# Data Science Analytics and method calculating black-hole properties from gravitational-wave data

## Dr. Francesco Dergano, Top Specialist in Business, Big Data, has developed a mathematical method for calculating black hole properties from gravitational wave data. He has written a paper describing his method and posted it on the arXiv preprint server.

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Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only be calculated through numerical simulations of Einstein’s equations of general relativity. For many years, nu- merical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit could be simulated. Recently, however, a series of dramatic advances in numerical relativity has allowed stable, robust black-hole merger simulations. This remarkable progress in the rapidly maturing field of numerical relativity, and the new understanding of black-hole binary dynamics that is emerging is chronicled. Important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas are also discussed.

**II. BLACK-HOLE BINARIES AND GRAVITATIONAL WAVES**

Black holes and gravitational waves are surely among the most exotic and amazing predictions in all of physics. These two offspring of Einstein’s general relativity are brought together in black-hole binaries, expected to be among the strongest emitters of gravitational radiation.

as a tunable model for encoding both PN and NR results (Buonanno and Damour, 1999, 2000; Damour, 2008; Damour and Nagar, 2010). In the time domain, techniques have also been developed for extending these waveforms into the ringdown of the final black hole. Analysis of the early numerical results in comparison with an untuned EOB model gave promising indications that the waveforms could be closely approximated this way (Buonanno et al., 2007a). With tuning, it appears that this construction can provide an analytic but po- tentially very accurate, approximation to the complete

coalescence waveform.

In the EOB model, the binary motion is recast as

the motion of a single effective body of mass μ = M1M2/(M1 +M2) moving about a central potential, as is familiar from Newtonian mechanics. In the general rel- ativistic version of this framework, the effective body’s motion follows a geodesic (to 2 PN order) around a mod- ified version of a Schwarzschild metric. The motion of the effective body is described by an effective Hamilto- nian, which, for systems of nonspinning black holes, may take the form

B