Lorentzian Form Research Articles

Wormholes and black hole microstates in AdS/CFT

It has long been known that the coarse-grained approximation to the black hole density of states can be computed using classical Euclidean gravity. In this work we argue for another entry in the dictionary between Euclidean gravity and black hole physics, namely that Euclidean wormholes describe a coarse-grained approximation to the energy level statistics of black hole microstates. To do so we use the method of constrained instantons to obtain an integral representation of wormhole amplitudes in Einstein gravity and in full-fledged AdS/CFT. These amplitudes are non-perturbative corrections to the two-boundary problem in AdS quantum gravity. The full amplitude is likely UV sensitive, dominated by small wormholes, but we show it admits an integral transformation with a macroscopic, weakly curved saddle-point approximation. The saddle is the “double cone” geometry of Saad, Shenker, and Stanford, with fixed moduli. In the boundary description this saddle appears to dominate a smeared version of the connected two-point function of the black hole density of states, and suggests level repulsion in the microstate spectrum. Using these methods we further study Euclidean wormholes in pure Einstein gravity and in IIB supergravity on Euclidean AdS5× S5. We address the perturbative stability of these backgrounds and study brane nucleation instabilities in 10d supergravity. In particular, brane nucleation instabilities of the Euclidean wormholes are lifted by the analytic continuation required to obtain the Lorentzian spectral form factor from gravity. Our results indicate a factorization paradox in AdS/CFT.

Chen-like inequalities on null hypersurfaces with closed rigging of a Lorentzian manifold

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.

Biharmonic curves in $3$-dimensional Lorentzian Sasakian space forms

Biharmonic curves in $3$-dimensional Lorentzian Sasakian space forms

Gauss-Bonnet theorem in Lorentzian Sasakian space forms

<abstract> In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of $ 3 $-dimensional Lorentzian Sasakian space forms. Based on these results, we get a Gauss-Bonnet theorem in the Lorentzian Sasakian space forms. </abstract>

Parameters optimization of optical pumped Mz/Mx magnetometer based on rf-discharge lamp

Optical pumped magnetometer (OPM) aiming at the measurement of Earth’s magnetic field, is firstly optimized by optical simulation, as to maximize the efficient pumping light. Then Mz-magnetometer and Mx-magnetometer are respectively realized in this work, and the correspondent signals are analyzed. The temperature of rf-discharge lamp, the temperature of vapor cell and the amplitude of radio frequency field (RF) are optimized. In Mz mode, the FWHM/SNR of the absorption curve of magnetic resonance (Mz signal) gives 1.3 Hz under 10, 000 nT, with a correspondent field resolution 29.6 pT. Additionally, the scanning rate of RF should be set to be lower than 40 kHz/s, as to obtain a well Lorentzian form of Mz signal. In Mx mode, the free induction decay (FID) signal and Rabi signal are obtained and analyzed. By sweeping the frequency of RF, a so-called “peak splitting” of Mx signal is found to be in existence at the magnetic resonance point theoretically and experimentally, and thereby a suitable amplitude of RF needs to be carefully determined for achieving a satisfied amplitude of Mx signal, as well as for a better sensitivity of magnetometer.

Lorentzian quintessential inflation

From the assumption that the slow-roll parameter [Formula: see text] has a Lorentzian form as a function of the e-folds number [Formula: see text], a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of [Formula: see text] to [Formula: see text] at the end of the inflationary epoch. At the late universe, [Formula: see text] becomes small again and this leads to the dark energy epoch. The observables that the models predict fits with the latest Planck data: [Formula: see text]. Naturally, a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appearance, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions — one inflationary and one as a dark energy with slow-roll behavior.

Some characterizations of timelike rectifying curves in de sitter 3 space

De Sitter space is a non-flat Lorentzian space form with positive constant curvature which plays an important role in the theory of relativity. In this paper, we define the notions of timelike rectifying curve and timelike conical surface in De Sitter 3-space as Lorentzian viewpoint. Moreover, we give some nice characterizations and results of a timelike rectifying curves with respect to curve-hypersurface frame in De Sitter 3-space which is a three dimensional pseudo-sphere in Minkowski 4-space.

Null screen quasi‐conformal hypersurfaces in semi‐Riemannian manifolds and applications

AbstractWe introduce a class of null hypersurfaces of a semi‐Riemannian manifold, namely, screen quasi‐conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvature of the ambient space is different from zero. As applications, we study umbilical, isoparametric and Einstein null hypersurfaces in Lorentzian space forms and provide several classification results.

Quintessential inflation from Lorentzian slow roll

From the assumption that the slow-roll parameter varepsilon has a Lorentzian form as a function of the e-fold number N, a successful model of a quintessential inflation is obtained, as succinctly studied in[1]. The form corresponds to the vacuum energy both in the inflationary and in the dark-energy epochs and satisfies the condition to climb from small values of varepsilon to 1 at the end of the inflationary epoch. We find the corresponding scalar quintessential inflationary potential with two flat regions. Moreover, a reheating mechanism is suggested with numerical estimation for the homogeneous evolution of the universe. The suggested mechanism is consistent with the BBN bound.

