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Albert Einstein
Gravitational Wave Astronomy: A New
Window to the Universe
Albert Einstein
Einstein,Albert 1916, Sitzungsberichte der Königlich
Preußischen Akademie der Wissenschaften (Berlin), 1,
688-696
Einstein, Albert 1918, der
Königlich Preußi
Sitzungsberichte schen
Akademie der Wissenschaften
(Berlin), 1, 154-167
Rainer Weiss, Kip
Thorne, Ronald Drever
and 2016 Kavli Prize,
2016 Shaw Prize,
2016 Gruber
Cosmology Prize,
2016 Breakthrough
Prize, ..., 2016 Nobel
Sudarshan Karki, University
of Oregon, physics graduate
student
SUMMARY
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According to Einstein, a pair of black holes orbiting each
other emit gravitational waves causing them to gradually
approach each other over billions of years. Gravitational
waves are produced during the final fraction of a second
before the merger of the two black holes. During the
merger, the black holes collide at nearly one-half the
speed of light to form a single black hole converting
a portion of the black holes’ mass to energy, primarily
gavitational wave radiation.
The event was detected on September 14, 2015 at 5:51
a.m. Eastern Daylight Time (09:51 UTC) by the twin
Laser Interferometer Gravitational-wave Observatory
(LIGO) detectors in Livingston, Louisiana, and Hanford,
Washington. The masses of the black holes were
estimated to be about 29 and 36 times the mass of the
sun, and that the event took place 1.3 billion years ago
(z=0.09). Three times the mass of the sun was converted
into gravitational waves in a fraction of a second. The
detector in Livingston recorded the event 7 milliseconds
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Event?
A big mosquito has mass 2.5 grams and flies
at 2 km/h, kinetic energy 4x10-4 Joule (J)
A 1 kilogram shoe moving at 23 km/h carries
20 J (drop a shoe from a height of 2 m)
The Sun radiates 4x1026 watt (1 watt is 1
J/s). Over the Sun’s lifetime of 10 billion
years, it will produce ~1.2x1044 J.
The Milky Way galaxy shines with power ~
4x1037 watt (the combined light of 100-200
billion stars).
The outburst lasted a fraction of a second. It
converted about 3 Solar masses into energy which
corresponds to 5.4x1047 J (using Einstein’s E=mc2)!
A swarm of 1051 big mosquitos
A shower of 3x1046 1 kg shoes
>4,000 times the energy the Sun produces
over its lifetime.
50-100 billion times more power than the
Milky Way galaxy radiates and, in fact, is
greater than the combined light of all the
other galaxies in the Universe!
What are
Gravitational Waves?
If you weigh 65 kg, you may be surprised to learn that if
you ride in an elevator which accelerates upward, your
weight increases. If you ride in an elevator that accelerates
downward, your weight decreases. If the elevator cable
snaps and you accelerate due only to the gravitational pull
of the Earth (you fall in the Earth’s gravitational field), your
weight becomes 0, you are weightless.
Events are defined by both space and time.
Einstein suggests that space-time is
malleable.
Einstein posited that gravity is not a force.
Gravity is understood because space-time is
curved and mass curves space-time. Objects
moving near the mass move along geodesics,
natural, unforced paths. They are not forced to
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Minkowski metric
In flat space, scale factors are 1. In curved
space, scale factors are not 1; their size
depends on how curved is the space-time.
The strain is how much the scale factors
differ from 1.
LIGO measures the strain, the distortion
from a flat space-time, technically, the
distortion from a 4-dimensional flat spacetime, Minkowski space-time.
General Theory of Relativity
Field Equation, metric, and Wave Equation
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The existence of gravitational waves was demonstrated in the 1970s to 1990s by Joseph Taylor, Jr., and colleagues. In 1974 Taylor and Russell Hulse discovered a binary star
system composed of a pulsar orbiting about another pulsar. Taylor and Joel M. Weisberg found that the orbit of the pulsar was shrinking over time because of the loss of
energy in gravitational waves. Hulse and Taylor were awarded the Nobel Prize in Physics in 1993.
