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Abstract Cauchy-characteristic evolution (CCE) is a powerful method for accurately extracting gravitational waves at future null infinity. In this work, we extend the previously implemented CCE system within the numerical relativity code SpECTRE by incorporating a scalar field. This allows the system to capture features of beyond-general-relativity theories. We derive scalar contributions to the equations of motion, Weyl scalar computations, Bianchi identities, and balance laws at future null infinity. Our algorithm, tested across various scenarios, accurately reveals memory effects induced by both scalar and tensor fields and captures Price’s power-law tail ( $u^{-l-2}$) in scalar fields at future null infinity, in contrast to the $t^{-2l-3}$tail at future timelike infinity. 

Abstract Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our Universe. 

We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is achieved by monitoring the relative power in the highest mode of the reconstructed polynomial and reducing the order when the polynomial series no longer converges. Our approach is similar to the multidimensional optimal order detection strategy, but differs in several ways. The approach isa prioriand so does not require retaking a time step. It can also readily be combined with positivity-preserving flux limiters that have gained significant traction in computational astrophysics and numerical relativity. This combination ultimately guarantees a physical solution both during reconstruction and time stepping. We demonstrate the capabilities of the method using a standard suite of very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamics test problems. 

Abstract The recent detections of the ∼10 s longγ-ray bursts (GRBs) 211211A and 230307A followed by softer temporally extended emission (EE) and kilonovae point to a new GRB class. Using state-of-the-art first-principles simulations, we introduce a unifying theoretical framework that connects binary neutron star (BNS) and black hole–NS (BH–NS) merger populations with the fundamental physics governing compact binary GRBs (cbGRBs). For binaries with large total masses,M_tot≳ 2.8M_⊙, the compact remnant created by the merger promptly collapses into a BH surrounded by an accretion disk. The duration of the pre-magnetically arrested disk (MAD) phase sets the duration of the roughly constant power cbGRB and could be influenced by the disk mass,M_d. We show that massive disks (M_d≳ 0.1M_⊙), which form for large binary mass ratiosq≳ 1.2 in BNS orq≲ 3 in BH–NS mergers, inevitably produce 211211A-like long cbGRBs. Once the disk becomes MAD, the jet power drops with the mass accretion rate as $\dot{M}\sim t^{-2}$, establishing the EE decay. Two scenarios are plausible for short cbGRBs. They can be powered by BHs with less massive disks, which form for otherqvalues. Alternatively, for binaries withM_tot≲ 2.8M_⊙, mergers should go through a hypermassive NS (HMNS) phase, as inferred for GW170817. Magnetized outflows from such HMNSs, which typically live for ≲1 s, offer an alternative progenitor for short cbGRBs. The first scenario is challenged by the bimodal GRB duration distribution and the fact that the Galactic BNS population peaks at sufficiently low masses that most mergers should go through an HMNS phase.