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S. V. DHURANDHAR

THE CHANGING FACE OF GENERAL RELATIVITY. S. V. DHURANDHAR. IUCAA PUNE. General Relativity and other disciplines. GR finds its home in astronomy & astrophysics The binary blackhole problem No exact two body solution : PN + Numerical Relativity

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S. V. DHURANDHAR

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  1. THE CHANGING FACE OF GENERAL RELATIVITY S. V. DHURANDHAR IUCAA PUNE 25th IAGRG meeting Kolkata

  2. 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 25th IAGRG meeting Kolkata

  3. Effect on a ring of test particles Metric: General Wave: 25th IAGRG meeting Kolkata

  4. But h is awfully small ! Quadrupole formula : Change in arm-length: d L ~ h L 25th IAGRG meeting Kolkata

  5. LIGO Louisiana 4 km armlength (US) 25th IAGRG meeting Kolkata

  6. We did it ! *http://www.ligocaltech.edu/~lazz/distribution/LSC_Data 25th IAGRG meeting Kolkata

  7. LISA: Space based detector for detecting low frequency GW 25th IAGRG meeting Kolkata

  8. Laser frequency noise 25th IAGRG meeting Kolkata

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  11. Tinto, Eastabrook, Armstrong; SVD, Nayak, Vinet, Pai 25th IAGRG meeting Kolkata

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  16. Open Problems 25th IAGRG meeting Kolkata

  17. 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 25th IAGRG meeting Kolkata

  18. 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 25th IAGRG meeting Kolkata

  19. Example of a filter A sinusoidal signal is embedded in noise Data: Signal: 25th IAGRG meeting Kolkata

  20. Filtering the data Best filter is the Fourier Transform: Statistic: Provides parameters of the signal: eg. frequency Generalisation: Matched Filter 25th IAGRG meeting Kolkata

  21. Matched filtering the inspiraling binary signal 25th IAGRG meeting Kolkata

  22. Statistics and geometry • Statistic: c(t) • 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 25th IAGRG meeting Kolkata

  23. Parameter space metric Coordinates: li gik Dli Dlk = e Choosecoordinates so that metric is simplest: Cartesian coordinates For inspiral choose chirp times instead of masses: t0 , t3 Metric const: Uniform placement of templates Number of templates = volume of parameter space / template size 25th IAGRG meeting Kolkata

  24. GEO: 0.6km VIRGO: 3km LIGO-LHO: 2km, 4km TAMA: 0.3km LIGO-LLO: 4km AIGO: (?)km International Network of GW Interferometers 1. Detection confidence 2. Source direction 3. Polarisation info 25th IAGRG meeting Kolkata

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

  26. Optimum location of a detector Courtesy A. Sengupta & S. Mitra 25th IAGRG meeting Kolkata

  27. Optimum location 25th IAGRG meeting Kolkata

  28. Network Sensitivity AIGO/INDIGO network doubles sensitivity 25th IAGRG meeting Kolkata

  29. Angular Resolution An order of magnitude improvement 25th IAGRG meeting Kolkata

  30. Summary • Connection of GR to several fields: • Astrophysics, Mathematics, Statistics, Engineering … • Numerical Relativity • Gravitation going experimental 25th IAGRG meeting Kolkata

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