Gravity and Black-Hole Reference

The Gravity and Black-Hole Reference is a fast route to a formula, chart, method, domain, or causal structure. Each concise record points to the complete scientific treatment instead of duplicating the Library.

Choose the object you need

Conventions and Symbols fixes the site’s metric and curvature signs, index and bracket notation, orientation and volume forms, and unit conventions, together with tetrad, Newman–Penrose, GHP, and two-spinor symbols. Its five compact cards give translation rules and checks, so a source convention is converted coherently rather than repaired one sign or factor at a time.

Equations collects convention-controlled forms of the geodesic and Jacobi, Einstein, Raychaudhuri, ADM, and Teukolsky systems. Each card keeps its signs, normalizations, hypotheses, limiting checks, and exact derivation link together.

Constants and Scales separates exact definitions, measured constants, nominal conversions, derived Planck and geometric units, stationary Kerr scales, and distinct compactness or curvature diagnostics.

Tensor and Curvature Identities covers Riemann and Bianchi identities, derivative commutators, hypersurface projections, curvature decomposition, and differential-form signs with their dimension, orientation, and boundary hypotheses visible.

Spacetimes and Coordinates compares chart domains, horizon coverage, and invariant checks. In particular, its Schwarzschild card separates the static chart’s horizon failure from the spacetime’s curvature singularity.

Conformal Diagrams is for global causal questions. The maximally extended Schwarzschild diagram identifies the two exteriors, black- and white-hole interiors, four horizon branches, infinities, bifurcation sphere, and spacelike singularities. It also states the crucial limitation: the eternal maximal extension is not the same spacetime as a one-sided black hole formed by stellar collapse.

Theorems maps exact hypotheses to typed conclusions. Its realized cards keep the Penrose, Hawking, and Hawking–Penrose incompleteness results distinct, state the global and regularity assumptions behind classical event-horizon area nondecrease, compare bounded black-hole classification and positive-mass variants without merging their hypotheses, and separate local Cauchy evolution from the universal maximal globally hyperbolic development. Each card also states what the theorem does not prove and routes to the exact Library proof pages.

Regimes and Approximations turns a proposed approximation into a checkable contract: the small parameter, quantities held fixed, controlled norm or observable, overlap region, first omitted effect, breakdown surface, and independent check. Its five cards distinguish weak-field from slow-motion assumptions; compare PN, PM, self-force, and EOB; locate geometric-optics failures; test black-hole perturbative control; and separate fixed-background QFT from semiclassical mean and fluctuation regimes.

Methods routes a mathematical task to bounded preparation, a physical use, and the minimum check that makes the result credible. Its Distributions and Generalized Functions record fixes test spaces, derivative and delta conventions, singular-source normalizations, and the boundary beyond which a product or regularized limit needs additional structure.

Observables and Parameters starts from defining operations. Its six cards cover gravitational charges; horizon quantities; clocks, redshift, and lensing; gravitational-wave variables; quasinormal, tail, scattering, and tidal response; and astrophysical parameters. Each keeps the observer, boundary, operator, frame, detector response, or nuisance structure visible and routes derivations or mutable values to the full scientific treatment.

Software records the identities and comparison rules needed to reconstruct a finite computation, while keeping rerun evidence distinct from verification, validation, and correctness. It does not maintain a volatile catalog of current tools.

Open Data Products guides a reader through four exact public releases: GWOSC O4a and O4b strain products, calibrated 2017 M87 interferometric data, and the pinned imaging pipelines used with that release. The guides keep availability, quality, calibration, processing, reconstruction, and scientific interpretation in separate layers.

Bibliography and Primary Sources maps five evidence domains to exact source locators, supported conclusions, and exclusions.

History offers five finite, sourced chronologies: Newtonian gravity to general relativity; the black-hole concept from exact solution to astrophysical candidate; global causality and singularity theorems; gravitational waves from theory to detection; and black-hole thermodynamics and information.

Misconceptions uses counterexamples and operational checks to separate singular endpoints, Newtonian scale estimates, Schwarzschild coordinate time, gravitational-wave gauge choices, and the Hawking pair cartoon from the corresponding invariant physics.

How to read a record

Start with the domain. An equation without its dimension, matter assumptions, parameter range, or differentiability hypotheses is often too ambiguous to use. Next check conventions: metric signature, curvature sign, index position, mass parameter, units, orientation, and time direction can change the visible form of a correct statement. Finally follow the canonical derivation link if the lookup result will carry substantial weight in a proof or computation.

Compact checks make silent errors harder: a trace, divergence, limiting case, invariant, chart overlap, or boundary test may expose a mismatch. They support the card but do not replace its derivation.

What the Reference preserves—and omits

Reference preserves stable mathematical content, precise domains, aliases, source provenance, and a route to the deeper treatment. Its active inventory contains only substantive records: it does not reserve empty routes for a future catalog or alphabetical index. It does not reproduce long proofs, build a parallel sequence of lessons, or turn a compact card into an unbounded survey. The Library remains the place to learn why a result is true and how it fits into the surrounding theory.

Mutable empirical bounds, catalog values, and unsettled research conclusions also require more context than a timeless card can carry. Those belong with a dated evidence assessment, including the data release, model assumptions, competing interpretations, and possible tests. A Reference record may point to that assessment, but should not freeze a moving frontier into an apparently permanent fact.

Move from lookup to explanation or execution

Use the Library when you need the complete chain of definitions, derivation, interpretation, limitations, and exercises. Use Computational Relativity for numerical formulations, algorithms, convergence practice, and reproducible execution methods; reviewed downloads remain attached to the canonical scientific treatment. Use Research when the answer depends on current observations or an open theoretical dispute.