Magnetic and electric properties, ESR, XPS and NEXAFS spectroscopy of CaCu3Ti4O12 ceramics

ESR, XPS and NEXAFS spectra, as well as magnetic and electric properties of CaCu3Ti4O12 synthesized by the solid-phase method within 6,12,24,48 and 60 h were studied. The analysis of magnetic susceptibility of CaCu3Ti4O12 and magnesium-containing solid solutions of CaCu3-3xMg3xTi4O12 revealed antiferromagnetic exchange interactions between Cu paramagnetic atoms, while the effective magnetic moment of copper atoms corresponds to the electronic state of Cu(II). In CaCu3Ti4-4хMg4хO12-δ samples within the whole concentration range the impurity phase MgTiO3 was observed. The magnetic properties of calcium copper titanate were found to be inconsistent depending on the synthesis duration. The extreme point of magnetic susceptibility was found among samples synthesized within 48 h. Modelling and interpretation of the XPS spectra of CaCu3Ti4O12 were performed. Based on the NEXAFS and XPS spectroscopy data, copper and calcium atoms in ceramics display oxidation state +2, while titanium atoms – Ti(IV). ESR spectra of CaCu3Ti4O12 samples show an exchange-narrowing signal from copper (II) atoms at g = 2.15. In the ESR spectra of CaCu3-3xMg3xTi4O12 the only intense exchange-narrowed line of Lorentzian form of Cu2+ ions is observed. The impedance spectroscopy study of electric properties of CaCu3Ti4O12 found the media to feature temperature-dependent reach-through conductivity with activation energy of 0.79–0.71 eV. At 255–300°С, the dominant polarization process is in line with the Gerischer model. It indicates the formation of anionic-cationic associates accompanied by decreased low-frequency capacitance of the samples. With temperatures of over 300°С the samples start displaying ion-migrating polarization which contributes to higher capacitance and dielectric loss at low frequencies. As the temperature grows further to 400°С, the ion migration process gets to dominate within the whole frequency range under study. Based on the study, a conclusion was made on movable cations of copper participating in the polarization process at room temperature.

On 4‐dimensional Lorentzian affine hypersurfaces with an almost symplectic form

AbstractIn this paper we study 4‐dimensional affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure ω. We prove that the rank of the shape operator is at most one if or for some positive integer k. This result is the final step in a classification of Lorentzian affine hypersurfaces with higher order parallel almost symplectic forms.

On profiles of hydrogenic spectral lines under stochastic electric fields of plasma turbulence: Applications to diagnostics of the Langmuir turbulence

Studies of the effects of various oscillatory electric fields on hydrogenic spectral lines have a long history. Over the years various effects of a monochromatic linearly-polarized electric field were analyzed and applied to spectroscopic diagnostics of laboratory and astrophysical plasmas.Then in 1996 a paper was published where the author analyzed how profiles of hydrogen spectral lines are affected by a multi-mode non-monochromatic linearly-polarized electric field E(t). Specifically it concerned the situation where the power spectrum of the field E(t) has the Lorentzian form. In the present paper we obtained a general analytical result for the shape of hydrogenic (i.e., hydrogen and hydrogenlike) spectral lines under the same kind of the field E(t), but whose power spectrum has the Gaussian form. We consider this kind of electric field to be caused by the Langmuir turbulence in plasmas. We show that if the power spectrum of the field is Gaussian, then for the relatively small value of the average Langmuir field, the profile of each Stark component is Lorentzian, while for the relatively large value of the average Langmuir field, the profile of each Stark component is Gaussian. We analyze theoretical profiles of the hydrogenic Ly-beta line under the Langmuir field of either one of the above two kinds of the power spectrum. On the basis of this analysis, we propose a new diagnostic method allowing for the first time not only to measure experimentally the average field of the Langmuir turbulence in dense plasmas, but also to find out the information on the power spectrum of the Langmuir turbulence. This diagnostic method is not limited to using the Ly-beta line: it would work while using other intense hydrogenic spectral lines that do not have the central Stark components, such as, e.g., Ly-delta, Balmer-beta, and Balmer-delta.

On the classification of homogeneous affine tube domains with large automorphism groups in arbitrary dimensions

We classify tube domains in Cn+1 (n≥1) with affinely homogeneous base of their boundary and a.) with positive definite Levi form and b.) with Lorentzian type Levi form and affine isotropy of dimension at least (n−2)(n−3)2.

The Quantum Theory of the Lorentzian Fermionic Differential Forms

We consider the quantum theory of the Lorentzian fermionic differential forms and the corresponding bispinor quantum fields, which are expansion coefficients of the forms in the bispinor basis of Becher and Joos. We describe the canonical quantization procedure for the bispinor gauge theory in terms of its Dirac spinor constituents in detail and derive the corresponding Feynman rules and also all possible mass terms for massive fermions in the bispinor gauge theory. We classify the solutions by a scalar spin quantum number, a number with no analogue in the standard gauge theory and in the Standard Model. The possible mass terms correspond to combinations of scalar spin-zero singlets and scalar spin-1/2 doublets in the generation space. We describe the connection between the Lorentz spin of bispinors and the scalar spin of bispinor constituents.

