Images & edition notesImages & edition notes
A visual reading edition#A visual reading edition
This edition preserves the complete 24-chapter derivation sequence and adds a prerequisite Chapter 0, new worked calculations, historical context, an index-practice appendix, chapter questions and checkpoints, original SVG diagrams, and three interactive experiments. The intended entry point is basic calculus and linear algebra. The later quantum and global-geometry discussions distinguish explanations from complete proofs and mark their additional assumptions.This edition preserves the complete 24-chapter derivation sequence and adds a prerequisite Chapter 0, new worked calculations, historical context, an index-practice appendix, chapter questions and checkpoints, original SVG diagrams, and three interactive experiments. The intended entry point is basic calculus and linear algebra. The later quantum and global-geometry discussions distinguish explanations from complete proofs and mark their additional assumptions.
The supplied comparison document was treated as reference material, not as instructions. Its coverage was compared with the manuscript, and useful gaps were filled. Several of its claims needed correction: a massless homogeneous scalar is not dust; curvature gives relative acceleration per separation; Kerr merger areas cannot be inferred from mass squared alone; and the two common factors of two involving pressure and light bending answer different questions. The editorial comparison in the repository records the decisions.The supplied comparison document was treated as reference material, not as instructions. Its coverage was compared with the manuscript, and useful gaps were filled. Several of its claims needed correction: a massless homogeneous scalar is not dust; curvature gives relative acceleration per separation; Kerr merger areas cannot be inferred from mass squared alone; and the two common factors of two involving pressure and light bending answer different questions. The editorial comparison in the repository records the decisions.
The original diagrams#The original diagrams
Every diagram in the visual atlas is an original, reproducible SVG generated from the geometric or schematic construction stated in its caption. Axes, units, projection effects, approximation regimes, and exaggerated amplitudes are identified where relevant. SVG keeps the labels and lines sharp at any zoom. The equations are rendered as HTML and MathML, with locally hosted math fonts; no remote equation-rendering service is required.Every diagram in the visual atlas is an original, reproducible SVG generated from the geometric or schematic construction stated in its caption. Axes, units, projection effects, approximation regimes, and exaggerated amplitudes are identified where relevant. SVG keeps the labels and lines sharp at any zoom. The equations are rendered as HTML and MathML, with locally hosted math fonts; no remote equation-rendering service is required.
The diagrams are teaching models, not photographs of spacetime. A grid drawn with curved lines does not establish intrinsic curvature. A spacetime sketch does not preserve ordinary Euclidean lengths. Large visible gravitational-wave distortions are deliberate magnifications of a first-order model.The diagrams are teaching models, not photographs of spacetime. A grid drawn with curved lines does not establish intrinsic curvature. A spacetime sketch does not preserve ordinary Euclidean lengths. Large visible gravitational-wave distortions are deliberate magnifications of a first-order model.
Historical photographs and documents#Historical photographs and documents
Four historical assets are used in Chapter 1. Source pages identify these as public-domain works or faithful reproductions of public-domain two-dimensional works. Dates below refer to the original work. The files were proportionally resized and JPEG-compressed without new cropping or retouching. The asset manifest records source URLs, creator, copyright rationale, processing, and file hashes, checked on September 8, 2026.Four historical assets are used in Chapter 1. Source pages identify these as public-domain works or faithful reproductions of public-domain two-dimensional works. Dates below refer to the original work. The files were proportionally resized and JPEG-compressed without new cropping or retouching. The asset manifest records source URLs, creator, copyright rationale, processing, and file hashes, checked on September 8, 2026.
| Image | Creator and date | Source and rights |
|---|---|---|
| Einstein beside a chalkboard | Ferdinand Schmutzer, 1921 | Commons source; public domain under the source page’s Austrian and US rationales. |
| Portrait of Isaac Newton | Godfrey Kneller, 1689 | Commons source; expired copyright, PD-Art reproduction. |
| First-edition Principia title page | Isaac Newton, 1687 | Commons source; public domain. |
| Die Grundlage der allgemeinen Relativitätstheorie title page | Albert Einstein, 1916 | Commons source; pre-1931 US publication, life-plus-70 term expired at the end of 2025, PD-Art reproduction. |
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The final image is a printed 1916 title page. It is not Einstein’s November 1915 paper, a notebook, or a handwritten field equation. Public-domain status is jurisdiction-dependent; the manifest preserves the source’s rationale rather than applying one blanket license to every historical work.The final image is a printed 1916 title page. It is not Einstein’s November 1915 paper, a notebook, or a handwritten field equation. Public-domain status is jurisdiction-dependent; the manifest preserves the source’s rationale rather than applying one blanket license to every historical work.
