structure
definition
def or abbrev
MetricTensor
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formal statement (Lean)
39structure MetricTensor where
40 g : Idx → Idx → ℝ
41 symmetric : ∀ mu nu, g mu nu = g nu mu
42
43/-- The inverse metric g^{mu nu} (satisfying g^{mu rho} g_{rho nu} = delta^mu_nu). -/
used by (40)
-
energy_conservation -
HamiltonianDensity -
hamiltonian_equivalence -
H_EnergyConservation -
H_HamiltonianEquivalence -
inverse_metric -
IsTimeTranslationInvariant -
metric_det -
MetricTensor -
StressEnergyTensor -
TotalHamiltonian -
metric_compatibility -
minkowski -
hilbert_variation_holds -
jacobi_variation -
jacobi_variation_structural -
einstein_symmetric -
einstein_tensor -
sourced_efe_coord -
vacuum_efe_coord -
contracted_bianchi -
efe_with_source -
perfect_fluid -
vacuum_is_special_case -
H_HomogenizationLimit -
homogenization_limit -
metric_det -
MetricTensor -
metric_FRW -
einstein_hilbert_action