
How does a Black Hole evaporate?
Stephen Hawkins proposed the theory. It makes sense.
1.
Quantum mechanics tells us that particles can be created "of nothing", and
disappear into the same.
a. The law of conservation of mass and energy CAN be violated for short
periods of time
b.
The law of conservation of mass and energy CANNOT be violated for
extended periods of time.
2.
Energy can be "positive" or "negative", not the charge, but a state of the
energy itself. One could have a negative charge on positive energy, or a
positive charge on negative energy.
3.
A "particle" is created out of nowhere.
a.
The "particle" splits into a particle and an "antiparticle".
b.
The two will annihilate each other, if possible
c. If near the Rs radius, the one particle (or "antiparticle"), is pulled into the
black hole as NEGATIVE energy, where it eliminates itself AND an equal
amount of POSITIVE energy within the black hole. The black hold loses
energy, and it also loses mass.
Black Holes are described on pages 580 - 594 in the
Astronomy Today Text.
Section 22.5 - 22.8