The quantum theory of the Lorentzian fermionic differential forms

Рассматривается квантовая теория лоренцевых фермионных дифференциальных форм и соответствующих биспинорных квантовых полей, которые являются коэффициентами разложения дифференциальных форм по биспинорному базису Бехера и Йоса. Подробно описано каноническое квантование биспинорной калибровочной теории в терминах ее дираковских спинорных составляющих и выведены соответствующие правила Фейнмана. Также получены все возможные массовые члены для массивных фермионов в биспинорной калибровочной теории. Решения классифицируются в соответствии со значением квантового числа скалярного спина, которое не имеет аналога в стандартной калибровочной теории и в Стандартной модели. Возможные массовые члены отвечают комбинациям синглетов с нулевым скалярным спином и дублетов со скалярным спином $1/2$ в пространстве поколений. Описана связь лоренцева спина биспиноров и скалярного спина биспинорных составляющих.

On a Lorentzian Complex Space Form

The aim of the present paper is to study the theory of general relativity in a Lorentzian Kahler space. In this paper, we have considered the Lorentzian complex space form with constant sectional curvature and proved that a Lorentzian complex space form satisfying Einstein’s field equation is a Ricci semi-symmetric space and the energy–momentum tensor is covariant constant. Such space reduces to a flat space for a purely electromagnetic distribution. The existence of the Killing vector field and conformal Killing vector field has been discussed and proved that the cosmological term is proportional to sectional curvature. Further, it is shown that the perfect fluid in a Lorentzian complex space form satisfying Einstein’s field equation does not admit heat flux.

Conformally flat Willmore spacelike hypersurfaces inRn+1

In this paper, we give the equation satisfied by umbilics-free Willmore spacelike hypersurfaces using the conformal invariants in Lorentzian space forms. At the same time, we give the equation satisfied by hyperelastic spacelike curves in $2$-dimensional Lorentzian space forms and classify the closed hyperelastic spacelike curves. Finally conformally flat Willmore spacelike hypersurfaces are classified in terms of the hyperelastic spacelike curves in $2$-dimensional Lorentzian space forms.

Some Properties Curvture of Lorentzian Kenmotsu Manifolds

Abstract In this paper different curvature tensors on Lorentzian Kenmotsu manifod are studied. We investigate constant ϕ–holomorphic sectional curvature and ℒ-sectional curvature of Lorentzian Kenmotsu manifolds, obtaining conditions for them to be constant of Lorentzian Kenmotsu manifolds in such condition. We calculate the Ricci tensor and scalar curvature for all the cases. Moreover we investigate some properties of semi invariant submanifolds of a Lorentzian Kenmotsu space form. We show that if a semi-invariant submanifold of a Lorentzian Kenmotsu space form M is totally geodesic, then M is an η−Einstein manifold. We consider sectional curvature of semi invariant product of a Lorentzian Kenmotsu manifolds.

Wavefronts of traveling trajectories of geometric particles

Confining the traveling trajectory of a tachyon to the two-dimensional Lorentzian space forms, we describe the trajectory as a spacelike front in these Lorentzian space forms. Introducing the differential geometry of singular curves in Lorentzian space forms, that is, the hyperbolic space and de Sitter space, and applying the Legendrian duality theorems, we establish the moving frame along the front, whereby the definitions of the evolutes of spacelike fronts in Lorentzian space forms are presented and the geometric properties of these evolutes are investigated in detail. It is shown that these evolutes can be interpreted as wavefronts under the viewpoint of Legendrian singularity theory.

On the classic geometrodynamics of a spherically-symmetric configuration of gravitational and electromagnetic fields

Analytical aspects of the classical geometrodynamics for the spherically-symmetric configuration of the electromagnetic and gravitational fields in GR are considered. The feature of such configurations is that they admit two motion integrals – the total mass and charge. The Einstein-Hilbert action for the configuration, after dimensional reduction, by means of the Legendre transformation is reduced to the Hamiltonian action. Using the conservation laws for the mass and charge, as well as the Hamiltonian constraint, the momenta are found as functions of configuration variables. The set of equations, which associate momenta and functional derivatives of the action in the configuration space (CS) is integrable. This allows us to obtain the action functional as a solution of the Einstein-Hamilton-Jacobi equation in functional derivatives. Variations of the action functional with respect to mass M and charge Q of the configuration lead to the motion trajectories in the CS. We note that the minisuperspace metric, which is induced by the kinetic part of the Lagrangian, does not coincide with the CS metric that arises when the function of lapse N is excluded from the action. The space-time metric for which the indicated metrics coincide in the T-region up to a coefficient are considered. The metric of CS is constructed and its geometry is studied. Under the trivial embedding of hypersurfaces of the foliation into a dynamical T-region, the CS is flat. It allows introducing pseudo-Cartesian coordinates in which the CS metric takes the Lorentz form.