1. 30 th January 200925 th IAGRG meeting Kolkata S. V. DHURANDHAR IUCAA PUNE

2. 30 th January 200925 th IAGRG meeting Kolkata General Relativity and other disciplines GR finds its home in astronomy & astrophysics - The binary blackhole problem - No exact two body solution: PN + Numerical Relativity - Cosmology: observational data, COBE, WMAP, PLANCK Mathematics: Commutative algebra, differential geometry in statistics Statistics: Hypothesis testing, statistical tests, maximum likelihood, etc. - Signal processing Gravitation has gone experimental: Gravitational waves

3. 30 th January 200925 th IAGRG meeting Kolkata Effect on a ring of test particles Metric: General Wave:

4. 30 th January 200925 th IAGRG meeting Kolkata But h is awfully small !  L ~ h L Quadrupole formula : Change in arm-length:

5. 30 th January 200925 th IAGRG meeting Kolkata LIGO Louisiana 4 km armlength (US)

6. 30 th January 200925 th IAGRG meeting Kolkata We did it ! *http://www.ligocaltech.edu/~lazz/distribution/LSC_Data

7. 30 th January 200925 th IAGRG meeting Kolkata LISA: Space based detector for detecting low frequency GW

8. 30 th January 200925 th IAGRG meeting Kolkata Laser frequency noise

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10. 30 th January 200925 th IAGRG meeting Kolkata

11. 30 th January 200925 th IAGRG meeting Kolkata  into, Eastabrook, Armstrong; SVD, Nayak, Vinet, Pai

12. 30 th January 200925 th IAGRG meeting Kolkata

13. 30 th January 200925 th IAGRG meeting Kolkata

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16. 30 th January 200925 th IAGRG meeting Kolkata Open Problems

17. 30 th January 200925 th IAGRG meeting Kolkata Inspiraling compact binaries GW Broadband source best for interferometric detectors Waveform is well modeled by PN approximations – waveform obtained to 3.5 PN Numerical Relativity: great advances – merger Signal is way below the noise – data analysis: filtering

18. 30 th January 200925 th IAGRG meeting Kolkata Breakthrough in Numerical Relativity Numerical Relativity solves merger waveform 3.5% of total restmass energy as compared to 1.5 % in inspiral waveform! Work in progress on stitching together waveforms India has the right talent/aptitude for NR

19. 30 th January 200925 th IAGRG meeting Kolkata Example of a filter A sinusoidal signal is embedded in noise Data: Signal:

20. 30 th January 200925 th IAGRG meeting Kolkata Filtering the data Best filter is the Fourier Transform: Statistic: Generalisation: Matched Filter Provides parameters of the signal: eg. frequency

21. 30 th January 200925 th IAGRG meeting Kolkata Matched filtering the inspiraling binary signal

22. 30 th January 200925 th IAGRG meeting Kolkata Statistics and geometry Statistic: c(  ) Where does one set the threshold? – False alarm probability – choose threshold such that this is small Detection probability: choose this high Signal depends on many parameters: masses, kinematical parameters: initial phase, time of arrival … Parameter space Parameter space can be viewed as a manifold with the parameters as coordinates Metric: mismatch between signal and template

23. 30 th January 200925 th IAGRG meeting Kolkata Parameter space metric Coordinates: i g ik  i  k  Choose coordinates so that metric is simplest: Cartesian coordinates For inspiral choose chirp times instead of masses:  0  3 Metric const: Uniform placement of templates Number of templates = volume of parameter space / template size

24. 30 th January 200925 th IAGRG meeting Kolkata International Network of GW Interferometers International Network of GW Interferometers LIGO-LLO: 4km LIGO-LHO: 2km, 4km GEO: 0.6km VIRGO: 3km TAMA: 0.3km AIGO: (?)km 1. Detection confidence 2. Source direction 3. Polarisation info

25. 30 th January 200925 th IAGRG meeting Kolkata  eed for a (or two) detector(s) in Asia/Australia AIGO: Australian project INDIGO: Indian detector? Advantages: sky coverage, resolution of sources

26. 30 th January 200925 th IAGRG meeting Kolkata Optimum location of a detector Courtesy A. Sengupta & S. Mitra

27. 30 th January 200925 th IAGRG meeting Kolkata  ptimum location

28. 30 th January 200925 th IAGRG meeting Kolkata Network Sensitivity  IGO/INDIGO network doubles sensitivity

29. 30 th January 200925 th IAGRG meeting Kolkata Angular Resolution An order of magnitude improvement

30. 30 th January 200925 th IAGRG meeting Kolkata Summary  Connection of GR to several fields:  Astrophysics, Mathematics, Statistics, Engineering …  Numerical Relativity  Gravitation going experimental