2002/01/31 by Vadim Borokhov
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Curvature #Einstein tensor #Energy–momentum relation #Exact solutions in general relativity #Geometry #Lanczos tensor #Mathematical physics #Mathematics #Physics #Quantum mechanics #Riemann curvature tensor #Solar and Space Plasma Dynamics #Stress–energy tensor #Symmetric tensor #Tensor (intrinsic definition) #Tensor contraction #Tensor density #Tensor field #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.65.125022
published as Phys.Rev. D65 (2002) 125022 · 10 pages, LaTex; misprints corrected, references added; to appear in Physical Review D
arxiv created 2002/06/03 · openalex publication_date 2002/06/17 · arxiv updated 2020/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that any generally covariant coupling of matter fields to gravity gives rise to a conserved, on-shell symmetric energy-momentum tensor equivalent to the canonical energy-momentum tensor of the flat-space theory. For matter fields minimally coupled to gravity our algorithm gives the conventional Belinfante tensor. We establish that different matter-gravity couplings give metric energy-momentum tensors differing by identically conserved tensors. We prove that the metric energy-momentum tensor obtained from an arbitrary gravity theory is on-shell equivalent to the canonical energy-momentum tensor of the flat-space theory.