scholarly journals Regularization, renormalization and consistency conditions in QED with x-electric potential steps

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
S. P. Gavrilov ◽  
D. M. Gitman
Keyword(s):  
Consistency Condition ◽  
Momentum Tensor ◽  
Inner Product ◽  
Uniform Electric Field ◽  
Back Reaction ◽  
Refined Formulation ◽  
Vacuum Instability ◽  
Important Addition ◽  
Finite Distance ◽  
Reaction Problem

AbstractThe present article is an important addition to the nonperturbative formulation of QED with x-steps presented by Gavrilov and Gitman (Phys. Rev. D. 93:045002, 2016). Here we propose a new renormalization and volume regularization procedures which allow one to calculate and distinguish physical parts of different matrix elements of operators of the current and of the energy–momentum tensor, at the same time relating the latter quantities with characteristics of the vacuum instability. For this purpose, a modified inner product and a parameter $$\tau $$ τ of the regularization are introduced. The latter parameter can be fixed using physical considerations. In the Klein zone this parameter can be interpreted as the time of the observation of the pair-production effect. In the refined formulation of QED with x-steps, we succeeded to consider the back-reaction problem. In the case of an uniform electric field E confined between two capacitor plates separated by a finite distance L, we see that the smallness of the back-reaction implies a restriction (the consistency condition) on the product EL from above.

The thermodynamical approach to the back reaction problem

1993 ◽  
Vol 25 (12) ◽  
pp. 1267-1275 ◽  
Author(s):  
Chao Guang Huang ◽  
Liao Liu ◽  
Zheng Zhao
Keyword(s):  
Back Reaction ◽  
Reaction Problem

On the nonlinear evolution of a pair of oblique Tollmien–Schlichting waves in boundary layers

1997 ◽  
Vol 340 ◽  
pp. 361-394 ◽  
Author(s):  
XUESONG WU ◽  
S. J. LEIB ◽  
M. E. GOLDSTEIN
Keyword(s):  
Boundary Layer ◽  
Phase Angle ◽  
Spatial Scales ◽  
Asymptotic Methods ◽  
Three Dimensional ◽  
Critical Layer ◽  
Back Reaction ◽  
Finite Distance ◽  
Tollmien Schlichting ◽  
High Reynolds

This paper is concerned with the nonlinear interaction and development of a pair of oblique Tollmien–Schlichting waves which travel with equal but opposite angles to the free stream in a boundary layer. Our approach is based on high-Reynolds-number asymptotic methods. The so-called ‘upper-branch’ scaling is adopted so that there exists a well-defined critical layer, i.e. a thin region surrounding the level at which the basic flow velocity equals the phase velocity of the waves. We show that following the initial linear growth, the disturbance evolves through several distinct nonlinear stages. In the first of these, nonlinearity only affects the phase angle of the amplitude of the disturbance, causing rapid wavelength shortening, while the modulus of the amplitude still grows exponentially as in the linear regime. The second stage starts when the wavelength shortening produces a back reaction on the development of the modulus. The phase angle and the modulus then evolve on different spatial scales, and are governed by two coupled nonlinear equations. The solution to these equations develops a singularity at a finite distance downstream. As a result, the disturbance enters the third stage in which it evolves over a faster spatial scale, and the critical layer becomes both non-equilibrium and viscous in nature, in contrast to the two previous stages, where the critical layer is in equilibrium and purely viscosity dominated. In this stage, the development is governed by an amplitude equation with the same nonlinear term as that derived by Wu, Lee & Cowley (1993) for the interaction between a pair of Rayleigh waves. The solution develops a new singularity, leading to the fourth stage where the flow is governed by the fully nonlinear three-dimensional inviscid triple-deck equations. It is suggested that the stages of evolution revealed here may characterize the so-called ‘oblique breakdown’ in a boundary layer. A discussion of the extension of the analysis to include the resonant-triad interaction is given.

scholarly journals VACUUM QUANTUM EFFECTS OF NONCONFORMAL SCALAR FIELD IN A NONSINGULAR COSMOLOGICAL MODEL

1998 ◽  
Vol 07 (05) ◽  
pp. 779-792 ◽  
Author(s):  
M. NOVELLO ◽  
V. B. BEZERRA ◽  
V. M. MOSTEPANENKO
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Negative Energy ◽  
Back Reaction ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Negative Energy Density ◽  
Stress Energy ◽  
Nonsingular Cosmological Model ◽  
Reaction Problem

The total vacuum stress-energy tensor of nonconformal scalar field is calculated in a nonsingular metric determined by some background matter with the effective negative energy density and pressure. The corrections due to the field nonconformity are shown to dominate the conformal contributions for some cases. The back reaction problem of vacuum stress-energy tensor upon the background metric is also discussed.

