Introduction to Numerical Relativity

Abstract

Numerical Relativity is a multidisciplinary field including relativity, magneto-hydrodynamics, astrophysics and computational methods, among others, with the aim of solving numerically highly-dynamical, strong-gravity scenarios where no other approximations are available. Here we describe some of the foundations of the field, starting from the covariant Einstein equations and how to write them as a well-posed system of evolution equations, discussing the different formalisms, coordinate conditions and numerical methods commonly employed nowadays for the modeling of gravitational wave sources.

Accepted by Frontiers Astronomy and Space Sciences, invited review for the Research Topic "Gravitational Waves: A New Window to the Universe"

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• Turbulent magnetic field amplification in binary neutron star mergers
• Review on stochastic approach to inflation
• Applications of machine learning in gravitational wave research with current interferometric detectors
• Search for lensing signatures in the gravitational-wave observations from the first half of LIGO-Virgo's third observing run
• Gravitational Radiation from Eccentric Binary Black Hole System in Dynamical Chern-Simons Gravity
• Waveform systematics in identifying strongly gravitationally lensed gravitational waves: Posterior overlap method
• On constraint preservation and strong hyperbolicity
• Populating the landscape in an inhomogeneous universe
• 3+1 formalism of the minimally extended varying speed of light model
• Black hole spectroscopy of collapsing and merging neutron stars
• Impact of magnetic field gradients on the development of the MRI: Applications to binary neutron star mergers and proto-planetary disks