Periodic Reporting for period 2 - ACFD (Acoustical and Canonical Fluid Dynamics in numerical general relativity)
Reporting period: 2018-12-15 to 2019-12-14
Binary neutron stars are astrophysical scale particle colliders, where all four fundamental forces come into play. Gravitational and electromagnetic waves, emitted during their inspiral and merger, carry valuable information about weak and strong nuclear interactions in their interior, where matter reaches the most extreme densities known in nature. Detection and parameter estimation of gravitational wave signals requires precise modelling of their sources. Numerical relativity and computational fluid dynamics are vital for simulating the inspiral of these systems and computing their gravitational waves.
Why is it important for society?
The first observed event, GW170817, had striking implications. It resolved the 50-year mystery of the origin of short gamma-ray bursts; it provided strong evidence for mergers as the main source of half the heaviest elements (the r-process elements); and gave an independent measurement of the Hubble constant. Future events, from galaxies not too far away, can also address a major goal of multimessenger astrophysics: From the imprint of tides on inspiral waveforms, we can measure the radius and tidal deformation of the inspiraling stars and infer the behavior of cold matter above nuclear density.
What are the overall objectives?
We develop a new, well-posed formulation of relativistic fluid dynamics, based on Hamilton's principle. We utilize this canonical formulation of the Euler-Einstein system in order to perform high-precision computational fluid dynamic simulations in numerical general relativity. The programme contributes towards a deeper understanding of fluid dynamics in curved spacetime, and how Kelvin's circulation theorem, Helmholtz's third theorem, and other the relevant features imprint themselves in gravitational waveforms. It explores the utility of such waveforms as probes of dense matter physics.
The relativistic Euler equation has been replaced by a simpler, Hamilton-Jacobi equation for the velocity potential, or its gradient, a covariant flux-conservative form of Hamilton’s equation.
We have performed a hyperbolicity analysis which proves that the formulation is well-posed for positive sound speed.
We have demonstrated that Kelvin's circulation theorem and its corollary, Helmholtz's third theorem, hold exactly during binary neutron star inspiral.
We developed a constraint-damping scheme that preserves these theorems during simulations in numerical general relativity.
We have performed a variety of numerical tests, including Bondi accretion, propagation of smooth or discontinuous perturbations, and neutron star oscillations.