ON THE SUPERSTRING BLACK HOLE

2007 ◽  
Vol 16 (01) ◽  
pp. 123-140 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Black Hole ◽  
Energy Momentum Tensor ◽  
Energy Content ◽  
Momentum Tensor ◽  
Back Reaction ◽  
Effective Energy ◽  
De Sitter ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Effective Lagrangian

The effective Lagrangian for the heterotic superstring theory of Gross et al. contains higher-derivative gravitational terms [Formula: see text], n ≥ 2, which become important at large curvatures. This leads to a natural realization of the limiting-curvature hypothesis of Frolov et al., which was formulated to describe the interior of black holes. Assuming a purely geometrical, four-dimensional Schwarzschild black hole, for which all matter fields are zero, this interior consists of two regions: a shell of effective energy-density ρ immediately beyond the event horizon at r+ = 2M, due to the back reaction of the [Formula: see text] on the Schwarzschild metric, extending inward to a transition radius r0 ≈ M⅓, where the shell signature (- + - -) reverts to the exterior Lorentzian form (+ - - -), and an innermost core tending asymptotically to anti-de Sitter space as r → 0. The total mass-energy content of the hole M can be expressed in terms of the effective energy–momentum tensor Sij as the Nordström mass [Formula: see text], since the space–time is static and free of physical singularities. The conjecture that ρ N (r) is positive in the shell, which is necessary for the contribution to M N to be positive, is shown to be true for the term [Formula: see text], due to the unrenormalized [Formula: see text]. The corresponding "potential" energy–momentum tensor calculated in the Schwarzschild background is isotropic in the region r0 ≪ r ≪ r+, where [Formula: see text], while the dominant "kinetic" contribution is [Formula: see text], so that [Formula: see text].

scholarly journals Hawking Radiation and Black Hole Gravitational Back Reaction—A Quantum Geometrodynamical Simplified Model

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 297
Author(s):  
João Marto
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Quantum States ◽  
Simplified Model ◽  
Back Reaction ◽  
Black Hole Evaporation ◽  
Quantum Geometrodynamics ◽  
Reaction Problem

The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schrödinger’s type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states in this model.

scholarly journals The Final Stage of Gravitationally Collapsed Thick Matter Layers

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Piero Nicolini ◽  
Alessio Orlandi ◽  
Euro Spallucci
Keyword(s):  
Black Holes ◽  
Final Stage ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Minimal Length ◽  
Curvature Singularity ◽  
Finite Distance ◽  
Extremal Configuration ◽  
Proper Modification ◽  
Area Law

In the presence of aminimal length, physical objects cannot collapse to an infinite density, singular, matter point. In this paper, we consider the possible final stage of the gravitational collapse of “thick” matter layers. The energy momentum tensor we choose to model these shell-like objects is a proper modification of the source for “noncommutative geometry inspired,” regular black holes. By using higher momenta of Gaussian distribution to localize matter at finite distance from the origin, we obtain new solutions of the Einstein equation which smoothly interpolates between Minkowski’s geometry near the center of the shell and Schwarzschild’s spacetime far away from the matter layer. The metric is curvature singularity free. Black hole type solutions exist only for “heavy” shells; that is,M ≥Me, whereMeis the mass of the extremal configuration. We determine the Hawking temperature and a modified area law taking into account the extended nature of the source.

A Comparison of Various Approaches to the Back-Reaction Problem

1993 ◽  
Vol 221 (2) ◽  
pp. 217-228 ◽  
Author(s):  
T. Padmanabhan ◽  
T.P. Singh
Keyword(s):  
Back Reaction ◽  
Reaction Problem
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