Abstract We study the energy–momentum characteristics of the rotating black hole–Kerr solution of general relativity in the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR). The previously constructed spacetime-covariant and Lorentz-invariant expressions for conserved Noether currents, superpotentials, and charges are used. The Noether charges describe the total energy, momentum, or angular momentum of a gravitational system depending on the choice of displacement vector $$\xi $$ ξ . To define the covariant and invariant conserved quantities in both TEGR and STEGR, one needs to use external fields which are flat teleparallel connections. To determine the non-dynamical connections in TEGR and STEGR, we use the unified “turning-off” gravity principle. In addition, to analyze the Noether conserved quantities in these theories, we use the concept of “gauges.” Changes in the gauge can affect the Noether conserved quantities. We highlight two ways to turn off gravity—by $$M \rightarrow 0$$ M → 0 and by $$M \rightarrow 0, ~ a \rightarrow 0$$ M → 0 , a → 0 —which give us different gauges in TEGR and STEGR. In both kinds of gauges, we obtain the expected values of black hole mass and angular momentum. Our attempts to find gauges which could lead to a correspondence to Einstein’s equivalence principle for the Kerr solution were unsuccessful in both TEGR and STEGR. However, these exercises helped us to find a related gauge for the Schwarzschild solution in STEGR that is a novel finding.

We study the energy–momentum characteristics of the plane “+”-polarized gravitational wave solution of general relativity in the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR) using the previously constructed Noether currents. The current components describe energy–momentum locally measured by an observer if the displacement vector ξ is equal to the observer’s 4-velocity. To determine the non-dynamical connection in these theories, we use the unified “turning off” gravity principle. For a constructive analysis of the values of Noether currents and superpotentials in TEGR and STEGR, we use the concept of “gauges”. The gauge changing can affect the Noether current values. We study under what conditions the Noether current for the freely falling observer is zero. When they are established, the zero result can be interpreted as a correspondence to the equivalence principle, and it is a novelty for gravitational waves in the TEGR and STEGR. We highlight two important cases with positive and zero energy, which reproduce the results of previous works with a different approach for determining gravitational energy–momentum in the TEGR, and give their interpretation.

We derive conservation laws in Symmetric Teleparallel Equivalent of General Relativity (STEGR) with direct application of Noether’s theorem. This approach allows us to construct covariant conserved currents, corresponding superpotentials and invariant charges. A necessary component of our constructions is the concept of “turning off” gravity, introduced in the framework of STEGR to define the flat and torsionless connection. By calculating currents, one can obtain local characteristics of gravitational field like energy density. Surface integration of superpotentials gives charges which correspond to global quantities of the system like mass, momentum, etc. To test our results for the obtained currents and superpotentials, we calculate the energy density measured by freely falling observer in the simple solutions (Friedman universe, Schwartzchild black hole) and total mass of the Schwartzchild black hole. We find ambiguities in obtaining the connection, which explicitly affect the values of conserved quantities, and discuss possible solutions to this problem.

A presentation of the Vaidya type Schwarzschild-like black holes with flat, AdS and dS asymptotics in 4-dimensional general relativity in the form of a pointlike mass is given. True singularities are described by making the use of the Dirac δ -function in a non-contradictory way. The results essentially generalize previous derivations where the usual Schwarzschild black hole solution is represented in the form of a point particle. The field-theoretical formulation of general relativity, which is equivalent to its standard geometrical formulation, is applied as an alternative mathematical formalism. Then perturbations on a given background are considered as dynamical fields propagating in a given (fixed) spacetime. The energy (mass) distribution of such field configurations is just represented as a point mass. The new description of black holes’ structure can be useful in explaining and understanding their features and can be applied in calculations with black hole models. A possibility of application of the field-theoretical formalism in studying the regular black hole solutions is discussed.

We study the energy-momentum characteristics of the plane ''+''-polarised gravitational wave solution of general relativity in the Teleparallel Equivalent of General Relativity (TEGR) and the Symmetric Teleparallel Equivalent of General Relativity (STEGR) using the previously constructed Noether currents. These currents can describe locally measured by observer energy-momentum if the displacement vector $\xi$ is equal to the observer's 4-velocity. To determine the non-dynamical connection in these theories we use the unified ''turning off'' gravity principle. For a constructive analysis of the values of Noether currents and superpotentials in TEGR and STEGR, we use the concept of ''gauges''. The gauge changing can affect the Noether current values. We study under what conditions the Noether current for the freely falling observer is zero because this can be interpreted as the equivalence principle. We highlight two important cases with positive and zero energy, which reproduce the results of previous works with a different approach to determine gravitational energy-momentum in TEGR, and give their interpretation.

It is the first article of the two ones related to the Sagnac effect, the one of the main relativistic effects to be taken into account for synchronization of clocks in working global navigation satellite systems. Its sense consists of retarding/advancing signals propagating in opposite directions at the perimeter of a rotating disc. In the present article its theoretic foundation is given both within the framework of a kinematical effect in special relativity and in that of general relativity, where the effect is analyzed as a result of centrifugal forces potential’s action. Besides, in both the theories two various approaches are applied. This enables delving into physical sense of the phenomenon. This theoretical presentation is used in the second article of the series to outline the effect under real conditions at location on the surface of rotating Earth, when optical fiber link is used for synchronization of atomic clocks.

