Transcript Black Holes - High Energy Physics at Wayne State

Chapter 23: Black Holes
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Fact, Fiction, or Unknown

This is a game where you (or I) make
statements about black holes (or wormholes)
and then we discuss whether these are fact,
fiction, or unknown.
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General Relativity
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To understand what black holes are, we begin
with an introduction to Einstein’s theory of
general relativity.
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It improves on Newton’s theory of gravity.
Newton’s gravity works well in most situations
(planetary orbits, binary stars) but fails when:
Gravity becomes extremely intense.
 Large masses move rapidly.
 Light is effected by a large mass.

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The Equivalence Principle

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The equivalence principle
says that an object will
behave the same whether
in gravity or accelerating at
an equivalent rate.
No experiment can
distinguish between gravity
and acceleration. We must
get the same result.
Astronauts feel weightless
in orbit because their
acceleration cancels
gravity.
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Here’s the Rub

Aim a laser beam from the rear to front of a shuttle.
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In zero gravity the laser will hit the front center of the shuttle.
In free fall around the Earth, the laser must hit the same spot
-- but from the time the light leaves the laser until it reaches
the front, the shuttle has moved!
The light is bent by gravity to hit the front center!
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General Relativity: Warped Space
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Light “Bends”
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Tests of General Relativity
Einstein’s theory says that the presence of
matter warps space and time. Gravity is
replaced by warping of space-time.
 Predictions:

Precession of the perihelion of Mercury
 Light will be bent when passing near large objects
 Time will slow down near a large mass
 Gravitational redshift of light
 Massive objects will collapse to a singularity (black
hole).

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Deflection of Light
Arthur Eddington mounted two expeditions in
1919, one to Brazil and the other to West Africa,
to view a total eclipse and measure the
deflection of starlight passing near the Sun.
 Both obtained measurements that agreed with
GR predictions  fame for Einstein &
Eddington.
 Gravitational lensing is now a tool:
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multiple images of distant objects
 microlensing: one image but brightness changes
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gravitational lens -- gravity
can bend light around a very
heavy obstacle
possible
gravitational lens
observed
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Lensing of Distant Galaxies
Hubble picture of
distant galaxies
lensed by nearer
galaxy (bright fuzzy
structure). Lensed
galaxies appear as
arcs in the picture.
Can be used to
estimate the mass of
the intermediate
galaxy.
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Gravity's Final Victory
A star more massive than about 18 Msun leaves
behind a core larger than 3 Msun
 Neutron degeneracy pressure fails
 Nothing can stop its gravitational collapse.
 Core collapses to a singularity:

zero radius
 infinite density
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Near the singularity gravity is so strong that not
even light can escape.
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Escape Velocity: Rocket Analogy
light:
299,792 km/s
Black Holes: Key Concepts
Black Holes are totally collapsed objects
 gravity so strong not even light can escape
 predicted by General Relativity
 Find them by their Gravity – Binary stars

Orbit of visible partner
 Accretion disk – matter sucked in from partner
 X-ray Binaries
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Gravitational microlensing
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Black Hole Formation
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Supernovae explosion
collapsing core passes through a neutron star stage
 neutron star not stable
 degeneracy pressure insufficient
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Core becomes a Black Hole:
"Black" because it neither emits nor reflects light.
 "Hole" because nothing entering can ever escape.
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Only its enormous mass remains
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Near the Singularity
 Gravity
is so strong
that nothing, not
even light, can
escape.
 Infalling matter is
shredded by
powerful tides and
crushed to infinite
density.
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Schwarzschild Radius

Light cannot escape from a Black Hole if it comes from
a radius closer than the Schwarzschild radiius
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M = Mass of the Black Hole, c = speed of light, G = newton’s
constant
At this distance: escape velocity = speed of light
Light speed is the fastest possible speed!
mass of 1 Msun  a Schwarzschild Radius of 3 km.
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Event Horizon

Schwarzschild radius marks the Event Horizon
surrounding the black hole's singularity:
Events occurring inside are invisible to the outside
universe.
 Anything closer to the singularity can never leave
the black hole

The Event Horizon hides the singularity from
the outside universe.
 “Point of No Return” for objects falling into a
black hole.
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Gravity Around Black Holes
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Far away from a black hole:
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Gravity is the same as for a star of the same mass.
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If the Sun became a Black Hole, all the planets
would continue in the same orbits.
Close to a black hole:

