recognition /
Gravity /
Gravity.RicciTensor /
explainer
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formal statement (Lean)
65 noncomputable def einstein_tensor
66 (met : MetricTensor) (ginv : InverseMetric)
67 (gamma : Idx → Idx → Idx → ℝ)
68 (dgamma : Idx → Idx → Idx → Idx → ℝ)
69 (mu nu : Idx) : ℝ :=
proof body
Definition body.
70 ricci_tensor gamma dgamma mu nu -
71 (1/2) * scalar_curvature ginv gamma dgamma * met.g mu nu
72
73 /-- Einstein tensor vanishes for flat spacetime. -/
used by (10)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (15)
Lean names referenced from this declaration's body.
gamma
in IndisputableMonolith.Constants.EulerMascheroni
decl_use
mu
in IndisputableMonolith.Cost.Ndim.Projector
decl_use
MetricTensor
in IndisputableMonolith.Foundation.Hamiltonian
decl_use
for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
decl_use
Idx
in IndisputableMonolith.Gravity.Connection
decl_use
InverseMetric
in IndisputableMonolith.Gravity.Connection
decl_use
MetricTensor
in IndisputableMonolith.Gravity.Connection
decl_use
ricci_tensor
in IndisputableMonolith.Gravity.RicciTensor
decl_use
scalar_curvature
in IndisputableMonolith.Gravity.RicciTensor
decl_use
MetricTensor
in IndisputableMonolith.Meta.Homogenization
decl_use
gamma
in IndisputableMonolith.NetworkScience.SmallWorldFromSigma
decl_use
einstein_tensor
in IndisputableMonolith.Relativity.Geometry.Curvature
decl_use
ricci_tensor
in IndisputableMonolith.Relativity.Geometry.Curvature
decl_use
MetricTensor
in IndisputableMonolith.Relativity.Geometry.Metric
decl_use
gamma
in IndisputableMonolith.Relativity.ILG.PPN
decl_use