Three types of superpotentials for perturbations in the Einstein-Gauss-Bonnet gravity

Superpotentials (antisymmetric tensor densities) in Einstein-Gauss-Bonnet (EGB) gravity for arbitrary types of perturbations on arbitrary curved backgrounds are constructed. As a basis, the generalized conservation laws in the framework of an arbitrary D-dimensional metric theory, where conserved currents are expressed through divergences of superpotentials, are used. Such a derivation is exact (perturbations are not infinitesimal) and is approached, when a one solution (dynamical) is considered as a perturbed system with respect to another solution (background). Three known prescriptions are elaborated: these are the canonical N{\oe}ther theorem, the Belinfante symmetrization rule and the field-theoretical derivation. All the three approaches are presented in an unique way convenient for comparisons and a development. Exact expressions for the 01-component of the three types of the superpotentials are derived in the case, when an arbitrary static Schwarzschild-like solution in the EGB gravity is considered as a perturbed system with respect to a background of the same type. These formulae are used for calculating the mass of the Schwarzschild-anti-de Sitter black hole in the EGB gravity. As a background both the anti-de Sitter spacetime in arbitrary dimensions and a not maximally symmetric "mass gap" vacuum in 5 dimensions are considered. Problems and perspectives for a future development, including the Lovelock gravity, are discussed.Comment: Erratum, where the canonical superpotential and correspondent formulae are corrected, is adde

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 $\delta$-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.Comment: 25 pages. arXiv admin note: text overlap with arXiv:gr-qc/0410041 by other author

AC Stark effect in ThO H3Δ1H^3\Delta_1 for the electron EDM search

A method and code for calculations of diatomic molecules in the external variable electromagnetic field have been developed. Code applied for calculation of systematics in the electron's electric dipole moment search experiment on ThO $H^3\Delta_1$ state related to geometric phases, including dependence on $\Omega$-doublet, rotational level, and external static electric field. It is found that systematics decrease cubically with respect to the frequency of the rotating transverse component of the electric field. Calculation confirms that experiment on ThO $H^3\Delta_1$ state is very robust against systematic errors related to geometric phases.Comment: 4 page

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.Comment: 29 pages, to appear in Class. Quantum Gra

Perturbations in the Einstein theory of gravity: Conserved currents

General relativity in the form where gravitational perturbations together with other physical fields propagate on an auxiliary background is considered. With using the Katz-Bi{\v{c}}\'ak-Lynden-Bell technique new conserved currents, divergences of antisymmetric tensor densities(superpotentials), in an arbitrary curved spacetime are constructed.Comment: LATEX, 8 page

The Rabi frequency on the H3Δ1H^3\Delta_1 to C1ΠC^1\Pi transition in ThO: influence of interaction with electric and magnetic fields

Calculations of the correlations between the Rabi frequency on the $H^3\Delta_1$ to $C^1\Pi$ transition in ThO molecule and experimental setup parameters in the electron electric dipole moment (eEDM) search experiment is performed. Calculations are required for estimations of systematic errors in the experiment due to imperfections in laser beams used to prepare the molecule and read out the eEDM signal

The field theoretical formulation of general relativity and gravity with non-zero masses of gravitons

It is a review paper. General relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary arbitrary curved background spacetime. Conserved currents are constructed and expressed through divergences of antisymmetrical tensor densities (superpotentials). This permits to connect local properties of perturbations with the quasi-local nature of the conserved quantities in GR. The problem of the non-localization of energy in GR is presented in exact mathematical expressions. A modification of GR developed recently by Babak and Grishchuk on the basis of the field formulation of GR is described. Their theory includes massive of spin-2 and spin-0 gravitons. All its local weak-field predictions are in agreement with experimental data. The exact equations of the massive theory eliminate the black hole event horizons and give an oscillator behavior for the homogeneous isotropic universe.Comment: LaTeX, 18 pages, no figures. It is a translation with very minor changes of the invited paper to the Russian book referred below. A compressed version of the paper is in the 2-nd volume of the Proceedings to PIRT-IX, London: 3-6 September, 2004, p.p. 433-44

Restoration of Many Electron Wave Functions from One-Electron Density

General theorem describing a relation between diagonal of one-electron density matrix and a certain class of many-electron ensembles of determinant states is proved. As a corollary to this theorem a constructive proof of sufficiency of Coleman's representability conditions is obtained. It is shown that there exist rigorous schemes for construction of energy of many-electron system as functionals of one-electron density.Comment: LaTex, 10 page

Conservation Laws for Large Perturbations on Curved Backgrounds

Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noether's theorem combined with Belinfante's "symmetrization" method applied to the group of displacements provide a conserved vector, a "superpotential" and a energy-momentum that are independent of any divergence added to the Hilbert Lagrangian of the perturbations. The energy-momentum is symmetrical and divergenceless only on backgrounds that are Einstein spaces in the sense of A.Z.Petrov.Comment: 13 pages, LaTeX, to appear in the Proceedings of the Conference on "Fundamental Interactions: From Symmetries to Black Holes" held in Brussels March 25 - 27, 199

Accurate calculations of the dissociation energy, equilibrium distance and spectroscopic constants for the Yb dimer

The dissociation energy, equilibrium distance, and spectroscopic constants for the $^1\Sigma_g^+$ ground state of the Yb$_2$ molecule are calculated. The relativistic effects are introduced through generalized relativistic effective core potentials with very high precision. The scalar relativistic coupled cluster method particularly well suited for closed-shell van-der-Waals systems is used for the correlation treatment. Extensive generalized correlation basis sets were constructed and employed. The relatively small corrections for high-order cluster amplitudes and spin-orbit interactions are taken into account using smaller basis sets and the spin-orbit density functional theory.Comment: 10 pages, 3 tables, 1 figure (the paper was extended