Sources and reproducibility#Sources and reproducibility
Research and historical references appear at the point of use and in Appendix D. A successful render is a typesetting check, not an independent peer review of an entire general-relativity textbook. The edition’s numerical checks cover the new clock and curvature examples and selected geometric models, and the visual review checks the exported diagrams and desktop and mobile layouts.Research and historical references appear at the point of use and in Appendix D. A successful render is a typesetting check, not an independent peer review of an entire general-relativity textbook. The edition’s numerical checks cover the new clock and curvature examples and selected geometric models, and the visual review checks the exported diagrams and desktop and mobile layouts.
The current publication target is this HTML book. The older PDF and LaTeX files in the repository are archival material from the previous edition; they do not contain these revisions. The HTML is built and deployed through the repository’s GitHub Actions workflow.The current publication target is this HTML book. The older PDF and LaTeX files in the repository are archival material from the previous edition; they do not contain these revisions. The HTML is built and deployed through the repository’s GitHub Actions workflow.
The explorable edition#The explorable edition
The visual overhaul includes nine original Three.js labs: an Earth-centered free-fall grid, covector level planes, light cones, spherical parallel transport, tidal deformation, Flamm’s paraboloid, gravitational-wave detector rings, FLRW expansion, and ADM slicing. Each states its dimensional reductions and approximation limits. The Earth grid animates only while visible, can be paused with Space when focused, and starts paused when reduced motion is requested. The other models render on interaction.The visual overhaul includes nine original Three.js labs: an Earth-centered free-fall grid, covector level planes, light cones, spherical parallel transport, tidal deformation, Flamm’s paraboloid, gravitational-wave detector rings, FLRW expansion, and ADM slicing. Each states its dimensional reductions and approximation limits. The Earth grid animates only while visible, can be paused with Space when focused, and starts paused when reduced motion is requested. The other models render on interaction.
The interface uses Hugeicons Stroke Rounded icons from its free core package. Reading typography pairs Newsreader with Manrope; the fonts are locally hosted under the SIL Open Font License. Equations and interactive labels use KaTeX. Mathematical labels in the static figures are compiled from explicit LaTeX using MathJax and stored as vector glyphs. No third-party font or script request is needed to read the deployed book.The interface uses Hugeicons Stroke Rounded icons from its free core package. Reading typography pairs Newsreader with Manrope; the fonts are locally hosted under the SIL Open Font License. Equations and interactive labels use KaTeX. Mathematical labels in the static figures are compiled from explicit LaTeX using MathJax and stored as vector glyphs. No third-party font or script request is needed to read the deployed book.
The language of color documents the five semantic roles and the limits of automatic classification. Color identifies recognized mathematical objects; indices, constants, and ambiguous notation stay neutral. Where a comparative plot distinguishes several models, its own labels identify the series. The two reading themes each supply their own colors, including inside inline vector figures and WebGL scenes. Bundled software notices and font license files are included with the site.The language of color documents the five semantic roles and the limits of automatic classification. Color identifies recognized mathematical objects; indices, constants, and ambiguous notation stay neutral. Where a comparative plot distinguishes several models, its own labels identify the series. The two reading themes each supply their own colors, including inside inline vector figures and WebGL scenes. Bundled software notices and font license files are included with the site.
The falling Earth grid#The falling Earth grid
The opening visualization is an original implementation inspired by Alessandro Roussel’s A new way to visualize General Relativity, ScienceClic English (2020), especially the time-slicing explanation beginning at 8:22. No video frames or artwork from ScienceClic are reproduced. The mathematical model follows Hamilton and Lisle’s The river model of black holes, using the exterior Schwarzschild solution for an idealized spherical Earth. The model assumptions and integrated trajectories are explained beside the interactive figure. The view is populated with older falling grids at startup and continuously replenished from a distant boundary, so there is no flat startup or global reset.The opening visualization is an original implementation inspired by Alessandro Roussel’s A new way to visualize General Relativity, ScienceClic English (2020), especially the time-slicing explanation beginning at 8:22. No video frames or artwork from ScienceClic are reproduced. The mathematical model follows Hamilton and Lisle’s The river model of black holes, using the exterior Schwarzschild solution for an idealized spherical Earth. The model assumptions and integrated trajectories are explained beside the interactive figure. The view is populated with older falling grids at startup and continuously replenished from a distant boundary, so there is no flat startup or global reset.
The Earth texture is NASA’s Blue Marble: Next Generation, December 2004 base map, a satellite-data composite. The original 5400 × 2700 map was resized to 2048 × 1024 and WebP-compressed. NASA’s media guidelines permit educational use of its generally uncopyrighted US government imagery, including texture maps. NASA is credited as the source; this book is not endorsed by NASA. The Earth asset manifest records the exact source and processing.The Earth texture is NASA’s Blue Marble: Next Generation, December 2004 base map, a satellite-data composite. The original 5400 × 2700 map was resized to 2048 × 1024 and WebP-compressed. NASA’s media guidelines permit educational use of its generally uncopyrighted US government imagery, including texture maps. NASA is credited as the source; this book is not endorsed by NASA. The Earth asset manifest records the exact source and processing.