Physics 616

  • Prof. Andrew W. Steiner
    (or Andrew or "Dr. Steiner")
  • Office hour: 103 South College, Thursday 11am
  • Email: awsteiner@utk.edu
  • Homework: Electronically as .pdf
  • You may work with each other on the homework, but you must write the solution in your own words
 
 
 
Use down and up arrows to proceed to the next or previous slide.

Outline

Gravitational Waves I

Gravitational Waves II

Transverse-traceless Gauge

Choose a coordinate system

Analogy with QED

From "An Introduction to QFT" by Sterman

Analogy with QED II

Gravitational Wave Polarizations

Using Light as a Probe of GWs

  • Wave traveling in z direction with "+" polarization $$ ds^2 = -dt^2 + \left[ 1+h_+ \left(z-t\right)\right] dx^2 + \left[ 1-h_+ \left(t-z\right)\right] dy^2 + dz^2 $$ and presume two objects, one at $x=0$ and the other at $x=L$.
  • A photon moving between the two objects has an effective coordinate speed $$ \left(\frac{dx}{dt}\right)^2 = \frac{1}{1+h_+} $$ so that the time taken to go to $x=L$ is $$ t_{\mathrm{far}} = t_{\mathrm{start}}+\int_0^{L} \left\{1+h_+[t(x)]\right\}^{1/2}~dx \approx t_{\mathrm{start}}+L+\frac{1}{2} \int_0^{L} h_+(x+t_{\mathrm{start}}) dx $$ and the total time is $$ t_{\mathrm{return}} \approx t_{\mathrm{start}}+ 2L+\frac{1}{2} \int_0^{L} h_+(t_{\mathrm{start}}+ x) dx +\frac{1}{2} \int_0^{L} h_+(t_{\mathrm{start}}+x+L) dx $$

Using Light as a Probe of GWs II

Generation by a Slowly Moving Source

Generation by a Slowly Moving Source II

Generation by a Slowly Moving Source III

Generation by a Slowly Moving Source IV

Choosing Coordinates