A problem of an ambiguity in constructing conserved quantities in the framework of Teleparallel Equivalent of General Relativity is considered. A formalism based on the Noether procedure for constructing conserved currents and which is covariant with respect to both coordinate and local Lorentz transformations is studied. As a model for applications, a Schwarzschild black hole moving with constant velocity (with respect to distant static observers) is considered, for which conserved total energy and momentum are calculated. To avoid an ambiguity in such calculations an appropriate gauge defined by a pair of tetrad and related inertial spin connection has to be defined. Such a gauge is found and, as a result, acceptable (reasonable and unambiguous) conserved quantities are obtained. The found gauge is compared with previous ones. The results are related also to those obtained in the framework of well known Brown-York’s and Arnowitt-Deser-Misner’s formalisms.

Abstract We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $$\xi $$ ξ and we consider two different options where $$\xi $$ ξ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained generalised freely falling frame with an arbitrary initial velocity. We also demonstrate how to determine an inertial spin connection for various tetrads used in our calculations, and find a certain ambiguity in the “switching-off” gravity method where different tetrads can share the same inertial spin connection.

We construct conserved quantities in pure Lovelock gravity for both static and dynamic Vaydia-type black holes with anti-de Sitter, de Sitter and flat asymptotics, applying field-theoretical formalism developed earlier. Global energy (where applicable), quasi-local energy together with fluxes of these quantities are presented for both types of black holes, considering asymptotic spacetime as background. The same quantities are constructed for dynamic black holes on the background of the related static black holes. Besides, for the dynamic black holes, energy densities and densities of energy flux are calculated in the frame of freely and radially falling observer on the background of the related static black holes. All the constructed energetic characteristics are analyzed and discussed in detail.

Possibilities of the covariant with respect to both coordinate and local Lorentz transformations formalism developed earlier in the framework of Teleparallel Equivalent of General Relativity (TEGR) are studied. The formalism is applied to a solution for a moving with constant velocity (with respect to distant static observers) Schwarzschild black hole. Coordinate and Lorentz invariant global conserved mass and momentum are constructed. The acceptable results are obtained in spite of the solution under consideration has no, at least, Killing vectors of space displacements. Calculations are quite analogous to calculating the mass and momentum of a moving matter ball in Minkowski space, and this analogy is used essentially.

The field-theoretical methods are used to construct conserved currents and related superpotentials for perturbations on arbitrary backgrounds in the Lovelock gravity. The perturbations are considered as a dynamic field configuration propagating in a given spacetime. The field-theoretical formalism is exact (without approximations) and equivalent to the original metric theory. As Lagrangian based formalism, it allows us to apply the Noether theorem. As a result, we construct conserved currents and superpotentials, where we use arbitrary displacement vectors, not only the Killing ones or other special vectors. The developed formalism is checked in calculating mass of the Schwarzschild-anti-de Sitter (AdS) black hole. The new formalism is adopted to the case of a so-called pure Lovelock gravity, where in the Lagrangian only a one polynomial in Riemannian tensor presents. We construct conserved charges and currents for static and dynamic black holes of the Vaidya type with AdS, dS and flat asymptotics. New properties of the solutions under consideration have been found. The more results are discussed. The first section in your paper

GR and other metric theories of gravity are formulated with an arbitrary auxiliary curved background in a Lagrangian formalism. A new sketch of how to include spinor fields is included. Conserved quantities are obtained using Noether's theorem and expressed as divergences of antisymmetric densities, connecting local perturbations with quasi-local conserved quantities. The background's arbitrariness matches the so-called non-localizability of gravitational energy (infinity of localizations). The formalism has two partly overlapping uses: practical applications of pure GR (with fictitious background) and foundational considerations in which background causality facilitates quantization. The Schwarzschild solution is a primary application. Various possibilities for calculating the mass using surface integration are given. A field-theoretic curved spacetime is given from spatial infinity to the horizon and even to the true singularity. Trajectories of test particles in the Schwarzschild geometry are gauge-dependent in that even breakdowns at the horizon can be suppressed (or generated) by naive gauge transformations. This fact illustrates the auxiliary nature of the background metric and the need for some notion of maximal extension---much as with coordinate transformations in geometric GR. A continuous collapse to a point mass in the field-theoretic framework is given. The field-theoretic method is generalized to arbitrary metric theories in $D$ dimensions. The results are developed in the framework of Lovelock gravity and applied to calculate masses of Schwarzschild-like black holes. The bimetric formalism makes it natural to consider a graviton mass. Babak and Grishchuk's numerical and hence nonperturbative work sheds light on questions of a (dis)continuous massless limit for massive pure spin-2 and the classical (in)stability of spin-2/spin-0 theory.

