KN metric component g_{00} as a lifted (r, θ) function
ProvedExactVacuumAtlas.EinsteinMaxwell.KN.g_fun_0_0einstein-maxwellexact-spacetime-atlas-ivexact-vacuum-atlasgeneral-relativity
KN metric component g_{00} as a lifted (r, θ) function
gKN M a Q at index (0, 0) equals liftRT of the displayed closed-form expression, rational in r, sin θ and cos θ (with M, a and Q fixed).
Scope. Exactly the hypotheses printed in the formal statement.
中文摘要 KN 度规分量的 (r,θ) 闭式。
Preamble
import Mathlib import Definitions.Def_Atlas_Core_Basic import Definitions.Def_Atlas_Core_Lift import Definitions.Def_Atlas_EinsteinMaxwell_Basic import Definitions.Def_Atlas_EinsteinMaxwell_KN_Defs import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain import Definitions.Def_Atlas_Kerr_InAtoms open Real open ExactVacuumAtlas open scoped ContDiff open ExactVacuumAtlas.Kerr.In (Ui Wi) open ExactVacuumAtlas open ExactVacuumAtlas.EinsteinMaxwell open ExactVacuumAtlas.EinsteinMaxwell.KN set_option maxHeartbeats 8000000 set_option maxRecDepth 100000 set_option linter.unusedVariables false set_option linter.unusedSimpArgs false set_option linter.unusedTactic false set_option linter.unreachableTactic false variable (M a Q : ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.g_fun_0_0 : gKN M a Q 0 0 = liftRT (fun r θ => ((2:ℝ) * M) * r * Ui a r θ + ((1:ℝ) * a^2) * sin θ ^ 2 * Ui a r θ + ((-1:ℝ) * a^2) * Ui a r θ + ((-1:ℝ) * Q^2) * Ui a r θ + ((-1:ℝ)) * r ^ 2 * Ui a r θ) := by sorry
Source
He Wang, Exact Spacetime Atlas IV: Certified Einstein–Maxwell Backgrounds and First Variations. Local source, no public repository; commit 543904bfcfa3bb169f43fc4d9dbd569999b71886; Atlas/EinsteinMaxwell/KN/Tables.lean#L28-L33; SHA-256 82a10a4f76cd734d52eeb263411fc37d6c5cd44401612f53bdcd45891d6d7739. Registered definitions and literature: mission/PHYSICS_BOUNDARY.md (§H–§J); Müller–Grave arXiv:0904.4184; Newman et al., J. Math. Phys. 6 (1965) 918.
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.