ИСТИНА

In [1], we have developed the approach for constructing conserved quantities in Teleparallel Equivalent of General Relativity (TEGR) where dynamical variables are tetrad components. The main advantage with respect to many other methods is that conserved currents and related superpotentials are coordinate covariant and invariant with respect to local Lorentz rotations of tetrads. This property is achieved due to introducing a special inertial spin connection (ISC) with zero curvature. The general problem of any teleparallel theory is that ISC is not inner dynamical quantity and can be determined by external requirements only. In [1], we define ISC by a special "turning off gravity" principle. The Schwarzschild black hole (SBH) solution is simple and describes real physical models, so, it is used for checking various formalisms in general relativity. Here, we test methods of [1] by calculating energy characteristics for SBH in TEGR. We are interested in the total (global) energy of SBH and the energy density measured by a freely falling observer in the field of SBH. There is a huge variety of different coordinates and frames for SBH that initiates different definitions of ISC even with using the "turning off gravity" principle. The different choice of ISC leads to the different results. The main goal of the research is searching for the most appropriate ISC for SBH. Starting from the standard Schwarzschild metric and deriving the related ISC, we obtain the correct SBH mass, but a freely falling observer measures non-zero energy density that contradicts the equivalence principle. Basing on the Lemaitre metric and its related ISC we have the consistence with the equivalence principle, but do not get the correct mass. Only after constructing new generalized Lemaitre metric (assuming the free falling with arbitrary energy) the problem has been resolved. The new ISC different from others has been found, and we got both the correct mass and compliance with the equivalence principle. The novelty is in the following: 1) the Lemaitre presentation has been used in TEGR firstly; 2) the new generalized Lemaitre metric has been constructed; 3) the generalized Lemaitre presentation in TEGR has resolved the aforementioned outstanding problems; 4) the definitions of ISC in TEGR and in f(T) theories are compared; 5) the results help us to understand more on the SBHs themselves. [1] E.D. Emtsova, A.N. Petrov, A.V. Toporensky 1) J. Physics: Conference Series, 1557, 012017 (2020); 2) Class. Quantum Grav., 37, 095006 (2020).