Courses and Seminars

These five courses organize blackhole.org readings into focused, assessment-rich programs. Each declares an audience, prerequisites, ordered modules, assignments, a solution policy, transfer work, a capstone, and completion criteria. They can support independent study, a reading group, or an instructor’s local course, but they do not imply enrollment, a timetable, an institution, or a credential.

A course is the right form when you want fixed assessment and a common spine. Choose a learning path when you need more freedom to vary the sequence or strengthen your preparation along the way. Use Start Learning Gravity if the choice is still unclear.

Compare the five frameworks

Course	Intended work	Main assignments
First Graduate Course in General Relativity	a broad first technical treatment of geometry, Einstein dynamics, black holes, tests, waves, compact objects, and cosmology	derivations and calculations across the classical spine, followed by a synthesis capstone
Advanced General Relativity and Black-Hole Physics	formulations, global structure, exact black holes, mechanics, perturbations, asymptotics, and nonlinear or rigorous interfaces	proof architecture, geometric calculation, and comparison across local, global, and dynamical regimes
Gravitational Radiation and Compact Binaries	radiation at infinity, source multipoles, approximation schemes, two-body dynamics, waveforms, numerical comparison, and inference	a cross-regime waveform argument with explicit validity and uncertainty checks
Computational Relativity	symbolic tensors, ODE and spectral methods, PDE evolution, initial data, extraction, verification, validation, and uncertainty	a reproducible calculation with convergence tests, constraint and boundary checks, and a physical interpretation
Research Seminar: Evidence and Open Problems in Gravitation	exact dated Research records spanning theory, computation, observation, and contested interpretation	source reconstruction, bounded reproduction, evidence comparison, and a tractable research-question brief

The first course supplies breadth. The next three deepen a classical, radiative, or computational direction. The seminar is not simply “the most advanced” option: it develops a different capability—reasoning responsibly from incomplete and changing evidence.

What a course page contains

Audience and readiness

The audience statement describes work the course assumes, not demographic or credential categories. Required background is paired with a diagnostic and an specific topic to review. Helpful background can make a module more efficient but does not become an invisible gate.

If one prerequisite is uncertain, attempt its diagnostic before starting the course. Review the specific topic where you found a gap and then return to the original module. A long detour through unrelated material is not a stronger preparation strategy.

Modules and assignments

Module order encodes conceptual dependencies. Within each module, the course page identifies the exact assigned reading and the work to extract from it. Assignments require more than transcription: a derivation must expose its assumptions, a proof outline must retain its hypotheses, a computation must show numerical controls, and an inference must identify the data and model that support it.

Unless a course states otherwise, work an assignment before opening its hint or solution. Use the solution to check your reasoning. After comparing your attempt, write the correction in your own words and solve the transfer variant without copying the worked route.

Transfer and capstone

Transfer work changes the setting enough to reveal whether a method is portable. Typical changes include coordinates, gauge, approximation regime, initial or boundary data, source model, numerical resolution, or evidential hypothesis. The capstone then joins several course outcomes in one carefully justified artifact.

Each capstone rubric separates at least:

• scientific correctness;
• assumptions, conventions, and domain of validity;
• derivation, proof, computational, or inference quality;
• independent checks and treatment of uncertainty;
• interpretation and communication.

A polished conclusion cannot compensate for a missing check, and a correct calculation without an interpretable claim is not a finished capstone.

Using a framework independently

Work in module order, but let demonstrated capability—not a calendar—control the pace. For each module, retain a one-page record containing the question, the result, the decisive steps, one check, and one unresolved point. That record makes a restart possible without storing progress on the site.

For a reading group, participants can rotate three roles: reconstruct the argument, challenge assumptions or evidence, and reproduce one bounded step. Roles should rotate so that mathematical, computational, and interpretive work does not become permanently divided among people.

Adapting a framework for teaching

An instructor may select meeting dates, local grading weights, collaboration rules, and accessibility accommodations, but should preserve the dependency order and stated outcomes unless the public course description is revised. When shortening a course, remove an outcome together with its dependent assessment; adjust the learning goals if you remove the assignments that test them.

Equivalent demonstrations are welcome when they preserve the intellectual task. A spoken derivation, tactile or high-contrast diagram description, notebook, typeset proof, or structured data analysis can serve when it exposes the same reasoning and checks. Time pressure is not part of these frameworks.

Use the complete worked solutions as instructor and self-study resources, not as public answer keys detached from the questions. If an assessment is reused in a local graded setting, replace its numerical or model details and keep the original as practice.

Finishing and continuing

Completion means that the declared outcomes are supported by assignments, changed-setting transfer, and the capstone rubric. Attendance, page visits, and time spent do not substitute for solving those problems. A learner who has gaps in one outcome should preserve the successful work, review the topic that caused difficulty, and revisit only the affected work.

After a course, continue according to the unresolved question: follow a specialist path, reproduce a method through Computational Relativity, consult Reference while calculating, compare physical systems in the Black Hole Atlas, or move into dated evidence assessments in Research.