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Gravitational Wave Astronomy

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ayanna-wilson
13 diapositives · 307 Views · Nov 15, 2014

This work by Dr. Giles Hammond from the Institute for Gravitational Research at the University of Glasgow explores essential concepts in gravitational wave astronomy. It delves into geodesic deviation and how the separation between freely falling particles changes over time. The presentation includes calculations related to the Riemann tensor components and discusses different radiation types, including monopole, dipole, and quadrupole radiation. Emphasizing the local measurement of curvature and strain amplitude, this study sheds light on fundamental mechanisms behind gravitational wave generation.

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Gravitational Wave Astronomy
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  1. Gravitational Wave Astronomy Dr. Giles Hammond Institute for Gravitational Research SUPA, University of Glasgow Universität Jena, August 2010

  2. Gravitational Waves From our matrix all 3 terms are zero => A particle initially at rest will remain at rest. In the TT gauge we have a coordinate system which remains attached to individual particles Now consider two particles, one at (0,0,0) and the other at (,0,0) Proper distance between them is and this DOES change with time

  3. Geodesic Deviation The geodesic deviation between two freely falling objects separated by a vector a is given by (not proved here) A fundamental result which states that curvature can be measured locally by watching the proper distance between particles If particles are at rest and separated by  along the x-axis then

  4. Geodesic Deviation The components of the Riemann tensor can be calculated as So two particles separated by  along the x-axis will have a separation vector defined by

  5. Example of Rxoxo Term

  6. Geodesic Deviation The components of the Riemann tensor can be calculated as If the particles are separated by  along the y-axis it can be shown in a similar way that Previous result for x-axis

  7. Geodesic Deviation For the hxx component The metric has sinusoidal solutions And this gives sinusoidal solutions for the particle separation from earlier slide

  8. Geodesic Deviation Extending to a ring of test particles gives where there are 2 polarisations:

  9. Leading Order Radiation Consider analogy with Electromagnetic radiation Waves are formed by the time-change in the position and distribution of the “charges” in the system (q or m) Monopole Radiation =>Time variation of total charge (zeroth moment) in the system Charge/Energy conservation rules this out for EW’s and GW’s

  10. Leading Order Radiation Dipole Radiation => Time variation of the charge distribution (1st moment) Efficient production mechanism for EW’s Momentum conservation rules this out for GW’s (both linear + angular)

  11. Leading Order Radiation Quadrupole Radiation => Time variation of the charge distribution (2nd moment) No conservation rules left => leading order radiation term for GW’s 2nd moment depends on the moment of inertia tensor (Lij)

  12. Estimate of Strain Amplitude Consider two stars, mass M, radial separation r The quadrupole moment is R R

  13. Estimate of Strain Amplitude The magnitude of the metric stretch in the xx direction is or, using Kepler’s 3rd law, which gives modulated at 2