Misconceptions

Gravity slogans often compress several inequivalent statements into one: coordinates become observations, dimensional estimates become definitions, or a theorem’s precise conclusion becomes a picture of a physical place. These six corrections identify the hidden assumption, supply a decisive check, and route the full argument to its Library treatment.

Six corrections to use at the point of confusion

Familiar claim	Fast correction	Decisive check
“Every black-hole boundary is the event horizon.”	Event, Killing, apparent, trapping, isolated, dynamical, and acceleration horizons use different data and answer different questions.	Rindler horizons exist in flat spacetime, while Vaidya’s marginal tube and event horizon separate during accretion.
“A singularity is a place in spacetime.”	Incompleteness, curvature behavior, extendibility, and an ideal endpoint are different questions.	Remove a point from Minkowski spacetime: the result is incomplete, flat, and smoothly extendible.
“A black hole is where Newtonian escape speed exceeds light speed.”	The Newtonian calculation estimates the Schwarzschild length scale; a relativistic black hole is defined by causal access to future null infinity.	Rindler observers have horizons in flat spacetime even though no black-hole region exists.
“An infaller freezes at the horizon.”	Finite infaller proper time, divergent Schwarzschild coordinate time, and signals received by an exterior observer are three different statements.	Transform to a future-horizon-regular chart and compute a specified signal protocol.
“Gravitational waves are only coordinate ripples.”	Metric components are gauge dependent; radiative curvature, relative detector response, and Bondi news are not removable coordinate patterns.	Pure gauge has zero linearized Riemann tensor, while a TT wave produces tidal response and outgoing flux.
“Hawking radiation is a pair created at the horizon.”	The controlled result uses mode mixing, state and detector dependence, renormalized flux, and greybody propagation; it supplies no invariant local pair history.	Derive the exponential null-coordinate map and ask which detector, state, and asymptotic mode define “particle.”

Each card retains the limited statement that is useful. “The horizon” is good shorthand when equilibrium hypotheses make the notions coincide; the escape-speed calculation is a good dimensional estimate; Schwarzschild time is useful for the static exterior; gauge choices are essential computational tools; the pair story can recall correlations or energy balance; and ideal boundaries can organize missing endpoints. The error is promoting one of these qualified tools into an invariant definition.

Diagnose the hidden assumption

Before accepting a short claim, ask four questions:

1. What kind of object is named? A manifold point, chart boundary, causal set, worldline measurement, asymptotic field, or theorem conclusion cannot be substituted for another without an argument.
2. Whose time or frame is used? Proper time, coordinate time, radar time, detector time, tetrad components, and Bondi retarded time answer different operational questions.
3. What survives a change of description? Test curvature, causal relations, proper intervals, boundary flux, or a complete measurement protocol rather than one coordinate component.
4. What counterexample separates the claims? Rindler and Vaidya horizons, flat punctures, horizon-penetrating charts, pure-gauge perturbations, and detector-dependent particle response are useful precisely because they change one proposed criterion while holding the relevant physics fixed.

Follow the full treatment

Use Event, Killing, Apparent, Trapping, Isolated, and Dynamical Horizons for the horizon definitions; Completeness, Extendibility, and Singularities for the endpoint vocabulary; The Black-Hole Region and Future Null Infinity for the global causal definition; Schwarzschild and Reissner–Nordström for the coordinate and extension calculations; and Gravitational Radiation in Linearized Theory for gauge, curvature, and detector response. Use Black-Hole Quantum Fields and Hawking Radiation for the state, collapse, detector, greybody, and backreaction distinctions.

The cards are lookup tools. Follow those pages when a definition or calculation will carry weight in a proof, numerical model, or physical interpretation.