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Gravitational Waves and LIGO

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Bardia Nadim

on 6 December 2013

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Transcript of Gravitational Waves and LIGO

Gravitational Waves: Theory and Observation
Vacuum Solution
Interactions with Matter
Einstein's Field Equations
Linearized Field Equations
Einstein's field equations are nonlinear and difficult...so consider weak gravitational fields!
Polarization States
General gauge transformation:
Let's perform a specific gauge transformation:
Einstein's field equations reduce to the wave equation if we impose the condition that:
Applying this, Einstein's full field equations reduce to:
The Einstein Tensor now takes the form:
The vacuum condition leads to the wave equation!
We consider a wave propagating at the speed of light in the x-direction with the form:
We can then separate the weak-field metric deviation into two parts:
The Einstein gauge conditions and symmetry simplify the results:
H-22 (Plus) Polarization
H-23 (Cross) Polarization

General relativity predicts the existence of gravitational radiation
Therefore detection of gravitational radiation would be strong evidence for supporting the theory of relativity
Supports potential connection to quantum physics
Direct Detection
Measure the interactions between free or bound particles
Laser Interferometer Gravitational Wave Observatory
Experimental efforts being made at LIGO (US), VIRGO (Italy), GEO (Germany), and TAMA (Japan)
Binary Pulsar PSR B1913 + 16
Built in 1999 with first observational experiments run in 2002
Two observatories: Hanford, WA and Livingston, LA
LIGO: Setup
Suspended laser interferometer
4 km arm lengths
High power infrared 1064 nm, 10 W Nd-YAG laser
Goal is to measure the change in the path length of light when a gravitational wave arrives
Quadrupole approximation gives us an order of magnitude for the relative path length perturbation
Therefore large arm lengths and mirrors in the paths increase the effective path length and help obtain higher precision in detection
In 1974, Russell Hurse and Joseph Taylor measured the orbit decay and period decrease of PSR B1913 + 16
Near perfect match with GR prediction!
Results & Future Outlook
No direct evidence of GW observed yet
But hope remains!
1. Advanced LIGO
180 W Laser
Increased test mass (40 kg)
Quadruple suspension pendulums
Laser Interferometer Space Antenna
Large scale interferometer with millions of km distance between free satellites!
Indirect Detection of Gravitational Waves
Radiative Energy Losses
Spin-up of Binary Systems
Quantum Limit
Current Limit
Practical Limit
LIGO: Setup
Effects of Gravitational Wave on Interferometer
Robert Brzozowski
Bardia Nadim

Physics 435

How sensitive do detectors need to be?
Total 10 M-bytes per second per interferometer
Dedicated gravitational wave channel 64 k-byte
Analyzed by a dedicated computer cluster
Mission Start 2015
Currently shut down, undergoing upgrades
Gravitational Radiators
Three types of radiation
well defined - infalling neutron stars
poorly known - supernovae
pulsing and rotating stars
CMB and other early universe processes
Superposition of distant sources
Resonant Detectors
Physical arms, measured change in thermal motion
More precise than resonant detectors
Can introduce additional mirror between laser a splitter to increase effective power
[10] Sturic, C. (2010). Gravitational waves plus polarization [Web]. Retrieved from http://www.you_tube.com/watch?v=U_hLM1WPDqM
[9] Sturic, C. (2010). Gravitational waves cross polarization [Web]. Retrieved from http://www.you_tube.com/watch?v=EtL9UyRx_Us
[4] Keesey, L. (n.d.). Nasa pursues atom optics to detect the imperceptible. Retrieved from http://www.nasa.gov/topics/technology/features/atom-optics.html
[11] Sturic, C. (2010). Gravitational waves with two polarizations [Web]. Retrieved from http://www.you_tube.com/watch?v=7VhXrDmC0OQ
[12] Weisberg, J. M., & Taylor, J. H. (2004). Relativistic binary pulsar B1913+ 16: thirty years of observations and analysis. arXiv preprint astro-ph/0407149.
[3] Hobson, M. P., Efstathiou, G., & Lasenby, A. N. (2006). General relativity: An introduction for physicists. (5th ed.). Cambridge: University Press
[2] D'Inverno, R. (1992). Introducing einstein's relativity. Oxford: Oxford University Press.
[6] Riles, K. (2012). Gravitational waves: Sources, detectors and searches. Progress in Particle and Nuclear Physics.
[8] Riles, K. (2013, June). To catch a wave - direct searches for gravitational radiation . Shanghai particle physics and cosmology symposium, Shanghai. Retrieved from http://gallatin.physics.lsa.umich.edu/~keithr/talks/SPPC2013_indico.pdf
[1] Coyne D 1996 IEEE Aerospace Applications Conf. Proc. vol 4 pp 31–61
[7] Riles, K. (2009, July). The present gravitational wave detection effort. Presentation at international conference on topics in astroparticle and underground physics. Retrieved from http://gallatin.physics.lsa.umich.edu/~keithr/talks/TAUP2009.pdf
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