Black Hole Ontology

FLOW ALGEBRA
BLACK HOLE ONTOLOGY — v1.1
Kireth Semantic Library | Entity Graph > Physical Entities > Astronomical Entities
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/astronomical-entities/black-hole-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Status: Independent scientific synthesis; source page not independently verified.
Date: 2026-10-12

01 | PURPOSE
Represent black holes, horizons, spacetime geometries, observations and theoretical claims as typed, qualified, machine-readable relationships. Distinguish directly observed evidence, model-dependent inferences and unresolved physics.

02 | ROOT TYPES
ENTITY: PhysicalEntity
ENTITY: AstronomicalEntity <: PhysicalEntity
ENTITY: CompactObject <: AstronomicalEntity
ENTITY: BlackHole <: CompactObject
ENTITY: StellarMassBlackHole <: BlackHole
ENTITY: IntermediateMassBlackHole <: BlackHole
ENTITY: SupermassiveBlackHole <: BlackHole
ENTITY: PrimordialBlackHoleCandidate <: BlackHole [hypothetical]
ENTITY: EventHorizon <: CausalBoundary
ENTITY: ApparentHorizon <: QuasiLocalBoundary
ENTITY: AccretionDisc <: AstrophysicalStructure
ENTITY: RelativisticJet <: AstrophysicalOutflow
ENTITY: GravitationalWave <: SpacetimePerturbation
ENTITY: SpacetimeMetric <: MathematicalField
ENTITY: Observation <: EvidenceRecord
ENTITY: Model <: ScientificModel

03 | CORE DEFINITION
BlackHole(B) := spacetime region from which no future-directed causal curve reaches future null infinity, when that asymptotic notion is well-defined.
NOTE: Event horizons are global causal boundaries; local trapped surfaces and apparent horizons are not generally interchangeable with them.

04 | TYPED PROPERTIES
mass: BlackHole -> Mass [kg]
angular_momentum: BlackHole -> AngularMomentum [kg m^2 s^-1]
electric_charge: BlackHole -> ElectricCharge [C]
spin_parameter: BlackHole -> DimensionlessReal
position: AstronomicalEntity -> CoordinateRecord
redshift: Observation -> DimensionlessReal
metric: Model -> SpacetimeMetric
horizon: BlackHole -> EventHorizon [model-dependent]
formation_channel: BlackHole -> FormationHypothesis
observation_status: Claim -> {measured,inferred,predicted,hypothetical,unknown}
uncertainty: Measurement -> NonnegativeReal

05 | RELATIONSHIPS
IS_A(BlackHole,CompactObject)
HAS_MASS(BlackHole,Mass)
HAS_SPIN(BlackHole,AngularMomentum)
HAS_HORIZON(BlackHole,EventHorizon)
CURVES_SPACETIME(BlackHole,Spacetime)
ACCRETES_FROM(BlackHole,AccretionFlow) [optional]
MAY_POWER(AccretingBlackHole,RelativisticJet)
ORBITS(Companion,BlackHole) [conditional]
MERGES_WITH(BlackHole,BlackHole) [event-dependent]
PRODUCES(Merger,GravitationalWave)
SUPPORTED_BY(ScientificClaim,Observation)
DERIVED_USING(ScientificClaim,Model)

06 | CLASSIFICATION
Stellar-mass: typically produced by stellar collapse or compact-object mergers.
Intermediate-mass: mass range between stellar and supermassive populations; boundaries are conventional.
Supermassive: commonly millions to billions of solar masses at galactic centres.
Primordial: proposed early-universe origin; not established as an observed population.
CLASSIFICATION_RULE: Do not infer formation channel solely from mass.

07 | SCHWARZSCHILD MODEL
ASSUME: isolated, uncharged, nonrotating, asymptotically flat black hole.
r_s = 2 G M / c^2
G = 6.67430e-11 m^3 kg^-1 s^-2
c = 299792458 m s^-1
M > 0
TYPECHECK: [G M / c^2] = m
INFERENCE: mass increase implies Schwarzschild radius increase within model.

08 | KERR MODEL
ASSUME: stationary, uncharged, rotating, asymptotically flat classical solution.
a = J/(M c) [length]
a_star = c J/(G M^2) [dimensionless]
r_plus = G M/c^2 + sqrt((G M/c^2)^2 - a^2)
HORIZON_CONDITION: |a_star| <= 1
NOTE: Astrophysical black holes are often approximated by Kerr, not guaranteed to match exactly in dynamic environments.

