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This work focuses on a fundamental problem in modern numerical rela- tivity: Extracting gravitational waves in a coordinate and gauge independent way to nourish a unique and physically meaningful expression. We adopt a new procedure to extract the physically relevant quantities from the numerically evolved space-time. We introduce a general canonical form for the Weyl scalars in terms of fundamental space-time invariants, and demonstrate how this ap- proach supersedes the explicit definition of a particular null tetrad. As a second objective, we further characterize a particular sub-class of tetrads in the Newman-Penrose formalism: the transverse frames. We establish a new connection between the two major frames for wave extraction: namely the Gram-Schmidt frame, and the quasi-Kinnersley frame. Finally, we study how the expressions for the Weyl scalars depend on the tetrad we choose, in a space-time containing distorted black holes. We apply our newly developed method and demonstrate the advantage of our approach, compared with methods commonly used in numerical relativity.
Astrophysical sources of gravitational waves, such as binary neutron star and black hole mergers or core-collapse supernovae, can drive relativistic outflows, giving rise to non-thermal high-energy emission. High-energy neutrinos are signatures of such outflows. The detection of gravitational waves and high-energy neutrinos from common sources could help establish the connection between the dynamics of the progenitor and the properties of the outflow. We searched for associated emission of gravitational waves and high-energy neutrinos from astrophysical transients with minimal assumptions using data from Advanced LIGO from its first observing run O1, and data from the Antares and IceCube neutrino observatories from the same time period. We focused on candidate events whose astrophysical origins could not be determined from a single messenger. We found no significant coincident candidate, which we used to constrain the rate density of astrophysical sources dependent on their gravitational-wave and neutrino emission processes.