R < 3 RS, there are no stable orbits - all matter
eventually gets sucked in.
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Simulated Views of a Black Hole
far away
up close
Falling into a Black Hole
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Falling toward a black hole wouldn’t be a pleasant experience…
Falling feet-first, your body would be scrunched sideways and
stretched along the length of your body by the tidal forces of the
black hole. Your body would look like a spaghetti noodle!
Stretching happens because your feet would be pulled much
more strongly than your head.
Sideways scrunching happens because all points of your body
would be pulled toward the center of the black hole.
Your shoulders would be squeezed closer together as you fell
closer to the center of the black hole.
Tidal stretching/squeezing of anything falling into a B.H. is
conveniently forgotten in Hollywood movies.
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Falling into a Black Hole
A friend watching you as you enter a B.H.,
would see your clock run slower and slower
(than his) as you approached the event horizon.
 This is the effect of "time dilation".
 Your friend would see you take an infinite
amount of time to cross the event horizon
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time would appear to stand still.
However, in your reference frame your clock
would run forward normally and you would
reach the center very soon.
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Gravitational Redshift
 If
you beamed back the progress of your
journey into a black hole, your friend
would have to tune to progressively longer
wavelengths (lower frequencies) as you
approached the event horizon.
 This is the effect of gravitational redshift.
 Eventually, the photons would be
stretched to infinitely long wavelengths.
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Seeing the Invisible
Question:
 If no light gets out of a black hole, how can we ever
hope to find one?
Answer:
 Look for the effects of their gravity on nearby objects.
For example, search for black holes in binary star
systems:
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A star orbiting around an unseen massive companion.
X-rays emitted by gas heated to extreme temperatures as it
falls into the black hole.
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What if a Binary Partner is a Black
Hole?
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black hole and visible star orbit around a center of
mass
motion of visible companion betrays black hole
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Kepler's 3rd law  total mass of the system.
If the mass of the unseen object is too big for a neutron
star or a white dwarf, then it is very likely a black hole!
orbit depends
mass of two
objects
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Accretion from Binary Partner
Motion of
Accretion
Disk from
Doppler
Shift
Measure
Black
Hole
mass
X-Ray Binaries
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Bright, variable X-ray sources identified by Xray observatory satellites:
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Spectroscopic binary with only one set of spectral
lines - the second object is invisible.
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Gas from the visible star is dumped on the
companion, heats up, and emits X-rays.
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Estimate the mass of the unseen companion from
the parameters of its orbit.
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X-Ray Emission
Visible Star
black hole
accretion
disk
Gas pulled off
Gas temperature
increases closer
to BH. Gas near
BH emits x-rays.
Chandra X-ray Observatory
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Detects/images X-ray sources
that are billions of LY away.
Chandra’s mirrors are the
largest, most precisely shaped
and aligned, and smoothest
mirrors ever constructed.
Images 25 times sharper than
the best previous X-ray
telescope.
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Launched
by Space Shuttle
Columbia on July 23, 1999.
One of NASA's Great Observatories.
This focusing power is equivalent
to the ability to read a newspaper
at a distance of half a mile.
Chandra's improved sensitivity is
making possible more detailed
studies of black holes,
supernovae, and dark matter.
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X-Ray Emission
Visible star close loses some of its gas to the
black hole
 Gas material forms an accretion disk as it
spirals onto the black hole
 gas particles in the disk rub against each and
heat up from friction
 friction increases inward causing increasing
temperature closer to the event horizon
 near event horizon, the disk is hot enough to
emit X-rays.
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Black Hole Candidates
A number of X-ray binaries have been found
with unseen companions with masses > 3 Msun,
too big for a neutron star.
 Some Candidates:
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Cygnus X-1: M = 6-10 Msun
 V404 Cygni: M > 6 Msun
 LMC X-3: M = 7-10 Msun
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None are as yet iron-clad cases, but in general
things are looking pretty good.
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Black Hole Theory
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Modern physics has two basic sets of laws for
the universe:
General relativity -- macro-scale
 Quantum field theory -- micro-scale

The two are not compatible!
 Most problems fall into one category only.
 Black holes need both.
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micro-size and macro-mass
The study of black holes (on paper) helps
understand how to combine the two theories.
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Black Hole Theory (cont’d)
Black holes are “simple” objects described by
their mass, spin, and electric charge.
 Black holes have no hair.
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All event horizons are spherical, no matter what the
mass looked like before collapse.
 Black holes have no magnetic field (internal).
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Black holes have entropy (a measure of
disorder) that is proportional to the size of the
event horizon.
 Black holes have a temperature  black body
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Stephen Hawking
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Black holes slowly "leak"
particles – Hawking radiation
Stephen W. Hawking (b1942)
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quantum mechanics near the
event horizon of a black hole.
Each particle carries off a little
of the black hole's mass
The smaller the mass of the
black hole, the faster it leaks.
Hawking radiation is equivalent
to black body radiation.
Evaporating Black Holes

Black Holes evaporate slowly by emitting
“Hawking radiation”
Black Holes will eventually vanish
 The smaller the mass, the faster the evaporation
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Questions Remain about Black Holes:
Is the information that falls into a Black Hole lost
forever?
 What is inside a black hole?
 Can wormholes be produced to travel in time and/or
space?

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Super Massive Black Holes
Observation of so-called active galaxies
provides strong evidence for the existence of
super massive black holes which provide a
simple explanation for the extremely energetic
nuclei.
 See Chapter 26.
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Discussion Question
Discuss the following question with a classmate
then write down your short answer:
 What would happen to the Earth’s orbit if the
Sun were suddenly replaced by a black hole
with the same mass as the Sun?
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Of course the Earth would become dark and cold. I
want you to discuss what would happen to the
Earth’s orbit.
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Hollywood and Reality
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Black holes are portrayed as cosmic vacuum cleaners
in TV and films, sucking up everything around them.
Black holes are dangerous only if something gets too
close to them.
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Because all of their mass is compressed to a point, it is
possible to get very close where the gravity gets very large.
Objects far enough away will not sense anything
unusual.
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If the Sun were replaced by a black hole of the same mass,
the orbits of the planets would remain unchanged
It would however be darker and colder. 
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