CTTK: A new method to solve the initial data constraints in numerical relativity

Abstract

In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the standard Conformal Transverse-Traceless (CTT) decomposition, in which instead of solving the Hamiltonian constraint as a 2nd order elliptic equation for a choice of mean curvature $K$, we solve an algebraic equation for $K$ for a choice of conformal factor. By doing so, we evade the existence and uniqueness problem of solutions of the Hamiltonian constraint without using the usual conformal rescaling of the source terms. This is particularly important when the sources are fundamental fields, as reconstructing the fields' configurations from the rescaled quantities is potentially problematic. Using an iterative multigrid solver, we show that this method provides rapid convergent solutions for several initial conditions that have not yet been studied in numerical relativity; namely (i) periodic inhomogeneous spacetimes with large random Gaussian scalar field perturbations and (ii) asymptotically flat black hole spacetimes with rotating scalar clouds.

14 pages, 4 figures, 1 appendix. Matches version published in CQG

References in corpus (18)

• Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
• GRChombo: An adaptable numerical relativity code for fundamental physics
• Evolution to a smooth universe in an ekpyrotic contracting phase with w > 1
• Supersmoothing through Slow Contraction
• Conformal Thin-Sandwich Solver for Generic Initial Data
• Black Hole Universe with $\Lambda$
• Primordial black hole formation with full numerical relativity
• Malaise and remedy of binary boson-star initial data
• The initial value problem as it relates to numerical relativity
• Non-uniqueness in conformal formulations of the Einstein constraints
• Robustness of slow contraction to cosmic initial conditions
• Inhomogeneous initial conditions for inflation: A wibbly-wobbly timey-wimey path to salvation
• Gravitational Waves from Fully General Relativistic Oscillon Preheating
• Gravitational dynamics in Higgs inflation: Preinflation and preheating with an auxiliary field
• The Effects of Multiple Modes and Reduced Symmetry on the Rapidity and Robustness of Slow Contraction
• NRPyElliptic: A Fast Hyperbolic Relaxation Elliptic Solver for Numerical Relativity, I: Conformally Flat, Binary Puncture Initial Data
• Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields
• Cosmological initial data for numerical relativity

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