Symmetries, conservation laws, reductions, and exact solutions for the Klein–Gordon equation in de Sitter space–times

2012 ◽  
Vol 90 (7) ◽  
pp. 667-674 ◽  
Author(s):  
S. Jamal ◽  
A.H. Kara ◽  
Ashfaque H. Bokhari
Keyword(s):  
Dynamical Systems ◽  
Exact Solutions ◽  
Gordon Equation ◽  
De Sitter Space ◽  
Fundamental Solutions ◽  
De Sitter ◽  
Klein Gordon ◽  
Symmetry Generators ◽  
Math Phys ◽  
Klein Gordon Equation

In this paper, we complement the analysis involving the “fundamental” solutions of the Klein–Gordon equation in de Sitter space–times given by Yagdjian and A. Galstian (Comm. Math. Phys. 285, 293 (2009); Discrete and Continuous Dynamical Systems S, 2(3), 483 (2009)). Using the symmetry generators, we classify and reduce the underlying equations and show how this process may lead to exact solutions by quadratures.

scholarly journals From Fock’s transformation to de Sitter space

2015 ◽  
Vol 93 (7) ◽  
pp. 734-737 ◽  
Author(s):  
T. Foughali ◽  
A. Bouda
Keyword(s):  
Coordinate Transformation ◽  
Gordon Equation ◽  
De Sitter Space ◽  
Space Time ◽  
Poisson Brackets ◽  
De Sitter ◽  
Deformed Algebra ◽  
Klein Gordon ◽  
The Universe ◽  
Klein Gordon Equation

As with Deformed Special Relativity, we showed recently that the Fock coordinate transformation can be derived from a new deformed Poisson brackets. This approach allowed us to establish the corresponding momentum transformation that keeps invariant the four-dimensional contraction pμxμ. From the resulting deformed algebra, we construct the corresponding first Casimir. After first quantization, we show by using the Klein–Gordon equation that the space-time of the Fock transformation is the de Sitter one. As we will see, the invariant length representing the universe radius in the space-time of Fock’s transformation is exactly the radius of the embedded hypersurface representing the de Sitter space-time.

scholarly journals FINITE ACTION KLEIN–GORDON SOLUTIONS ON LORENTZIAN MANIFOLDS

2006 ◽  
Vol 03 (07) ◽  
pp. 1349-1357 ◽  
Author(s):  
V. V. KOZLOV ◽  
I. V. VOLOVICH
Keyword(s):  
Mass Spectrum ◽  
Elliptic Equations ◽  
Gordon Equation ◽  
Infinite Family ◽  
De Sitter ◽  
Lorentzian Manifolds ◽  
Klein Gordon ◽  
Finite Action ◽  
Discrete Mass ◽  
Klein Gordon Equation

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this paper we consider such a problem for the hyperbolic Klein–Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein–Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.

scholarly journals Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Bahar ◽  
F. Yasuk
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Oscillator Potential ◽  
Ansatz Method ◽  
Harmonic Oscillator Potential ◽  
Klein Gordon ◽  
Dependent Mass ◽  
Mass Dependent ◽  
Klein Gordon Equation

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

scholarly journals ON THE CREATION OF SCALAR PARTICLES IN A FLAT ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 26 (35) ◽  
pp. 2639-2651 ◽  
Author(s):  
S. HAOUAT ◽  
R. CHEKIREB
Keyword(s):  
Exact Solutions ◽  
Effective Action ◽  
Gordon Equation ◽  
Transition Probability ◽  
Particle Creation ◽  
Pair Creation ◽  
Bogoliubov Transformation ◽  
Scalar Particles ◽  
Klein Gordon ◽  
Klein Gordon Equation

The problem of particle creation from vacuum in a flat Robertson–Walker spacetime is studied. Two sets of exact solutions for the Klein–Gordon equation are given when the scale factor is a2(η) = a+b tanh(λη)+c tanh2 (λη). Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. Some particular cosmological models such as radiation dominated universe and Milne universe are discussed. For both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.

ENTROPY OF SCHWARZSCHILD–de SITTER BLACK HOLE IN NON-THERMAL-EQUILIBRIUM

2001 ◽  
Vol 16 (11) ◽  
pp. 719-723 ◽  
Author(s):  
REN ZHAO ◽  
JUNFANG ZHANG ◽  
LICHUN ZHANG
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Thermal Equilibrium ◽  
Gordon Equation ◽  
Brick Wall ◽  
De Sitter ◽  
Logarithmic Term ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Wall Method

Starting from the Klein–Gordon equation, we calculate the entropy of Schwarzschild–de Sitter black hole in non-thermal-equilibrium by using the improved brick-wall method-membrane model. When taking the proper cutoff in the obtained result, we obtain that both black hole's entropy and cosmic entropy are proportional to the areas of event horizon. We avoid the logarithmic term and stripped term in the original brick-wall method. It offers a new way of studying the entropy of the black hole in non-thermal-equilibrium.

Sign in / Sign up

Export Citation Format

Share Document