09 | ELECTRICALLY CHARGED MODELS
Reissner–Nordström: nonrotating charged classical solution.
Kerr–Newman: rotating charged classical solution.
NOTE: Large persistent net electric charge is not normally expected for astrophysical black holes; do not assume Q=0 as a universal theorem.

10 | CAUSAL STRUCTURE
EVENT_HORIZON: global causal boundary.
ERGOSPHERE: rotating-spacetime region where stationary observers relative to infinity cannot remain static.
SINGULARITY: feature of classical general-relativistic solutions; a physical description requires care where classical theory breaks down.
RULE: ergosphere != event horizon.
RULE: photon sphere != event horizon.

11 | GEODESICS AND ORBITS
A test particle follows a timelike geodesic absent non-gravitational forces.
Light follows null geodesics in geometric optics.
ISCO depends on spin and orbital orientation for Kerr spacetime.
RULE: orbital speed and stability must be computed in a specified metric and frame.

12 | ACCRETION
Accretion can convert gravitational binding energy into radiation.
L = eta * Mdot * c^2 [simplified radiative-efficiency model]
eta is dimensionless; Mdot in kg/s.
NOTE: Efficiency depends on accretion geometry, spin and physical conditions.
RULE: a black hole itself need not emit light for surrounding accreting matter to radiate.

13 | EDDINGTON LUMINOSITY
L_Edd = 4 pi G M m_p c / sigma_T
ASSUME: spherical steady ionised-hydrogen flow, Thomson scattering approximation.
NOTE: Not a universal hard luminosity cap; geometry and opacity matter.

14 | GRAVITATIONAL WAVES
Compact-binary inspiral, merger and ringdown can produce gravitational radiation.
INFERENCE: waveform -> component masses and spins [conditional on waveform model, calibration and priors].
RULE: measured strain is not a direct image of an event horizon.

15 | BLACK HOLE SHADOW
A shadow-like brightness depression can arise from strong lensing and emitting plasma geometry.
INFERENCE: interferometric image -> constraints on compact-object scale and emission model.
RULE: observed shadow != literal photograph of the event horizon.

16 | HAWKING RADIATION
For a nonrotating uncharged black hole in semiclassical treatment:
T_H = hbar c^3 / (8 pi G M k_B)
ASSUME: semiclassical quantum fields on classical curved spacetime.
STATUS: theoretical prediction; astrophysical Hawking radiation not directly detected.
RULE: temperature inversely proportional to mass under stated assumptions.

17 | ENTROPY
S_BH = k_B c^3 A / (4 G hbar)
A is horizon area [m^2].
STATUS: semiclassical black-hole thermodynamics.
NOTE: microscopic interpretation and information recovery remain research topics.

18 | EVAPORATION
Simplified lifetime scaling for isolated, neutral, nonrotating black hole: t_evap proportional to M^3.
Do not apply approximate lifetime without emission species, environmental accretion and validity assumptions.

19 | FORMATION CHANNELS
Massive stellar core collapse [model-dependent].
Neutron-star or black-hole mergers [supported for some systems].
Direct collapse and accretion growth [candidate pathways for massive seeds].
Primordial formation [hypothetical].
RULE: candidate mechanism != verified historical origin of individual object.

20 | OBSERVATIONAL EVIDENCE
Stellar and gas orbital dynamics.
X-ray binaries and accretion signatures.
Gravitational-wave detections from compact mergers.
Very-long-baseline interferometric observations of compact galactic nuclei.
RULE: each evidence claim requires instrument, date, uncertainty and model context.

21 | MATHEMATICAL OPERATIONS
SCHWARZSCHILD_RADIUS(M): requires M > 0.
DIMENSIONLESS_SPIN(M,J): requires M > 0.
EDDINGTON_LUMINOSITY(M): requires assumptions in section 13.
HAWKING_TEMPERATURE(M): requires assumptions in section 16.
CLASSIFY_MASS(M): returns convention-dependent category and threshold provenance.

22 | WORKED EXAMPLE — SCHWARZSCHILD RADIUS
INPUT: M = 1 solar mass = 1.98847e30 kg.
COMPUTE: r_s = 2*6.67430e-11*1.98847e30/(299792458^2)
OUTPUT: approximately 2.953 km.
CHECK: radius scales linearly with M for the Schwarzschild model.

