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LIGO-G1200393
Gregory MendellLIGO Hanford Observatory
Black Holes And LIGOBlack Holes And LIGO
The Laser Interferometer Gravitational-wave Observatory: a Caltech/MIT collaboration supported by the National Science Foundation
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LIGO-G060233-00-W
600+ Scientist and Engineers
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Einstein Wondered:Einstein Wondered:
Photo: Albert Einstein at the first Solvay Conference, 1911; Public Domain
Can we catch light?
Mirror
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LIGO-G0900422-v1
Time Time DilationDilation
x=vt
= change in
T = time measured by motorcycle riders
t = time measured by observer at “rest”
v = speed of motercycles
c = speed of light
ct T= t 1-v2/c2
StartWarning: thought experiment only; do not try this at home.
Niels Bohr Albert Einstein
cT
Motorcycle: http://en.wikipedia.org/wiki/Motorcycle_racing
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The Pythagorean Theorem Of Spacetime
c2T2 + v2t2 = c2t2
c2T2 = c2t2 - v2t2
c2T2 = c2t2 - x2
c = 1 light-year/year
T2 = t2 - x2
x
t
x = 29 light-years
t =
30
year
s
t = 30 years; x = 29 lt-yrs.
v = 96.7% the speed of light
T2 = 302 – 292 = 59 yrs2
T = 7.7 years
T
SpacetimePythagorean Thm. of Spacetime
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LIGO-G0900422-v1
The Twin ParadoxThe Twin Paradox•Imagine twins, Betty and Bob, separated 1 year after birth.
•Betty takes a rocket travelling at 96.67% the speed of light and travels 29 lt-yrs from Earth and back.
•When Betty returns she is sweet 16, and Bob is 61 years old!!!
Baby Betty & Bob:
T= 30 yrs 1-(.9667)2=7.7 yrs
x
Figure: http://en.wikipedia.org/wiki/Twin_paradox
x = 29 light-years
t =
30
year
s
Spacetime DiagramSpacetime Diagram
t
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LIGO-G0900422-v1
EinsteinEinstein’’s Happiest Thought:s Happiest Thought:Gravity Disappears When You Free FallGravity Disappears When You Free Fall
http://en.wikipedia.org/wiki/Leaning_Tower_of_Pisa
Photo: NASA
Warning: thought experiment only; do not try this at home.
Einstein had this thought in 1907. This lead to the idea that gravity is the curvature of spacetime. Here I paraphrase a thought experiment I first heard from Kip Thorne. Suppose two friends jump parallel to each other off the Leaning Tower of Pisa. For the friends, gravity has disappeared, and they believe they are in empty space. Strangely though, they find their parallel paths converging at the center of the Earth. That can happen in empty space only if that space is not flat but curved. Einstein thought about the geometry of rotating objects, and other things, and after 8 more years produced General Relativity, which is a theory of gravity and spacetime. He had help from a mathematician, Marcel Grossmann.
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Pythagorean Theorem and Einstein’s General Theory of Relativity
d = infinitesimal change
dT2 = gttdt2 + gxxdx2
dT2 = gdxdx)(
2
1
;
2
1
84
gggg
R
RgRRR
RgRG
Tc
GG
Einstein’s Field Equations
In GR the components of a 4x4 symmetric matrix called the metric tensor define the curvature of spacetime.
UUgdT
dU
UgUUdT
dx
2
1
; U = 4-Vel.; T = Proper Time
Geodesic Equation
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LIGO-G0900422-v1
Schwarzschild Black HoleSchwarzschild Black Hole
222222
2
2
222
222
222222
2
222
22
sin
1
11
sin2
1
121
drdrdr
c
vdtc
c
vdTc
drdrdr
rcGM
dtcrc
GMdTc
esc
esc
2
2
2
c
GMR
r
GMv
s
esc
•Escape Velocity
•Schwarzschild Radius
Object Schwarzschild Radius
You 1 thousand, million, million, millionth the thickness of a human hair
Earth 1 cm (size of marble)
Sun 3 km (2 miles)
Galaxy ~ trillion miles
Karl Schwarzschild
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LIGO-G0900422-v1
Gravitational Time Dilation
trc
GMT
2
21
Photo:http://en.wikipedia.org/wiki/Leaning_Tower_of_Pisa
Gravity slows time down!
