Black Holes, Gravity to the Max

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Black Holes, Gravity to the Max

• By Dr. Harold Williams
• of Montgomery College Planetarium
• http//montgomerycollege.edu/Departments/planet/
• Given in the planetarium Saturday 19 November 2011

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Black Hole in front of the Milky Way, out galaxy
with 10 Solar Masses and viewed from 600km away
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Black Holes
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Just like white dwarfs (Chandrasekhar limit 1.4
Msun), there is a mass limit for neutron stars
Neutron stars can not exist with masses gt 3 Msun
We know of no mechanism to halt the collapse of a
compact object with gt 3 Msun.
It will collapse into a surface an Events
Horizon But only at the end of time relative to
an outside observer.
gt A black hole!
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Escape Velocity
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Velocity needed to escape Earths gravity from
the surface vesc 11.6 km/s.
vesc
Now, gravitational force decreases with distance
( 1/d2) gt Starting out high above the surface
gt lower escape velocity.
vesc
If you could compress Earth to a smaller radius
gt higher escape velocity from the surface.
vesc
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Escape Velocity Equation

• Newtonian gravity
• Vesv(2GM/R)
• Ves, escape velocity in m/s
• G, Newtonian universal gravitational constant,
  6.67259x10-11m3/(kg s2)
• M, mass of object in kg
• R, radius of object in m

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The Schwarzschild Radius
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gt There is a limiting radius where the escape
velocity reaches the speed of light, c
Vesc c
2GM
____
Rs
c2
G gravitational constant
M mass cspeed of light in a vacuum
Rs is called the Schwarzschild radius.
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General Relativity

• Extension of special relativity to accelerations
• Free-fall is the natural state of motion
• Spacetime (spacetime) is warped by gravity

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Black Holes

• John Michell, 1783 would most massive things be
  dark?
• Modern view based on general relativity
• Event horizon surface of no return
• Near BH, strong distortions of spacetime

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Schwarzschild Radius and Event Horizon
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No object can travel faster than the speed of
light
gt nothing (not even light) can escape from
inside the Schwarzschild radius

• We have no way of finding out whats happening
  inside the Schwarzschild radius.

• Event horizon

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0
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Black Holes Have No Hair
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Matter forming a black hole is losing almost all
of its properties.
black holes are completely determined by 3
quantities
mass
angular momentum
(electric charge) The electric charge is most
likely near zero
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The Gravitational Field of a Black Hole
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Gravitational Potential
Distance from central mass
The gravitational potential (and gravitational
attraction force) at the Schwarzschild radius of
a black hole becomes infinite.
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General Relativity Effects Near Black Holes
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An astronaut descending down towards the event
horizon of the black hole will be stretched
vertically (tidal effects) and squeezed laterally
unless the black hole is very large like
thousands of solar masses, so the multi-million
solar mass black hole in the center of the galaxy
is safe from turning a traveler into spaghetti .
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General Relativity Effects Near Black Holes
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Time dilation
Clocks starting at 1200 at each point. After 3
hours (for an observer far away from the black
hole)
Clocks closer to the black hole run more slowly.
Time dilation becomes infinite at the event
horizon.
Event horizon
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Observing Black Holes
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No light can escape a black hole
gt Black holes can not be observed directly.
If an invisible compact object is part of a
binary, we can estimate its mass from the orbital
period and radial velocity. Newtons version of
Keplers third Law.
Mass gt 3 Msun gt Black hole!
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Detecting Black Holes

• Problem what goes down doesnt come back up
• Need to detect effect on surrounding stuff Hot
  gas in accretion disks
  Orbiting stars
  Maybe gravitational lensing

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Compact object with gt 3 Msun must be a black hole!
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Stellar-Mass Black Holes

• To be convincing, must show that invisible thing
  is more massive than NS
• First example Cyg X-1
• Now more than 17 clear cases, around 2009.
• Still a small number!

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• Scientist witness apparent black hole birth,
• Washington Post, Tuesday, November 16, 2010.
• http//chandra.harvard.edu/photo/2010/sn1979c/

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SN 1979C
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Jets of Energy from Compact Objects
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Some X-ray binaries show jets perpendicular to
the accretion disk
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Model of the X-Ray Binary SS 433
Optical spectrum shows spectral lines from
material in the jet.
Two sets of lines one blue-shifted, one
red-shifted
Line systems shift back and forth across each
other due to jet precession
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Black Hole X-Ray Binaries
Accretion disks around black holes
Strong X-ray sources
Rapidly, erratically variable (with flickering on
time scales of less than a second)
Sometimes Quasi-periodic oscillations (QPOs)
Sometimes Radio-emitting jets
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Gamma-Ray Bursts (GRBs)
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Short ( a few s), bright bursts of gamma-rays
GRB of May 10, 1999 1 day after the GRB
2 days after the GRB
Later discovered with X-ray and optical
afterglows lasting several hours a few days
Many have now been associated with host galaxies
at large (cosmological) distances.
Probably related to the deaths of very massive (gt
25 Msun) stars.
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Black-Hole vs. Neutron-Star Binaries
Black Holes Accreted matter disappears beyond
the event horizon without a trace.
Neutron Stars Accreted matter produces an X-ray
flash as it impacts on the neutron star surface.
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Stars at the Galactic Center
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Gamma Ray Bubble in Milky Way
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Spectrum
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Black Holes and their Galaxies
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Gravitational Waves

• Back to rubber sheet
• Moving objects produce ripples in spacetime
• Close binary BH or NS are examples
• Very weak!

