GRTeclyn: AMReX-Enhanced Numerical Relativity

• GRTeclyn is a numerical-relativity codebase that leverages adaptive mesh refinement and GPU acceleration to perform fully relativistic 3D simulations of dynamical spacetimes.
• It employs advanced evolution frameworks like CCZ4 with matter and BSSN, integrating precise initial data setups, wave extraction techniques, and diagnostic tools.
• Applications include simulations of wormhole dynamics and early-universe tensor perturbations, demonstrating its utility in strong-field and cosmological research.

GRTeclyn is a numerical-relativity codebase for fully relativistic simulations of dynamical spacetimes. The published literature presents it most concretely as a “Port of GRChombo to AMReX” under active development, and uses it for three-dimensional evolutions of the unstable Ellis–Bronnikov wormhole with gravitational-wave extraction (Shirokov, 31 Mar 2026). A closely related cosmology study describes a tensor-perturbation pipeline implemented in GRChombo and states that the implementation is being actively ported to GRTeclyn, with the expectation that the GRTeclyn version will follow the GRChombo implementation closely (Florio et al., 2024). Taken together, these works place GRTeclyn within a GRChombo-derived, AMReX-based ecosystem for strong-field general relativity, adaptive mesh refinement, and relativistic perturbation analysis.

1. Identity, lineage, and scope

The clearest direct characterization of GRTeclyn appears in the wormhole-collapse study, where it is described as a codebase and specifically as a “Port of GRChombo to AMReX” (Shirokov, 31 Mar 2026). In that work, GRTeclyn is used to initialize exact isotropic wormhole data on a three-dimensional Cartesian grid, evolve the coupled Einstein–phantom-scalar system, apply CCZ4 with matter source terms, use adaptive mesh refinement (AMR), track collapse diagnostics, extract gravitational radiation through the Weyl scalar $\Psi_4$, and monitor constraints.

The inflationary tensor paper uses more qualified language. Its concrete numerical results are obtained with GRChombo, but the authors repeatedly state that they are actively porting a dedicated inflationary example to GRTeclyn and that the implementation in GRTeclyn is expected to follow closely (Florio et al., 2024). This establishes GRTeclyn not merely as a separate code name, but as the intended recipient of a validated computational pipeline for cosmological tensor initialisation, evolution, and extraction.

A plausible implication is that GRTeclyn is best understood not as a single-purpose application, but as a general infrastructure layer for numerical relativity. The available papers associate it with two distinct regimes: strong-field compact-object dynamics and early-universe tensor perturbations.

2. Evolution formalisms and computational infrastructure

The literature associates GRTeclyn with two evolution frameworks. In the wormhole paper, the coupled geometry–matter system is evolved with CCZ4 with matter, and the scalar variables are advanced through the CCZ4RHSWithMatter module in GRTeclyn (Shirokov, 31 Mar 2026). The evolved state includes conformal metric variables, $\chi$, $K$, shift, lapse, and scalar variables $(\phi,\Pi)$. In the inflationary tensor pipeline, the evolution is formulated in BSSN, with evolved variables

$$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$

and matter supplied by the inflaton sector (Florio et al., 2024).

The wormhole study gives the more explicit implementation profile. It states that GRTeclyn uses an AMReX backend for block-structured AMR and GPU acceleration, and that production runs use NVIDIA H100 GPUs with one MPI rank per GPU (Shirokov, 31 Mar 2026). The reported production setup is

$$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$

with up to 5 AMR levels at 2:1 refinement, regridded on $\chi$-gradients, giving

$dx_{\rm fine}\approx 7.8\times 10^{-3}.$

Time integration uses 4th-order Runge–Kutta with dt_multiplier = 0.02; octant symmetry is imposed; inner boundaries use parity conditions; outer boundaries use Sommerfeld boundary conditions; and the wave-extraction radii satisfy

$R_{\rm ext}\in[12,24].$

Several numerical controls are also specified in that work: Kreiss–Oliger dissipation with

$\sigma_{\rm KO}=2.0,$

a floor on the conformal variable,

$\chi$0

and CCZ4 damping parameters

$\chi$1

Constraint monitoring is carried out with volume-weighted $\chi$2 norms on the unrefined level-0 grid (Shirokov, 31 Mar 2026).

By contrast, the inflationary tensor study emphasizes the gauge and perturbative-consistency aspects of the GRChombo/GRTeclyn workflow. For the tensor-only runs it uses geodesic gauge / synchronous gauge in cosmic time, with initial lapse $\chi$3, initial shift $\chi$4, and all Bona–Massó coefficients set to zero so that the gauge variables remain fixed (Florio et al., 2024). The same paper also states that the time evolution in GRChombo is second-order accurate, that the simulations are performed in a finite periodic box implicit in the Fourier-lattice construction, and that KO dissipation and CCZ4-type damping are disabled for the validation runs because they can distort the physical tensor spectrum.

