arXiv subjects

A. N. Petrov

Publications and source records attributed to A. N. Petrov.

At least 19 recordsLinked to original sources

arXiv2026

The field-theoretical formalism for TEGR

The teleparallel equivalent of general relativity (TEGR) is represented in a field-theoretical form, where tetrad and matter perturbations are propagated on a background solution of TEGR. Thus, the background tetrad and metric satisfy the background Einstein field equations. This presentation, where perturbations can be finite (not infinitesimal or approximate), is equivalent to the original form of TEGR. The background can be arbitrary, usually corresponding to the solution of TEGR under consideration. Such a formalism is Lagrangian based, where perturbations are classified as dynamic fields, and varying the Lagrangian with respect to dynamic variables leads to the equations for perturbations. Gauge (inner) transformations are defined, and the gauge invariance of the Lagrangian and the field equations are stated. Applying the Noether theorem to the Lagrangian we construct conserved currents, related superpotentials and charges. As an application, we have considered linear gravitational equations on the Ricci-flat background and analyzed their properties, finally deriving gravitational wave equations and the tetrad perturbations in TT-gauge. By new formulae for charges, we have calculated the mass for the Schwarzschild and Kerr black holes and the angular momentum for the Kerr solution. The results are quite acceptable, which signals that the new formalism is powerful, can be used further, and has a potential for future development that can be applied to generalizations of TEGR.

gr-qc↗

arXiv2025

The Noether formalism for constructing conserved quantities in teleparallel equivalents of general relativity

This paper brings a methodological character where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). It was developed in series of our earlier works and, here, we unite it into a complete form. By employing the Noether method within a tensor formalism, conserved currents, superpotentials, and charges are constructed. These are shown to be covariant under coordinate transformations and local Lorentz rotations in TEGR, while in STEGR, they are covariant under coordinate transformations. The teleparallel (flat) connections in both theories are defined using the "turning off gravity" principle. Uniting such defined flat connections with tetrad in TEGR and metric in STEGR a new fruitful in applications notion "gauge" is introduced. The choice of various initial tetrads in TEGR or initial coordinates in STEGR leads to different gauges, what gives different conserved quantities. Finally, we discuss an appropriate choice of gauges from a possible set of them.

gr-qc↗

arXiv2025

Mass and angular momentum for the Kerr black hole in TEGR and STEGR

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 total energy, momentum or angular momentum of gravitating system depending on a choice of the displacement vector $ξ$. To define covariant and invariant conserved quantities both in TEGR and in STEGR on 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. Besides, to analyse the Noether conserved quantities in these theories, we use the concept of ``gauges''. The gauge changing can affect the Noether conserved quantities. We highlight two ways to turn off gravity - by $M \to 0$ and by $M \to 0 , ~ a \to 0$ which gives us different gauges in TEGR and STEGR. In both kind of gauges we get 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 where unsuccessful both in TEGR and STEGR. However, these exercises helped us to find a related gauge for the Schwarzschild solution in STEGR that is a novelty.

physics.gen-ph↗

arXiv2024

The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity

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. The current components describe locally measured by observer energy-momentum 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 of'' 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, zero result can be interpreted as a correspondence to the equivalence principle, and it is a novelty for gravitational waves in TEGR and STEGR. 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.

gr-qc↗

arXiv2023

Conserved quantities in STEGR and applications

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.

gr-qc↗

arXiv2023

Black holes of the Vaidya type with flat and (A)dS asymptotics as point particles

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.

gr-qc↗

arXiv2023

A moving black hole in TEGR as a moving matter ball

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.

gr-qc↗

arXiv2021

Electric-field-dependent $g$ factor for the ground state of lead monofluoride, PbF

The electric-field-dependent $g$ factor and the electron electric dipole moment (eEDM)-induced Stark splittings for the lowest rotational levels of $^{207,208}$PbF are calculated. Observed and calculated Zeeman shifts for $^{207}$PbF are found to be in very good agreement. It is shown that the $^{207}$PbF hyperfine sublevels provide a promising system for the eEDM search and related experiments.

physics.atom-ph↗

arXiv2021

Conserved quantities for black hole solutions in pure Lovelock gravity

We construct conserved quantities in pure Lovelock gravity for both static and dynamic Vaydia-type black holes with AdS, dS 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.

