We present a new formulation of the Einstein equations based on a conformal and traceless decomposition of the covariant form of the Z4 system. This formulation combines the advantages of a conformal decomposition, such as the one used in the BSSNOK formulation (i.e. well-tested hyperbolic gauges, no need for excision, robustness to imperfect boundary conditions) with the advantages of a constraint-damped formulation, such as the generalized harmonic one (i.e. exponential decay of constraint violations when these are produced). We validate the new set of equations through standard tests and by evolving binary black hole systems. Overall, the new conformal formulation leads to a better behavior of the constraint equations and a rapid suppression of the violations when they occur. The changes necessary to implement the new conformal formulation in standard BSSNOK codes are very small as are the additional computational costs.

The Numerical–Relativity–Analytical–Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ∼100–200M⊙, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios ⩽4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe tested for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the $$\ell${}=1$ mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.

The merger of two neutron stars will in general lead to the formation of a torus surrounding a black hole whose rotational energy can be tapped to potentially power a short gamma-ray burst. We have studied the merger of equal-mass binaries with spins aligned with the orbital angular momentum to determine the maximum spin the black hole can reach. Our initial data consists of irrotational binaries to which we add various amounts of rotation to increase the total angular momentum. Although the initial data violates the constraint equations, the use of the constraint-damping conformal and covariant Z4 formulation yields evolutions with violations smaller than those with irrotational initial data and standard formulations. Interestingly, we find that a limit of $J/{M}^{2}$\simeq${}0.89$ exists for the dimensionless spin and that any additional angular momentum given to the binary ends up in the torus rather than in the black hole, thus providing another nontrivial example supporting the cosmic censorship hypothesis.

Motivated by the increasing interest in models which consider scalar fields as viable dark matter candidates, we have constructed a generalization of relativistic boson btars (BS) composed of two coexisting states of the scalar field, the ground state and the first excited state. We have studied the dynamical evolution of these multistate boson stars (MSBS) under radial perturbations, using numerical techniques. We show that stable MSBS can be constructed, when the number of particles in the first excited state, N(2), is smaller than the number of particles in the ground state, N(1). On the other hand, when N(2)>N(1), the configurations are initially unstable. However, they evolve and settle down into stable configurations. In the stabilization process, the initially ground state is excited and ends in a first excited state, whereas the initially first excited state ends in a ground state. During this process, both states emit scalar field radiation, decreasing their number of particles. This behavior shows that even though BS in the first excited state are intrinsically unstable under finite perturbations, the configuration resulting from the combination of this state with the ground state produces stable objects. Finally we show in a qualitative way, that stable MSBS could be realistic models of dark matter galactic halos, as they produce rotation curves that are flatter at large radii than the rotation curves produced by BS with only one state.

Following previous work in vacuum spacetimes, we investigate the constraint-damping properties in the presence of matter of the recently developed traceless, conformal and covariant Z4 (CCZ4) formulation of the Einstein equations. First, we evolve an isolated neutron star with an ideal gas equation of state and subject to a constraint-violating perturbation. We compare the evolution of the constraints using the CCZ4 and Baumgarte-Shibata-Shapiro-Nakamura-Oohara-Kojima (BSSNOK) systems. Second, we study the collapse of an unstable spherical star to a black hole. Finally, we evolve binary neutron star systems over several orbits until the merger, the formation of a black hole, and up to the ringdown. We show that the CCZ4 formulation is stable in the presence of matter and that the constraint violations are 1 or more orders of magnitude smaller than for the BSSNOK formulation. Furthermore, by comparing the CCZ4 and the BSSNOK formulations also for neutron star binaries with large initial constraint violations, we investigate their influence on the errors on physical quantities. We also give a new, simple and robust prescription for the damping parameter that removes the instabilities found when using the fully covariant version of CCZ4 in the evolution of black holes. Overall, we find that at essentially the same computational costs, the CCZ4 formulation provides solutions that are stable and with a considerably smaller violation of the Hamiltonian constraint than the BSSNOK formulation. We also find that the performance of the CCZ4 formulation is very similar to another conformal and traceless, but noncovariant formulation of the Z4 system, i.e., the Z4c formulation.