Dirac and Klein–Gordon–Fock equations in Grumiller’s spacetime

2018 ◽  
Vol 15 (04) ◽  
pp. 1850051
Author(s):  
A. Al-Badawi ◽  
I. sakalli
Keyword(s):  
Black Hole ◽  
Dirac Equation ◽  
Wave Equations ◽  
Massive Scalar ◽  
One Dimensional ◽  
Effective Potentials ◽  
Central Object ◽  
Klein Gordon ◽  
Rindler Acceleration ◽  
The Waves

We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.

On the metric perturbations of the Reissner–Nordström black hole

1979 ◽  
Vol 367 (1728) ◽  
pp. 1-14 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equations ◽  
Schwarzschild Black Hole ◽  
One Dimensional ◽  
Dimensional Wave

The two pairs of one-dimensional wave equations which govern the odd and the even-parity perturbations of the Reissner–Nordström black hole are derived directly from a treatment of its metric perturbations. The treatment closely parallels the corresponding treatment in the context of the Schwarzschild black hole.

scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

On the equations governing the perturbations of the Reissner–Nordström black hole

1979 ◽  
Vol 365 (1723) ◽  
pp. 453-465 ◽  
Keyword(s):  
Black Hole ◽  
Electromagnetic Waves ◽  
Wave Equations ◽  
Simple Relation ◽  
Opposite Parity ◽  
One Dimensional ◽  
Basic Equations ◽  
Dimensional Wave

By considering suitable combinations of the Weyl scalars and the spin coefficients, the basic equations governing the perturbations of the Reissner–Nordström black hole, in the Newman–Penrose formalism, are decoupled; a fundamental pair of decoupled equations are obtained. It is then shown how this pair of decoupled equations can be transformed into one dimensional wave equations which are appropriate for describing the perturbations of odd and of even parity. A simple relation is obtained which will allow derivation of a solution belonging to one parity from a solution belonging to the opposite parity. Finally, equations are derived in terms of which one can readily ascertain how an arbitrary superposition of gravitational and electromagnetic waves, incident on the black hole, will be reflected and absorbed.

scholarly journals Heun-Type Solutions of the Klein-Gordon and Dirac Equations in the Garfinkle-Horowitz-Strominger Dilaton Black Hole Background

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Marina-Aura Dariescu ◽  
Ciprian Dariescu ◽  
Cristian Stelea
Keyword(s):  
Black Hole ◽  
Dirac Equation ◽  
Einstein Frame ◽  
Covariant Approach ◽  
Dirac Equations ◽  
Black Hole Background ◽  
Klein Gordon ◽  
Dilaton Black Hole

We study the Klein-Gordon and the Dirac equations in the background of the Garfinkle-Horowitz-Strominger black hole in the Einstein frame. Using a SO(3,1)×U(1)-gauge covariant approach, as an alternative to the Newman-Penrose formalism for the Dirac equation, it turns out that these solutions can be expressed in terms of Heun confluent functions and we discuss some of their properties.

Explorations of many-body relativistic wave equations within a one-dimensional model

2009 ◽  
Vol 87 (10) ◽  
pp. 1499-1511 ◽  
Author(s):  
Marcel Nooijen
Keyword(s):  
Dirac Equation ◽  
Wave Equations ◽  
Mass Term ◽  
Finite Basis ◽  
Many Body ◽  
Harmonic Oscillator Potential ◽  
One Dimensional ◽  
Particle Potential ◽  
The Many ◽  
Variable Representation

A one-dimensional analog that reflects many of the features of the many-body Dirac equation is considered. The model can be solved numerically using a convenient finite basis discrete variable representation. Both an (unbound) harmonic oscillator potential and a (bound) inverse Gaussian one-particle potential are discussed for interacting particles. In a second thread in the paper, the mass term is neglected in the model many-body Dirac equation, and it is shown that the original equation, which has 2N coupled components for N particles can then be reduced to 2N decoupled one-component equations, which can be solved “analytically” for arbitrary many particles interacting through central two-body potentials.