The fault response of superconducting cables is of significant importance to their wider adoption in power grids. In particular, it is useful to understand how to most efficiently and accurately simulate the fault response and time of recovery after a high through fault overcurrent. To achieve that, rigorous modeling techniques must be established, which is done over several steps. A successful numerical model of magnetic field dependent behaviour of a Bi-2223 superconducting tape has been demonstrated. This model has been used to redefine and verify a homogenization technique for multifilamentary tapes that decreases the computation time by simplifying the geometry with a minimum to no accuracy penalty. Afterwards, the simulation of AC power losses in twisted tapes and cables is investigated, with reference models coming from literature and custom-built 3D models. The investigation produced methods to efficiently estimate the losses of multi-layer twisted in 2D FEM without resorting to 3D. Finally by capitalizing on the techniques established prior, a multiphysics model is built — electro-magneto-thermal — in three different space domains in order to simulate the AC losses, temperature and heat transfer in all important cable components. It is shown this type of complex multiphysics model can be set up to run and may produce fairly accurate results. One FEM simulation of the multiphysics model takes no more than 3 days to complete on a standard PC.

Applying directly the Noether theorem in the framework of the Teleparallel Equivalent of General Relativity (TEGR), we construct conserved quantities, currents and superpotentials. They are covariant both under coordinate transformations and under local Lorentz rotations, unlike earlier approaches. This advantage is achieved by a presence in expressions of conservation laws of a displacement vector that can be interpreted as a Killing vector, as a proper vector of an observer, etc. We introduce, as well, a principle for a definition of an inertial spin connection that is an undetermined quantity in TEGR in the original formulation. The new expressions for conserved quantities and the introduced principle are applied to calculate mass for the Schwarzschild black hole and energy density for an observer freely falling in spatially flat Friedmann world.

We study the teleparallel equivalent of general relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether theorem, we construct new expressions for conserved currents and related superpotentials. They are covariant both under coordinate transformations and local Lorentz rotations, and allow us to construct well defined conserved charges, unlike earlier approaches. The advantage is achieved by an explicit presence of a displacement vector in the new expressions that can be interpreted as a Killing vector, as a proper vector of an observer, etc. The new expressions are used to introduce a principle for definition of an inertial spin connection that is undetermined one in the TEGR from the start. Theoretical results are applied to calculate mass for the Schwarzschild black hole and densities of conserved quantities for freely falling observers both in Friedmann–Lemaître–Robertson–Walker world of all the three signs of curvature and in (anti-)de Sitter space.

Conserved currents and related superpotentials for perturbations on arbitrary backgrounds in the Lovelock theory are constructed. We use the Lagrangian based field-theoretical method where perturbations are considered as dynamical fields propagating on a given background. Such a formulation is exact (not approximate) and equivalent to the theory in the original metric form. From the very start, using Noether theorem, we derive the Noether–Klein identities and adopt them for the purposes of the current work. Applying these identities in the framework of Lovelock theory, we construct conserved currents, energy-momentum tensors out of them, and related superpotentials with arbitrary displacement vectors, not restricting to Killing vectors. A comparison with the well known Abbott–Deser–Tekin approach is given. The developed general formalism is applied to give conserved quantities for perturbations on anti-de Sitter (AdS) backgrounds. As a test we calculate mass of the Schwarzschild–AdS black hole in the Lovelock theory in arbitrary D dimensions. Proposals for future applications are presented.

The general manifestly generally covariant formalism for constructing the conservation laws and the conserved quantities in arbitrary metric-torsion theories of gravitation, which recently has been elaborated by the authors, is presented.

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a D-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a (D-2)-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.

An original way of presentation of the Schwarzschild black hole in the form of a point-like mass with making the use of the Dirac \(\delta \)-function, including a description of a continuous collapse to such a point mass, is given. A maximally generalized description restricted by physically reasonable requirements is developed. A so-called field-theoretical formulation of general relativity, being equivalent to the standard geometrical presentation of general relativity, is used. All of the dynamical fields, including the gravitational field, are considered as propagating in a background (curved or flat) spacetime. Namely these properties allow us to present a non-contradictive picture of the point mass description. The results can be useful for studying the structure of the black hole true singularities and could be developed for practical calculations in models with black holes.

The balanced methodology for assessing the Technology Project Readiness Level for commercialization (TPRL) is proposed. TPRL allows to determine the dynamics and balance of development projects that use the standardized approaches used in assessing the readiness of the technology. Validation of the methodology undertaken for the projects of Federal target programs “Research and development on priority directions of development of scientific-technological complex of Russia for 2007–2013” and “Research and development on priority directions of development of scientific-technological complex of Russia for 2014–2020”. The obtained results showed the possibility of application of the methodology for the evaluation of projects, improving efficiency of expert activity in the evaluation of projects, monitoring the status of individual project and group of projects (portfolio). The application of the methodology allowed us to improve the management of individual project and portfolio of projects. Methodology TPRL will allow the implementers, industry partners, investors, and innovative industrial companies to improve the efficiency of its activities.