Clock_Photos:http://en.wikipedia.org/wiki/Cuckoo_clock
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Gravity Slows TimeGravity Slows Time
Illustration: NASA
• Due to the orbital speed, clocks on the satellite lose 7 microseconds per day
•Due to the weaker gravitational field, clocks on the satellite gain 45 microseconds per day
•Satellite clocks gain a net of 38 microsecond per day
•Distance error = c*38 microseconds; c = 186,000 miles per second.
•Without calibrating clocks to account for Relativity, GPS distance would be off by 7 miles after one day!See Scientific American, Sept. 1994
Clock_Photos:http://en.wikipedia.org/wiki/Cuckoo_clock
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LIGO-G0900422-v1
Embedding DiagramEmbedding Diagram
22222
22222
222
2
2
]1)('[
)('
)(
21
1
drdrrfds
drrfdz
rfz
drdrdzds
drdr
rcGM
ds
Schwarzschild for t = 0, = /2:
z
xy
Flat space cylindrical coordinates:
(Surface of revolution about z-axis.)
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LIGO-G0900422-v1
Einstein-Rosen BridgeEinstein-Rosen Bridge
Our Universe
Another Universe?
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The Center Of The Milky WayThe Center Of The Milky Way
Credit: NASA/Chandra X-Ray Observatory
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Zooming in on the Zooming in on the galactic center…galactic center…
Credit: ESO PR Video Clip 02/02; ESO/European Organization for Astronomical Research in the Southern Hemisphere; Press Release 2002Credit: ESO PR Video Clip 02/02; ESO/European Organization for Astronomical Research in the Southern Hemisphere; Press Release 2002
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Black Hole DetectionBlack Hole Detection
2
3
2
32
)15(
)900(
4
yrs
AUM
GT
aM
= 3 million Solar Masses
Credit: ESO PR Photo 23c/02; ESO/European Organization for Astronomical Reseach in the Southern Hemisphere; Press Release 2002
Conclusion: there is a Black Hole at the center of our Galaxy that has a mass 3 millions times (or more precisely 3.95 million times) that of the Sun. S2 orbits this Black Hole at a distance of 12000 Schwarzschild Radii.
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LIGO-G0900422-v1
Falling Into A Black HoleFalling Into A Black Hole
20 yrs
40 yrs
60 yrs
yrs
3.5
hrs
Black Hole
White Hole
Singularity
Singularity
Another Universe?
- yrs
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LIGO-G0900422-v1
Embedding Diagram Inside Embedding Diagram Inside The Black HoleThe Black Hole
Schwarzschild for r = R, = /2:
ds2 = c2[2GM/(Rc2)-1]dt2 + R22.
z
xy
Flat space cylindrical coordinates:
ds2 = dz2 + dr2 + r2d2.
Comparing, it looks like in the flat space r = R = constant, so
ds2 = dz2 + R2d2.
We need to match up:
dz2 = c2[2GM/(Rc2)-1]dt2.
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LIGO-G0900422-v1
Schwarzschild Worm HoleSchwarzschild Worm Hole
Our Universe
Another Universe
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LIGO-G0900422-v1
Embedding With Interior DynamicsEmbedding With Interior DynamicsOur Universe
Another Universe
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LIGO-G0900422-v1
Nontraversable WormholeNontraversable WormholeOur Universe
Another Universe
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Stellar Collapse To Form A Black HoleStellar Collapse To Form A Black Hole
And it collapses to a Singularity.
When pressure can no longer support a star's gravity its mass falls through its horizon.
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Black Holes & Accretion DisksBlack Holes & Accretion Disks
LIGO-Gnnnnnn-00-W
http://researchnews.osu.edu/archive/fuzzballpic.htm (Illustration: CXC/M.Weiss)
image by Dana Berry/NASA; NASA News Release posted July 2, 2003 on Spaceflight Now.
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Gravitational WavesGravitational waves are
ripples in spacetime when it is stirred up by rapidly changing motions of large concentrations of matter or energy. The waves are extremely weak by the
times they reach Earth.
