**Gravitational Waves: Theory and Observation**

Theory

**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

Motivation

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

LIGO

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

LIGO

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

2. LISA

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

LISA

References

LIGO: Setup

Effects of Gravitational Wave on Interferometer

**Robert Brzozowski**

Bardia Nadim

Bardia Nadim

**Physics 435**

12/06/13

12/06/13

How sensitive do detectors need to be?

Data

Total 10 M-bytes per second per interferometer

Dedicated gravitational wave channel 64 k-byte

Analyzed by a dedicated computer cluster

Mission Start 2015

Questions?

Currently shut down, undergoing upgrades

Gravitational Radiators

Three types of radiation

bursts

well defined - infalling neutron stars

poorly known - supernovae

periodic

pulsing and rotating stars

stochastic

CMB and other early universe processes

Superposition of distant sources

Resonant Detectors

Physical arms, measured change in thermal motion

Interferometers

More precise than resonant detectors

Can introduce additional mirror between laser a splitter to increase effective power

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[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.

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[5] NASA/JPL-Caltech/STScI/CXC/SAO

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[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

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[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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