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Learn Gravity and Black-Hole Physics

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Learning gravity is not the same task for every reader. You may want a first physical picture of curved spacetime, the preparation needed for a graduate course, a sustained route through black-hole perturbation theory, or a way to enter an unfamiliar research literature. This directory starts from that task and connects it to exact readings, calculations, proofs, computational work, and evidence assessments across blackhole.org.

You can browse directly, use Start Learning Gravity for a short readiness check, follow a flexible learning path, choose an assessment-rich course, or strengthen a particular skill in Preparation and Capability Repair. No route assumes an institution, credential, account, timer, or stored progress.

Choose the form that matches the work

Section titled “Choose the form that matches the work”
FormBest when you needWhat demonstrates completion
StartOne honest next step from a goal and present preparationA transparent ready, review, or repair recommendation that you can accept, skip, or override
Learning pathA flexible self-study sequence through several subjectsCore checkpoints, a changed-setting transfer task, and a capstone covering the stated outcomes
Course or seminarFixed modules, assignments, and assessment criteria for individual or group studyChecked assignments, transfer work, and an assessed capstone—not attendance or page visits
Preparation moduleOne missing mathematical or physical capability is interrupting a routeA diagnostic followed by a successful transfer problem in a changed setting

Paths and courses point to the same scientific explanations, but they use them differently. A path lets you review prerequisites and vary your reading around a declared core. A course fixes module boundaries and asks for assessed work. Preparation is deliberately narrower: it should return you to the interrupted route rather than become a second textbook.

Start from a learning goal

Section titled “Start from a learning goal”

Build a first accurate picture

Section titled “Build a first accurate picture”

Begin with First Encounter with Gravity and Black Holes. It moves from Newtonian gravity and special relativity to curvature, horizons, observations, and gravitational waves while marking where intuition must eventually be replaced by mathematics.

Prepare for formal general relativity

Section titled “Prepare for formal general relativity”

Mathematics and Physics for Relativity diagnoses calculus, linear algebra, differential equations, mechanics, special relativity, fields, and tensor geometry. If you already know the gap, go directly to the preparation directory.

Learn graduate general relativity

Section titled “Learn graduate general relativity”

The Graduate General Relativity Self-Study Path is the complete flexible spine. The First Graduate Course in General Relativity follows the same scientific arc with fixed assignments and capstone criteria.

Specialize

Section titled “Specialize”

The path directory includes classical, computational, observational, mathematical, cosmological, semiclassical, quantum, and holographic routes. Choose by the capability you want to demonstrate, not by the prestige or apparent difficulty of the subject.

Choose an advanced branch or the evidence seminar

Section titled “Choose an advanced branch or the evidence seminar”

Advanced preparation is branch-specific. Each route in the path directory states and checks the prerequisites for the capabilities it promises; readiness for a mathematical-relativity path, a computational path, or a quantum path does not transfer automatically to the others.

The Research Seminar: Evidence and Open Problems in Gravitation develops source reconstruction, bounded reproduction, evidence comparison, and question-formulation skills using exact dated records from the Research Atlas. Its common Start check covers Einstein’s equation and elementary Bayesian inference only. Passing that check means ready to begin the common seminar work—not ready for research in every domain. Before the bounded technical reproduction, the selected case applies its own prerequisite profile and routes any gap to the relevant advanced path or preparation.

Assemble a course

Section titled “Assemble a course”

The courses and seminars directory provides five finite frameworks with audiences, prerequisites, modules, assignments, solution policies, transfer tasks, and capstones. They are reusable designs, not claims about an instructor, institution, enrollment system, or credential.

What the linked pages do

Section titled “What the linked pages do”

Learn helps you choose a sequence of readings and problems. A Library page develops a definition, derivation, proof, method, or synthesis. Computational Relativity explains numerical methods and how to reproduce their results. Reference provides compact lookup. The Black Hole Atlas assembles object-level facts. Research compares research results through an explicit cutoff date.

A curriculum therefore links rather than copies. When a path asks you to study Einstein’s equation, it points to the full derivation and then tells you what to extract, calculate, check, and transfer. When it uses a Research record, the date and uncertainty remain part of the task. One scientific page can serve several routes without acquiring several competing explanations.

Demonstrate what you have learned

Section titled “Demonstrate what you have learned”

The phrase “complete this path” means that you can produce the declared work. Your work may be a geometric calculation, a proof outline with its hypotheses stated, a converged computation, an inference with priors and selection effects exposed, or a comparison of claims and counterevidence. It does not mean that a browser recorded a visit.

Most substantial routes use the same progression:

  1. state the capability and check the preparation it actually uses;
  2. review only a topic where you found a gap;
  3. study the linked explanation and work a representative example;
  4. attempt a checkpoint before opening its hints or solution;
  5. transfer the method to a changed regime, representation, boundary condition, dataset, or hypothesis; and
  6. complete a capstone that combines several outcomes and includes an independent check.

You may keep your own notes or progress record, but the full route works without an account or stored state. If you leave and return, use the last piece of work you can still explain and verify—not the last URL in your history—as your starting point.

Why the design emphasizes problems and explanation

Section titled “Why the design emphasizes problems and explanation”

Strong graduate courses make preparation and problem work visible. MIT OpenCourseWare’s 8.962 General Relativity course (Spring 2020) publishes a coherent sequence with problem sets and hints, while the University of Cambridge Part III Guide to Courses 2023–24 (PDF) states expected preparation and the role of example sheets. Research on worked examples also finds value in prompting learners to explain the principle and conditions behind a step rather than merely reading it; see Chi et al. 2022, Physical Review Physics Education Research 18.

Those sources inform the learning design, not the scientific scope. The exact gravity sequence, conventions, checks, and completion tasks follow the scientific material linked from each blackhole.org route.

References

Section titled “References”