Illustration of Gravitational Waves:
Landry - Beamlines 2.0, 5 May 2010
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Sensing the Effect of a Gravitational Wave
Laser
signal
Gravitational wave changes arm lengths and amount of light in signal
Change in arm length is 10-18 meters,
or about 2/10,000,000,000,000,000 inches
beam splitterinput test mass
end test mass
recyclingmirror
4 km (2 km) Fabry-Perotarm cavity
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26
LIGO is in some ways like a space mission flying a few feet off the ground
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LIGO-G060233-00-W
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LIGO-G0900422-v1
Binary Black Hole Binary Black Hole CoalescenceCoalescence
Show movies from: Simulating Extreme Spacetimes – SXS - Caltech – Cornell Project. http://www.black-holes.org/explore2.html
Credit: Introduction to LIGO & Gravitational Waves: http://www.ligo.org/science/GW-Inspiral.php
Credit: Scott Hughs, MIT group:
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LIGO-G0900422-v1
What will a detection look and What will a detection look and sound like?sound like?
• During their 2009-2010 science runs, the LIGO Scientific Collaboration and the Virgo Collaboration did an end-to-end test with a blind hardware injection of a fake signal into the detectors.
• A signal was observed by several methods on Sept. 16, 2010. Subsequent analysis suggested it was a binary coalescence involving at least one black hole, with a 1/(7000 yr) false alarm rate.
•The Blind Injection Envelope was opened on March 14, 2011 revealing the Sept. 16, 2010 event was the fake injection of a neutron star – black hole coalescence signal.
• See: http://www.ligo.org/news/blind-injection.php; http://www.ligo.org/science/GW100916/ Data and Sound File from LIGO Hanford Observatory
with blind hardware injection of a fake signal.
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The End
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Landry - PAC28, 22 Jul 2010
Advanced LIGO Seismic Isolation
• Assembly of the Horizontal Access Module stacks is in full swing at both observatories.
• Active feedback control will be used.
• One assembly already was used in the Enhanced LIGO configuration.
31
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Suspension SystemsInitial Single vs. Advanced
Quad Pendulum
four stages
40kg silica masses
parallel reaction chain for control
Electro Static Drive (ESD) on last stage:
Reduces noise from electromagnets
silica fibers
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Nd:YAG Lasers: Initial LIGO 10W; Enhanced LIGO 35W; Advanced LIGO 150W
• Nd: YAG Neodymium-doped yttrium aluminum garnet.
• 1064 nanometers = infrared
• Stable to 1 part per million at 100 Hz.
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LIGO-G0900080-v1
Limiting Sources of NoiseInitial LIGO sensitivefrequency range:~ 40 – 6000 Hz. Advanced LIGO will lower this to10 Hz and push the noisedown by a factor of 10.
“Shot noise”
(photostatist
ics)
Internal
thermal noise
Ground m
otion
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Virginia Tech, 20 Feb 2009
LIGO-G0900080-v1
35
Reaching farther with Advance LIGO
E-LIGO
Likely event rates per year: ~40 binary NS mergers ~10 NS-BH ?? ~20 BH-BH ??
The LIGO Scientific Collaboration and Virgo Collaboration, Class. Quant. Grav. 27: 173001 (2010).
Other possible sources:
Intermediate-mass- ratio mergers to form a black hole.
Continuous signals from pulsars, low mass x-ray binaries, or unseen neutron stars.
Burst signals from supernovae (stellar core collapse) or cosmic strings.
Stochastic signal from the big bang or a population of sources.
2005
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LIGO-G0900422-v1
LIGO & Gravitational Waves
dxdxgdT 2
01
2
2
22
htc
hg
)/(2
0000
00
00
0000
cztifTT ehh
hhh
]2)/(2cos[1
)2/(ˆˆ
crtfr
hTT
Gravitational waves carry information about the spacetime around black holes & other sources.
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Detector Response
)(),,()(),,()(2
12
2
111
)1(
0
0
0
1
1
1
00
0
000
222
22
thFthFhhL
L
hL
LLtc
dxhdxhdtc
dxhdtc
dx
hhh
hhh
hhh
dxdtc
dxdxg
yyxx
xxx
L
xx
L
xx
t
xx
zzzyzx
yzyyyx
xzxyxx
(Light Travels On Null Geodesics)
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LIGO-G0900422-v1
Black Holes After 1960Black Holes After 1960•Kruskal-Szekeres Coordinates, 1960
•Wormholes, Wheeler and Fuller, 1962
•Black Holes, popularized by Wheeler, 1968
• Penrose Process,1969
•Black Hole Evaporation, Hawking, 1974
•Time Machines, Morris and Thorne, 1988
•BH Information Theory?