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How did LIGO detect
the Gravitational
Waves?
LIGO is made up of two widely
separated interferometers (4 km
arms): LIGO Hanford in
Washington and LIGO Livingston,
3002 km away in a pine forest near
Baton Rouge, Louisiana. LIGO
uses two detectors far apart
because its detectors are so
sensitive that they can 'feel' the
tiniest vibrations on Earth, from
sources nearby to sources
hundreds or thousands of
kilometers away, e.g., earthquakes,
acoustic noise (trucks driving on
nearby roads, farmers plowing
fields, things that people can hear
and feel), and even internal laser
fluctuations can cause
disturbances that can mask a
LIGO is a sensitive ruler.
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A binary system ripples space-time
sending out a stream of
gravitational radiation.
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Gravitational Waves
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× polarization
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+ polarization
The gravitational wave alternately stretches
and contracts each arm, leading to periodic
constructive and destructive interference
patterns.
The aLIGO design sensitivity
level is nearly at the quantum
limit
aLIGO DISCOVERY STRAINS
GW 150914
The measured strains
were on the order of
10-21, a signal-tonoise level of 24! For
aLIGO, despite the
highly significant
result, the measured
changes in the
lengths of the arms
were smaller than 1
% the diameter of a
nucleus!
Within months of the
discovery of gravitational
wave radiation, a second
merging massive black hole
source was discovered, GW
151226! This discovery was
important because it was
strong support that aLIGO
was operating as
advertised, and that the first
result was not a fluke.
aLIGO is ready to explore
the Universe.
Also, even though we don’t
understand how such
massive black holes form in
binary systems, the second
discovery shows that nature
knows how to do so. It is
now incumbent upon
astrophysicists to be as
Type II Supernovae: SN
1987A
Core Collapse of a
massive nonrotating
star
Fizzlers: Rapidly Rotating Core Collapse
Core Collapse in rapidly rotating massive stars may not
lead to Type II Supernovas. As core collapses, Ω
increases to conserve J. If initial J large enough,
centrifugal force halts collapse before ρnuc, nuclear
density is reached aborting the supernova. Core
radiates νs (deleptonizes) and loses pressure support.
Core contracts on deleptonization timescale. As core
contracts, Ω again rises and core becomes unstable to a
barlike deformation leading to a strong pulse of
gravitational radiation. The results shown are for 1.4
solar mass cores, one with large J and one with smaller J.
At distances of Virgo, 15 Mpc, the strain would be ~ 2x1023 for the high J case and <10-25 for the low J case
(more bizarre) Implications
Can show how an object
moves in space-time with a
worldline
Can curve space-time: wrap
time around on itself
Can curve space-time:
wrap space around to
meet itself
Exotic Space-Times
Gödel Solution
closed timelike curves
Wormhole, Einstein-Rosen
Bridge
Morris-Thorne traversable wormholes
Future Directions
Source Localization and Sensitivity
Advanced LIGO Worldwide Network
From 2007 to 2011, Virgo, LIGO and GEO600 have formed the first worldwide network of interferometers in history and have observed
the sky for gravitational waves. This collaboration will continue in the era of the Advanced Virgo and Advanced LIGO, which will
continue to share the data that will be collected in the coming years.
In the near future, the network will grow further, with the construction of two new antennas. The Kamioka Gravitational Wave Detector
(KAGRA), under construction in the Kamioka mine in Japan, which plans to begin operations in 2018. IndIGO will be a third twin of the
LIGO interferometers and will be built in India and start operation in 2019. This extended network, with more sensitive detectors will
improve our view of the gravitational wave Universe.
eLISA: Space-based
Gravitational Wave Observatory
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EPTA: European Pulsar Timing Array
Rough properties of PSR 1913+16
Accumulated change in orbital
period of PSR 1913+16