3. Initial data and matter content

One of the main published demonstrations of GRTeclyn is the evolution of an Ellis–Bronnikov wormhole supported by a massless phantom scalar field (Shirokov, 31 Mar 2026). The matter model is defined by

$\chi$5

with

$\chi$6

The wormhole is initialized in isotropic coordinates so that the conformal variable can be written in algebraically regularized form,

$\chi$7

while the static initial data satisfy

$\chi$8

The paper stresses that evolving $\chi$9 rather than $K$0 makes the compactified origin regular in moving-puncture-type variables.

The same study also details how collapse is forced. To select the compressive branch of the instability, the phantom stress-energy support is globally rescaled,

$K$1

with

$K$2

and a quadrupolar scalar perturbation is added,

$K$3

using

$K$4

The perturbation is applied to $K$5 rather than to $K$6 or $K$7, so that with $K$8 and $K$9, the momentum constraint remains exactly satisfied at the initial time (Shirokov, 31 Mar 2026).

The cosmological work describes a different initial-data pipeline that is intended for GRChombo/GRTeclyn. It constructs stochastic vacuum tensor perturbations from the Mukhanov–Sasaki mode functions, using a polarization decomposition

$(\phi,\Pi)$0

Gaussian random amplitudes in Fourier space, and a crucial $(\phi,\Pi)$1-dependent mode-function phase rather than a random phase alone (Florio et al., 2024). The paper is explicit that the improved method is

$(\phi,\Pi)$2

and that this phase is required to reproduce the smooth temporal power evolution predicted by linear theory.

That tensor data are then mapped into the BSSN variables through the tensor-only CPT–BSSN dictionary,

$(\phi,\Pi)$3

The authors state that they have developed a new initial-condition class in GRChombo which generates this random tensor perturbation on the lattice, and that this functionality is expected to be made public in a future release of GRChombo/GRTeclyn (Florio et al., 2024).

4. Diagnostics, extraction, and verification

The wormhole paper presents GRTeclyn as a platform for collapse diagnostics and gravitational-wave extraction (Shirokov, 31 Mar 2026). The areal-radius diagnostic is written as

$(\phi,\Pi)$4

and the sign of $(\phi,\Pi)$5 is interpreted through

$(\phi,\Pi)$6

so that $(\phi,\Pi)$7 indicates contraction and $(\phi,\Pi)$8 indicates expansion. Because there is no production elliptic apparent-horizon finder in GRTeclyn in that work, the authors implement a trapped-surface proxy by evaluating the outgoing null expansion $(\phi,\Pi)$9 on coordinate spheres and using the criterion

$$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$0

Gravitational radiation is extracted through the Newman–Penrose scalar

$$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$1

The extracted signal is decomposed into spin-weighted spherical harmonics, and the dominant mode is found to be $$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$2, consistent with the imposed $$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$3 perturbation. A key methodological test is the propagation-speed estimate

$$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$4

used to distinguish physical gravitational waves from superluminal CCZ4 constraint modes. For the perturbed collapse run, the paper reports

$$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$5

between $$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$6 and $$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$7, with mild numerical dispersion further out, while the unperturbed run yields only very weak, superluminal signals interpreted as constraint-related contamination (Shirokov, 31 Mar 2026).

The same work also defines a one-sided power spectral density for $$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$8,

$$\{\chi,\tilde{\gamma}_{ij},K,\tilde{A}_{ij},\alpha,\beta^i\},$$9

uses a Morlet-wavelet continuous wavelet transform for time–frequency analysis, and converts to strain through

$$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$0

These quantities are then compared to detector sensitivity curves.

The inflationary tensor study develops a different extraction and verification pipeline for the GRChombo/GRTeclyn framework (Florio et al., 2024). In the perturbative tensor-only regime it extracts the tensor perturbation as

$$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$1

For future scalar-plus-tensor runs it also provides a more general transverse-traceless projector,

$$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$2

The primary validation observable is the tensor power spectrum, obtained from the polarization fields $$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$3 and $$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$4 and compared against the Mukhanov–Sasaki prediction. Constraint behavior is analyzed through the Hamiltonian and momentum constraints, and the paper states that the tensor-only stochastic initial conditions violate constraints only at second order or smaller, with the corresponding numerical checks showing that these conditions are met (Florio et al., 2024).