Relativistic Wave Equations

2019 ◽  
pp. 25-42
Author(s):  
Michael E. Peskin
Keyword(s):  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Relativistic Wave Equations ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Klein Gordon ◽  
Klein Gordon Equation

This chapter presents the wave equations that govern the behavior of quantum mechanical particles with spin 0, 1/2, and 1 in relativistic theories. These equations are the Klein-Gordon equation, the Dirac equation, and Maxwell’s equations.

Relativistic Wave Equations

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Dirac Equation ◽  
Vector Fields ◽  
Wave Equations ◽  
Gordon Equation ◽  
Relativistic Wave ◽  
Wave Solutions ◽  
Lagrangian Formulations ◽  
Klein Gordon ◽  
Conserved Currents ◽  
Klein Gordon Equation

Relativistically covariant wave equations for scalar, spinor, and vector fields. Plane wave solutions and Green’s functions. The Klein–Gordon equation. The Dirac equation and the Clifford algebra of γ‎ matrices. Symmetries and conserved currents. Hamiltonian and Lagrangian formulations. Wave equations for spin-1 fields.

scholarly journals The Modified Fundamental Equations of Quantum Mechanics in Symmetric Forms

2021 ◽  
Author(s):  
Huai-Yu Wang
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Kinetic Energy ◽  
Time Derivative ◽  
Dinger Equation ◽  
Calculated Density ◽  
One Dimensional ◽  
Klein Gordon ◽  
Fundamental Equations ◽  
First Time

Up to now, Schrödinger equation, Klein-Gordon equation (KGE) and Dirac equation are believed the fundamental equations of quantum mechanics. Schrödinger equation has a defect that there is no NKE solutions. Dirac equation has positive kinetic energy (PKE) and negative kinetic energy (NKE) branches. Both branches should have low momentum, or nonrelativistic, approximations: one is Schrödinger equation and the other is NKE Schrödinger equation. KGE has two problems: it is an equation of second time derivative, and calculated density is not definitely positive. To overcome the problems, it should be revised as PKE and NKE decoupled KGEs. The fundamental equations of quantum mechanics after the modification have at least two merits. They are of unitary in that everyone contains the first time derivative and are symmetric with respect to PKE and NKE. This reflects the symmetry of the PKE and NKE matters, as well as matter and dark matter, of our universe. The problems of one-dimensional step potentials are resolved by means of the modified fundamental equations for a nonrelativistic particle.

scholarly journals Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 443-452
Author(s):  
Tianshu Jiang ◽  
Anan Fang ◽  
Zhao-Qing Zhang ◽  
Che Ting Chan
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Waves ◽  
Anderson Localization ◽  
Random Media ◽  
Normal Incidence ◽  
Disordered Media ◽  
One Dimensional ◽  
Gain Loss ◽  
The Waves ◽  
Localization Behavior

AbstractIt has been shown recently that the backscattering of wave propagation in one-dimensional disordered media can be entirely suppressed for normal incidence by adding sample-specific gain and loss components to the medium. Here, we study the Anderson localization behaviors of electromagnetic waves in such gain-loss balanced random non-Hermitian systems when the waves are obliquely incident on the random media. We also study the case of normal incidence when the sample-specific gain-loss profile is slightly altered so that the Anderson localization occurs. Our results show that the Anderson localization in the non-Hermitian system behaves differently from random Hermitian systems in which the backscattering is suppressed.

scholarly journals Universally bistable shells with nonzero Gaussian curvature for two-way transition waves

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nikolaos Vasios ◽  
Bolei Deng ◽  
Benjamin Gorissen ◽  
Katia Bertoldi
Keyword(s):  
Gaussian Curvature ◽  
Energy Landscape ◽  
Propagation Distance ◽  
Energy Landscapes ◽  
Bending Energy ◽  
Nonlinear Dynamic Response ◽  
One Dimensional ◽  
Doubly Curved Shells ◽  
Doubly Curved ◽  
The Waves

AbstractMulti-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.

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