81. Contracted Bianchi Identities and Energy Tensor

The  contracted Bianchi identities in the Riemannian geometry are not equivalent to the covariant derivatives of energy tensor in Albert Einstein's theory of general relativity. Both Kerr metric and Schwarzschild metric show that the energy tensor for vacuum is not always zero. The metric contradicts the theory of general relativity by proving that energy momentum tensor is not covariant.

Mainstream physics supplements GR (General Relativity) with additional assumptions, producing an augmented theory which can be called GR2. In GR2, the stress–energy tensor is defined externally by matter fields, such as:

• electromagnetic fields,

• perfect fluids,

• scalar fields,

• quantum fields,

• dark matter and dark energy models.

These stress–energy tensors are inserted into the Einstein equation by hand. They do not arise from the geometry of spacetime and therefore do not integrate with GR. Every External Stress–Energy Tensor Has Failed to Integrate. Examples include:

• the electromagnetic stress–energy tensor,

• fluid and hydrodynamic stress–energy tensors,

• scalar field stress–energy tensors,

• quantum field stress–energy tensors (divergent and renormalization-dependent),

• dark matter and dark energy stress–energy tensors.

None of these arise from geometry, and none unify with gravity. They coexist with GR but do not integrate into it.