5. Demonstrated scientific applications

The most direct GRTeclyn application in the current literature is three-dimensional wormhole dynamics (Shirokov, 31 Mar 2026). With exact initial data, full support

$$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$5

and flat initial lapse, the code keeps the wormhole nearly static up to $$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$6, after which truncation-level effects push the solution onto the rarefactive expansion branch. The throat then expands exponentially with measured rate

$$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$7

The paper reports that moving-puncture gauge is much better suited to collapse than to this inflationary expansion, since the lapse “anti-collapses,” coordinate stretching outruns AMR, and constraints grow.

For the perturbed collapse run,

$$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$8

the wormhole undergoes rapid compression. The areal radius drops from $$L_{\rm full}=64,\qquad N_{\rm full}=256,\qquad dx_{\rm coarse}=0.25,$$9 to approximately

$\chi$0

by $\chi$1; a trapped surface forms almost immediately; and $\chi$2, initially exactly zero, is dynamically generated up to $\chi$3. After horizon formation, the swallowed phantom matter produces a “phantom bounce”, the areal radius grows again to about

$\chi$4

and an outward curvature shock propagates through the grid. By

$\chi$5

the trapped-surface proxy disappears and the lapse falls to a floor near $\chi$6. This sequence is significant because it shows GRTeclyn evolving a topologically nontrivial, exotic-matter spacetime through collapse, apparent-horizon-proxy formation, rebound, and wave emission in full $\chi$7D.

The same paper also gives an astrophysical scaling argument. For a wormhole with

$\chi$8

at

$\chi$9

the dominant signal moves into the $dx_{\rm fine}\approx 7.8\times 10^{-3}.$0–$dx_{\rm fine}\approx 7.8\times 10^{-3}.$1 Hz band, but for the moderate perturbation amplitude

$dx_{\rm fine}\approx 7.8\times 10^{-3}.$2

the characteristic strain lies slightly below Advanced LIGO design sensitivity. The authors state that detectability would require closer sources, larger initial asymmetries, or next-generation detectors (Shirokov, 31 Mar 2026).

A second application area is early-universe tensor dynamics, although here the validated numerical results are explicitly presented for GRChombo, with GRTeclyn identified as the target of an ongoing port (Florio et al., 2024). That work presents a complete method for the initialisation and extraction of first-order inflationary tensor perturbations with full gravitational backreaction, shows agreement of the background quantities $dx_{\rm fine}\approx 7.8\times 10^{-3}.$3, $dx_{\rm fine}\approx 7.8\times 10^{-3}.$4, and $dx_{\rm fine}\approx 7.8\times 10^{-3}.$5 with the Friedmann/Klein–Gordon system, and reproduces the expected transition of the tensor spectrum from subhorizon

$dx_{\rm fine}\approx 7.8\times 10^{-3}.$6

to superhorizon

$dx_{\rm fine}\approx 7.8\times 10^{-3}.$7

behavior. It also reports preliminary non-Gaussianity diagnostics based on skewness and kurtosis, with the genuinely nonlinear signal appearing as subtle amplitude-dependent growth for large rescalings $dx_{\rm fine}\approx 7.8\times 10^{-3}.$8.

6. Limitations and development trajectory

The current literature also defines the main limitations of GRTeclyn and the near-term development path. In the wormhole study, there is no production elliptic apparent-horizon finder, so horizon identification is approximate; excision is not used, with moving-puncture gauge relied upon to handle horizon formation; finite-radius extraction is used instead of larger-radius extraction or Cauchy-characteristic extraction; and late-time bounce-driven shock-like gradients degrade convergence and eventually overwhelm the AMR strategy (Shirokov, 31 Mar 2026). The same work emphasizes that the perturbed collapse setup introduces a small Hamiltonian residual at $dx_{\rm fine}\approx 7.8\times 10^{-3}.$9, and explicitly suggests future use of an elliptic solver for fully constraint-satisfying large-amplitude data.

The cosmology pipeline carries a different set of caveats. Its published implementation is still in GRChombo, not yet in fully documented GRTeclyn form; the validation runs are tensor-only; the simple extraction formula

$R_{\rm ext}\in[12,24].$0

is appropriate only while trace and longitudinal contamination remain negligible; and the work does not yet provide a direct tensor bispectrum estimate (Florio et al., 2024). The planned next steps are to combine scalar and tensor stochastic initialisation methods, evolve scalar and tensor perturbations together in full numerical relativity, study mixed bispectra such as $R_{\rm ext}\in[12,24].$1, and connect the simulations to the MODAL bispectrum-estimation pipeline.

These limitations do not define GRTeclyn as incomplete in a generic sense; rather, they identify the specific frontier at which the codebase is being used. The published record shows a framework already capable of GPU-accelerated $R_{\rm ext}\in[12,24].$2D evolutions with AMR, exotic matter, and waveform extraction, while simultaneously serving as the intended destination for a perturbatively validated cosmological tensor pipeline (Shirokov, 31 Mar 2026, Florio et al., 2024).