The Physics Society of Iran Iranian Journal of Physics Research 1682-6957 25 3 2025 12 22 Comparison of tensor and vector theories of gravitation Comparison of tensor and vector theories of gravitation 61 87 3636 10.47176/ijpr.25.1.01981 FA Sergey Fedosin Perm State University: Permskij gosudarstvennyj nacional'nyj issledovatel'skij universitet, 614990, Bukireva 15, Perm, Russian Federation Journal Article 2024 10 02 Physical quantities in continuously distributed matter in curved spacetime, and equations for matter and fields are considered both from the point of view of tensor theory of gravitation and on the basis of vector theory of gravitation. An example in the first case is the general theory of relativity (GTR), which uses a scalar pressure field and a scalar acceleration field. In the second case, relativistic vector fields are taken into account, including the covariant theory of gravitation, the pressure vector field and the acceleration vector field. To analyze and compare the results in each approach, formulas derived from the principle of least action and from the corresponding Lagrangian are used. The problem of correlating scalar pressure with the principle of least action in the general relativity is considered. The conclusion is drawn that results of the general relativity, when scalar pressure is taken into account, are valid for relativistic uniform systems, but in a more general case, they require correction. Three versions of general relativity were analyzed: GTR¹, GTR² and GTR^m. The GTR¹ version is the closest version to the standard general theory of relativity, the GTR² version follows exactly the principle of least action, and the GTR^m version is characterized by the fact that the acceleration field and pressure field are represented not as scalar fields but as vector fields. Equations for metric, equations of motion, equations for fields, formulas for the energy and momentum, which follow from the Lagrangian formalism, are presented for all versions of general relativity. An explanation is given of where dark energy comes from and what it is whithin general relativity. Physical quantities in continuously distributed matter in curved spacetime, and equations for matter and fields are considered both from the point of view of tensor theory of gravitation and on the basis of vector theory of gravitation. An example in the first case is the general theory of relativity (GTR), which uses a scalar pressure field and a scalar acceleration field. In the second case, relativistic vector fields are taken into account, including the covariant theory of gravitation, the pressure vector field and the acceleration vector field. To analyze and compare the results in each approach, formulas derived from the principle of least action and from the corresponding Lagrangian are used. The problem of correlating scalar pressure with the principle of least action in the general relativity is considered. The conclusion is drawn that results of the general relativity, when scalar pressure is taken into account, are valid for relativistic uniform systems, but in a more general case, they require correction. Three versions of general relativity were analyzed: GTR¹, GTR² and GTR^m. The GTR¹ version is the closest version to the standard general theory of relativity, the GTR² version follows exactly the principle of least action, and the GTR^m version is characterized by the fact that the acceleration field and pressure field are represented not as scalar fields but as vector fields. Equations for metric, equations of motion, equations for fields, formulas for the energy and momentum, which follow from the Lagrangian formalism, are presented for all versions of general relativity. An explanation is given of where dark energy comes from and what it is whithin general relativity. https://ijpr.iut.ac.ir/article_3636_48042b1dae4950fef2bd2aafa0b971a1.pdf