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Black Hole HistoryBlack Hole History
• Dark Stars, John Michell 1784 (Also Pierre-Simon Laplace, 1796)
• General Relativity, Einstein, 1915
• Spherically Symmetric Solution, Karl Schwarzschild, 1916
• Einstein-Rosen Bridge, 1935
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In a moving frame its energy is U + K1.
E=mc2: What Einstein Said
v
v
After it emits pulses of light with energy 0.5 E in opposite directions, the particles energy is H. Note that v does not change.
Consider a particle with energy U.
After it emits pulses of light with energy 0.5 (1 +/- v/c) in opposite directions the particle’s energy is H + K2. Note the relativistic blue/red shift factor is used.
By conservation of energy U = H + E and U + K1 = H + K2 + . Thus, (-1)E = K1 – K2 = K so ½ (v2/c2)E = ½ (m)v2 to lowest order. The particle lost mass m. For m max. equal to m: E = mc2.
“Does The Inertia Of A Body Depend Upon Its Energy-Content?” by A. Einstein, in “The Principle Of Relativity” translated by W. Perrett & G. B. Jeffery (Dover: 1952) from A. Einstein, Annalen der Physik, 17, 1905.
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E=mc2
c2t2 = c2T2 + v2t2
m2c4t2 = m2c4T2 + m2c2v2t2
m2c4t2/T2 = m2c4 + m2c2v2t2/T2
[mc2/(1-v2/c2)1/2]2 = [mc2]2 + [mv/(1-v2/c2)1/2]2c2
[mc2 + 1/2mv2] 2 = E2 = [mc2]2 + p2c2
For v = 0: E = mc2 Approximate to order v2/c2 == Newtonian Kinetic Energy
New
tonian Mom
entum
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• Einstein is famous for his thought experiments.• In 1895, around age 16, he wondered, can we catch
light?• If yes, your image in a mirror would disappear.
You would know your speed independent of any outside frame of reference. This would violate Galilean relativity.
• Einstein decides we cannot catch light; nothing can go faster than light.
Einstein WonderedEinstein Wondered
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LIGO-G0900422-v1
The Speed of Lightc = 186,000 miles/s = 670,000,000 miles/hr
v t T
Car 60 mph 1 day 1 day - .35 nanoseconds
Plane 600 mph 1 day 1 day – 35 nanoseconds
Shuttle 17,000 mph 1 day 1 day – 28 microseconds
Voyager 38,000 mph 1 day 1 day – 140 microseconds
Andromeda 300,000 mph 1 day 1 day – 8.7 milliseconds
Electrons 99% c 1 day 3.4 hours
The faster you go the slower time goes!
Nothing can go faster than light!
Pho
to:
Stan
ford
Lin
ear
Acc
eler
ator
Cen
ter
(SL
AC
); P
ubli
c D
omai
n
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LIGO-G0900422-v1
Eddington Finkelstein Eddington Finkelstein CoordinatesCoordinates
If we introduce the following form of the Eddington Finkelstein time coordinate, t',
t = t' – (2GM/c2)ln|rc2/(2GM) – 1|
outside the horizon, and
t = t' – (2GM/c2)ln|1-rc2/(2GM)|
inside the horizon, then inside or outside, we get
ds2 = -c2[1-2GM/(rc2)]dt’2 + 4GM/(rc2)dt’dr + [1+2GM/(rc2)]dr2 + r2d2 + r2sin2d2.
Note that there is no coordinate singularity at the horizon.
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LIGO-G0900422-v1
Schwarzschild Worm HoleSchwarzschild Worm Hole
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Black Hole DetectionBlack Hole Detection
LIGO-Gnnnnnn-00-W
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Black Hole Detection
LIGO-Gnnnnnn-00-W
http://chandra.harvard.edu/photo/2006/j1655/; Credit: Illustration: NASA/CXC/M.Weiss; X-ray Spectrum: NASA/CXC/U.Michigan/J.Miller et al.
http://chandra.harvard.edu/photo/2004/rxj1242/index.html; Credit: Illustration: NASA/CXC/M.Weiss; X-
ray: NASA/CXC/MPE/S.Komossa et al.; Optical: ESO/MPE/S.Komossa
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Black Holes DetectionBlack Holes Detection
LIGO-Gnnnnnn-00-W
http://antwrp.gsfc.nasa.gov/apod/ap060528.html; GRO J1655-40: Evidence for a Spinning Black Hole; Drawing Credit: A. Hobart, CXC