A deterministic, computing and raytracing engine for General Relativity, Post-Newtonian celestial mechanics, relativistic hydrodynamics, and polarized radiative transfer across curved spacetimes.
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Spacetime Geometries:
- Exact electrovacuum metrics: Minkowski, Schwarzschild, Kerr, Reissner-Nordström, Kerr-Newman, Schwarzschild-de Sitter / Kottler.
- Regular formulations: Kerr-Schild, Eddington-Finkelstein, Painlevé-Gullstrand, Isotropic coordinates.
- Cosmological & Exotic metrics: FLRW (
$k \in {-1, 0, 1}$ ), Morris-Thorne traversable wormholes, Alcubierre warp drive. - Numerical Spacetimes: 3+1 BSSN metric grid with tricubic and quintic Hermite temporal interpolation.
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Differential Integrators:
- Adaptive explicit: Runge-Kutta 4/5 (Dormand-Prince), Cash-Karp, Vernier 9 (16 stages, 9th order).
- Symplectic: Gauss-Legendre (4th & 6th order), Forest-Ruth / Yoshida.
- Predictor-corrector: Hermite 4th-order with Aarseth variable timestep control.
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Post-Newtonian Celestial Dynamics:
- Conservative orders: 1PN, 2PN, 3PN.
- Radiation reaction: 2.5PN and 3.5PN gravitational wave dissipation.
- Spin couplings: Spin-Orbit (Lense-Thirring / geodetic) and Spin-Spin precession.
- Spherical Harmonics: High-degree gravitational potential expansions (
$J_2, J_3, J_4, C_{nm}, S_{nm}$ ).
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Relativistic Hydrodynamics (GRHD / GRMHD):
- High-Resolution Shock Capturing: WENO5-Z, MP5 spatial reconstruction.
- Riemann Solvers: HLL, HLLC, HLLD.
- Equations of State: Ideal gas, Synge, Mathews, Relativistic Degenerate Fermi gas, Polytropic, and 3D Tabulated Nuclear tables (SFHo, Shen, LS220, SLy4, APR4).
- Accretion Models: Novikov-Thorne thin disk, Fishbone-Moncrief thick torus.
- Divergence-Free Magnetism: 2D/3D Constrained Transport (
$\nabla \cdot \mathbf{B} = 0$ ).
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Polarized Radiative Transfer & CIE Spectrum Pipeline:
- Raytracing: GPU Compute shader pipeline with native FP64 and Double-Single arithmetic.
- Full Stokes transport:
$\mathbf{S} = (I, Q, U, V)^T$ with Delano matrix exponential integration. - Radiative processes: Relativistic synchrotron, Bremsstrahlung, inverse Compton scattering with Maxwell-Jüttner velocity sampling.
- Radiometry: Continuous spectral integration (
$10^{-14}$ to$10^{3}$ m) convolved with CIE 1931 color matching functions and ACES HDR tonemapping.
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Formal Uncertainty Quantification:
- Interval arithmetic (IEEE 1788) & Zonotopes with Girard order reduction.
- Continuous Lyapunov phase covariance propagation along geodesics.
- Generalized Polynomial Chaos Expansion (gPCE) on Gauss-Hermite / Gauss-Legendre quadratures.
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Scientific I/O:
- NASA JPL SPICE SPK binary kernels and HORIZONS API ingestion.
- FITS 2D images and 3D spectral cubes with WCS metadata.
- HDF5 trajectory and metric tensor series serialization.
- VTK PolyData XML format for ParaView/VisIt rendering.
- C++23 compliant compiler: GCC 13+, Clang 16+, or MSVC 2022 (v19.36+).
- CMake 3.25+.
- OpenGL and GLFW (automatically fetched via CMake FetchContent).
cmake -B build -DCMAKE_BUILD_TYPE=Release -DENABLE_LTO=ON
cmake --build build --config Release -j $(nproc)cmake -B build-pgo -DCMAKE_BUILD_TYPE=Release -DENABLE_PGO_GENERATE=ON
cmake --build build-pgo --config Release -j $(nproc)
./build-pgo/headless_exporter --validate-benchmarkscmake -B build-opt -DCMAKE_BUILD_TYPE=Release -DENABLE_PGO_USE=ON
cmake --build build-opt --config Release -j $(nproc)ctest --test-dir build --output-on-failurecd build
cpack -G TGZ
cpack -G DEB # Linux Debian/Ubuntu
cpack -G RPM # Linux Fedora/RHEL
cpack -G NSIS # Windows Installer./build/engine_cliRun help to list available commands (warp, step, set mass, status, etc.).
./build/headless_exporter --validate-benchmarks
./build/headless_exporter --scenario scenarios/kerr_accretion_disk.yaml --output-dir ./output --width 3840 --height 2160This project is licensed under the MIT License. See LICENSE for details.