23 | WORKED EXAMPLE — SPIN
INPUT: J = 0, M > 0.
COMPUTE: a_star = 0.
INFER: Kerr model reduces to Schwarzschild when charge is also zero.
CHECK: no assumption about astrophysical prevalence follows.

24 | INFERENCE RULES
R01: BlackHole(x) -> CompactObject(x).
R02: Schwarzschild(x) AND Mass(x,M) -> Radius(x,2GM/c^2).
R03: Kerr(x) AND |a_star(x)|<=1 -> HorizonRadius(x,r_plus) [classical idealisation].
R04: MergerEvent(e) AND CompactBinary(e) -> CandidateGravitationalWaveSource(e).
R05: ObservedEmission(d) AND AccretionModel(d,x) -> EvidenceForAccretion(x), NOT ProofOfHorizon(x).
R06: TheoryPrediction(HawkingRadiation) -> NOT DirectDetection(HawkingRadiation).
R07: EvidenceFor(x,c) AND Confidence(c,p) -> PreserveUncertainty(x,p).
R08: DifferentCoordinateSystems(a,b) -> RequireInvariantComparison(a,b).

25 | CONSTRAINTS
C01: M > 0 for black-hole mass parameters.
C02: Distances, masses, times and temperatures must carry units.
C03: A dimensionless spin is not the dimensional Kerr parameter a.
C04: Inferred mass is not identical to a direct measurement.
C05: Event-horizon properties must state model assumptions.
C06: Quantum-gravity conjectures must not be labelled experimentally established.
C07: Superluminal escape claims must not be inferred from coordinate artefacts.

26 | SEMANTIC_EQUIVALENCE
"black hole" ~ "black-hole spacetime region" [context-dependent].
"Schwarzschild radius" ~ "Schwarzschild horizon areal radius" [specified model].
"spin parameter" ambiguous: resolve a versus a_star.
NOT_EQUIVALENT(event_horizon,apparent_horizon).
NOT_EQUIVALENT(black_hole_shadow,event_horizon).
NOT_EQUIVALENT(black_hole,accretion_disc).

27 | CONFIDENCE
CONFIDENCE.type = epistemic status, not an invented numerical certainty.
Established: general-relativistic black-hole evidence and gravitational-wave observations.
Model-dependent: inferred masses, spins, accretion efficiencies, horizon imaging interpretations.
Theoretical: Hawking radiation and semiclassical entropy.
Hypothetical: primordial black-hole population, specific quantum-gravity interiors.

28 | PROVENANCE
For each claim store: source_id, publication_date, method, model, measured_quantity, uncertainty, status, review_date.
Do not promote unverified webpage assertions to empirical facts.

29 | VALIDATION TESTS
TEST_01: Schwarzschild radius at solar mass within rounding of 2.953 km -> PASS.
TEST_02: Units of GM/c^2 are length -> PASS.
TEST_03: a_star dimensionless -> PASS.
TEST_04: Horizon and ergosphere are distinct -> PASS.
TEST_05: Hawking radiation status remains theoretical prediction -> PASS.
TEST_06: Unknown formation channel does not trigger false classification -> PASS.
TEST_07: All required sections and END marker present -> PASS.

30 | FLOW_HASH
FLOW_HASH.algorithm = SHA-256
FLOW_HASH.scope = canonical UTF-8 content excluding mutable hash value
FLOW_HASH.value = COMPUTE_ON_PUBLICATION
FLOW_HASH.note = Never invent a digest; calculate after final canonicalisation.

31 | UPDATE_MODEL
Version = 1.1
Update triggers: new observational constraints, revised physical constants, major theory advances, ontology schema changes.
Update steps: ingest -> verify -> classify evidence -> validate dimensions -> compare semantics -> version -> compute hash -> publish.
Preserve historical revisions and provenance.

32 | AI_CONSUMPTION
input: natural-language question | structured observation | ontology triple.
resolve: entity identity, units, physical model, evidence status.
reason: apply typed inference with assumptions and uncertainty.
output: conclusion, derivation, units, model, confidence status, provenance.
forbidden: invent measurements, conflate hypotheses with detections, silently drop conditions.

33 | COMPLETENESS CHECK
Required sections: 01 through 33.
Section sequence: complete.
Closing marker: present.
Scientific scope: black-hole ontology and related models, not an assertion of a complete quantum-gravity theory.

END FLOW ALGEBRA — BLACK HOLE ONTOLOGY v1.1