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Abstract:
Recent "planet-scale" very long baseline interferometry (VLBI) efforts
at millimetre wavelengths have resulted in the first detailed images
near the event horizon of the supermassive black hole (SMBH) at the
centre of M87 by the Event Horizon Telescope (EHT)
collaboration. Calibration of the radio signals received by such
widely separated VLBI stations is one of the key challenges in the
accurate reconstruction of images. Closure phases and amplitudes in
co-polar interferometry, have long provided calibration-independent
observables immune to multiplicative, station-dependent
corruptions. Very recently, "closure traces" for full polarimetric
interferometry have been introduced and used in the recent study of
the magnetic field structures around the M87 central black hole. So
far, a systematic method for explicitly exhibiting a full set of
invariants has still remained unclear. Using the mathematical
framework of the gauge theories of particle physics and Lorentz
transformations, I will describe a general formalism, applicable to
interferometer arrays of arbitrary size, that uses only triangular
combinations of correlations as basic building blocks to precisely
isolate a complete and independent set of invariants, and unifies the
treatment for all closure invariants, from which the closure phases
and closure amplitudes familiar in co-polar interferometry naturally
emerge. These results can find significant applications in ongoing and
future (including space-based) observations of SMBHs using the current
and the next-generation EHT (ngEHT), and more generally, polarimetric
radio interferometry.
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