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Gravitational Wave Detectors
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Numerical Relativity

• For colliding BH, equations cant be solved
  analytically
  Coupled, nonlinear, second-order
  PDE!
• Even numerically, extremely challenging Major
  breakthroughs in last 3 years
• Now many groups have stable, accurate codes
• Can compute waveforms and even kicks

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Colliding BH on a Computer From NASA/Goddard
Group
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What Lies Ahead

• Numerical relativity continues to develop
  Compare with post-Newtonian analyses
• Initial LIGO is complete and taking data
• Detections expected with next generation, in less
  than a decade
• In space LISA, focusing on bigger BH
  Assembly of structure in early universe?

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Mass Inertial vs. Gravitational

• Mass has a gravitational attraction for other
  masses
• Mass has an inertial property that resists
  acceleration
• Fi mi a
• The value of G was chosen to make the values of
  mg and mi equal

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Einsteins Reasoning Concerning Mass

• That mg and mi were directly proportional was
  evidence for a basic connection between them
• No mechanical experiment could distinguish
  between the two
• He extended the idea to no experiment of any type
  could distinguish the two masses

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Postulates of General Relativity

• All laws of nature must have the same form for
  observers in any frame of reference, whether
  accelerated or not
• In the vicinity of any given point, a
  gravitational field is equivalent to an
  accelerated frame of reference without a
  gravitational field
• This is the principle of equivalence

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Implications of General Relativity

• Gravitational mass and inertial mass are not just
  proportional, but completely equivalent
• A clock in the presence of gravity runs more
  slowly than one where gravity is negligible
• The frequencies of radiation emitted by atoms in
  a strong gravitational field are shifted to lower
  frequencies
• This has been detected in the spectral lines
  emitted by atoms in massive stars

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More Implications of General Relativity

• A gravitational field may be transformed away
  at any point if we choose an appropriate
  accelerated frame of reference a freely falling
  frame
• Einstein specified a certain quantity, the
  curvature of spacetime, that describes the
  gravitational effect at every point

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Curvature of Spacetime

• There is no such thing as a gravitational force
• According to Einstein
• Instead, the presence of a mass causes a
  curvature of spacetime in the vicinity of the
  mass
• This curvature dictates the path that all freely
  moving objects must follow

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General Relativity Summary

• Mass one tells spacetime how to curve curved
  spacetime tells mass two how to move
• John Wheelers summary, 1979
• The equation of general relativity is roughly a
  proportion
• Average curvature of spacetime a energy density
• The actual equation can be solved for the metric
  which can be used to measure lengths and compute
  trajectories

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Testing General Relativity

• General Relativity predicts that a light ray
  passing near the Sun should be deflected by the
  curved spacetime created by the Suns mass
• The prediction was confirmed by astronomers
  during a total solar eclipse

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Other Verifications of General Relativity

• Explanation of Mercurys orbit
• Explained the discrepancy between observation and
  Newtons theory
• Time delay of radar bounced off Venus
• Gradual lengthening of the period of binary
  pulsars (a neutron star) due to emission of
  gravitational radiation

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Black Holes

• If the concentration of mass becomes great
  enough, a black hole is believed to be formed
• In a black hole, the curvature of space-time is
  so great that, within a certain distance from its
  center (whose radius, r, is defined as its
  circumference, C, divided by 2p, rC/2p), all
  light and matter become trapped on the surface
  until the end of time.

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Black Holes, cont

• The radius is called the Schwarzschild radius
• Also called the event horizon
• It would be about 3 km for a star the size of our
  Sun
• At the center of the black hole is a singularity
• It is a point of infinite density and curvature
  where space-time comes to an end (not in our
  universe!)

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Penrose Diagram of Spherical Black Hole
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All Real Black Holes will be Rotating, Kerr
Solution

• Andrew J. S. Hamiton Jason P. Lisle (2008) The
  river model of black holes Am. J. Phys. 76
  519-532, gr-qc/0411060
• Roy P. Kerr (1963) Gravitational field of a
  spinning mass as an example of algebraically
  special metrics Phys. Rev. Lett. 11 237--238
• Brandon Carter (1968) Global structure of the
  Kerr family of gravitational fields Phys. Rev.
  174 1559-1571