gr-qc↗

arXiv2021

On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity

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 $ξ$ and we consider two different options where $ξ$ 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 the 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.

gr-qc↗

arXiv2021

$\mathcal{P}$, $\mathcal{T}$-odd Faraday rotation in intracavity absorption spectroscopy with molecular beam as a possible way to improve the sensitivity of the search for the time reflection noninvariant effects in nature

The present constraint on the space parity ($\mathcal{P}$) and time reflection invariance ($\mathcal{T}$) violating electron electric dipole moment ($e$EDM) is based on the observation of the electron spin precession in an external electric field using the ThO molecule. We propose an alternative approach: observation of the $\mathcal{P}$,~$\mathcal{T}$-odd Faraday effect in an external electric field using the cavity-enhanced polarimetric scheme in combination with a molecular beam crossing the cavity. Our theoretical simulation of the proposed experiment with the PbF and ThO molecular beams shows that the present constraint on the $e$EDM in principle can be improved by a few orders of magnitude.

physics.atom-ph↗

arXiv2020

The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review

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.

gr-qc↗

arXiv2019

Field-theoretical construction of currents and superpotentials in Lovelock gravity

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.

gr-qc↗

arXiv2018

Interference between $E1$ and $M1$ transition amplitudes on the $H$ to $C$ transition in ThO

Calculations of Stark interference between $E1$ and $M1$ transition amplitudes on the $H^3Δ_1$ to $C^1Π$ transition in ThO is performed. Calculations are required for estimations of systematic errors in the experiment for electron electric dipole (eEDM) moment search due to imperfections in laser beams used to prepare the molecule and read out the (eEDM) signal.

physics.atom-ph↗

arXiv2018

HfF$^+$ as a candidate to search for the nuclear weak quadruple moment

Nuclei with a quadrupole deformation such as $^{177}$Hf have enhanced weak quadrupole moment which induces the tensor weak electron-nucleus interaction in atoms and molecules. Corresponding parity non-conserving (PNC) effect is strongly enhanced in the $^3Δ_1$ electronic state of the $^{177}$HfF$^+$ cation which has very close opposite parity levels mixed by this tensor interaction. In the present paper we perform relativistic many-body calculations of this PNC effect. It is shown that the tensor weak interaction induced by the weak quadrupole moment gives the dominating contribution to the PNC effects in $^{177}$HfF$^+$ which significantly exceeds contributions of the vector anapole moment and the scalar weak charge. The anapole and the weak charge can contribute due to the nonadiabatic mechanism proposed here. Therefore, corresponding experiment will allow one to separate the tensor weak PNC effect from the other PNC effects and to measure the quadrupole moment of the neutron distribution which gives the dominating contribution to the weak quadrupole moment.

physics.atom-ph↗

arXiv2018

Evaluation of CP-violation in HfF$^+$

CP violation effects produced by the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment (EDM) and scalar$-$pseudoscalar nucleus$-$electron neutral current (SP) interaction in $^{177}$Hf$^{19}$F$^+$ and $^{179}$Hf$^{19}$F$^+$ are calculated. The role of the hyperfine interaction is investigated. It is shown that the MQM shift can be distinguished from the electron EDM and SP ones due to the implicit dependence of MQM shift on the hyperfine sublevel. The MQM effect is expressed in terms of the proton (EDM), QCD vacuum angle $θ$ and quark chromo-EDMs.

physics.atom-ph↗

arXiv2017

A point mass and continuous collapse to a point mass in general relativity

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 $δ$-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.

gr-qc↗

arXiv2017

Study of systematic effects in the HfF$^+$ ion experiment to search for the electron electric dipole moment

The energy splitings for $J = 1$, $F=3/2$, $|M_F|=3/2$ hyperfine levels of the $^3Δ_1$ electronic state of $^{180}$Hf$^{19}$F$^+$ ion are calculated as functions of the external variable electric and magnetic fields within two approaches. In the first one transition to the rotating frame is performed, whereas in the second approach the quantization of rotating electromagnetic field is performed. Calculations are required for understanding possible systematic errors in the experiment to search for electron electric dipole moment (eEDM) on $^{180}$Hf$^{19}$F$^+$ ion.

physics.atom-ph↗