recognition /
Gravity /
Gravity.StressEnergyTensor /
explainer
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formal statement (Lean)
61 def efe_with_source (met : MetricTensor) (ginv : InverseMetric)
62 (gamma : Idx → Idx → Idx → ℝ)
63 (dgamma : Idx → Idx → Idx → Idx → ℝ)
64 (Lambda kappa : ℝ) (T : StressEnergy) : Prop :=
proof body
Definition body.
65 ∀ mu nu : Idx,
66 einstein_tensor met ginv gamma dgamma mu nu + Lambda * met.g mu nu =
67 kappa * T.T mu nu
68
69 /-- Vacuum EFE is a special case with T = 0. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (21)
Lean names referenced from this declaration's body.
gamma
in IndisputableMonolith.Constants.EulerMascheroni
decl_use
mu
in IndisputableMonolith.Cost.Ndim.Projector
decl_use
T
in IndisputableMonolith.Foundation.Breath1024
decl_use
MetricTensor
in IndisputableMonolith.Foundation.Hamiltonian
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
T
in IndisputableMonolith.Gap45.SyncMinimization
decl_use
Idx
in IndisputableMonolith.Gravity.Connection
decl_use
InverseMetric
in IndisputableMonolith.Gravity.Connection
decl_use
MetricTensor
in IndisputableMonolith.Gravity.Connection
decl_use
einstein_tensor
in IndisputableMonolith.Gravity.RicciTensor
decl_use
StressEnergy
in IndisputableMonolith.Gravity.StressEnergyTensor
decl_use
kappa
in IndisputableMonolith.Materials.ThermalConductivityRegimesFromPhiLadder
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
MetricTensor
in IndisputableMonolith.Meta.Homogenization
decl_use
gamma
in IndisputableMonolith.NetworkScience.SmallWorldFromSigma
decl_use
kappa
in IndisputableMonolith.NumberTheory.AnnularCost
decl_use
einstein_tensor
in IndisputableMonolith.Relativity.Geometry.Curvature
decl_use
MetricTensor
in IndisputableMonolith.Relativity.Geometry.Metric
decl_use
gamma
in IndisputableMonolith.Relativity.ILG.PPN
decl_use