scholarly journals Addendum to ‘‘The pseudodifferential operator square root of the Klein–Gordon equation’’ [J. Math. Phys.34, 3918 (1993)]

1994 ◽  
Vol 35 (7) ◽  
pp. 3769-3769 ◽  
Author(s):  
Claus Lämmerzahl
Keyword(s):  
Pseudodifferential Operator ◽  
Gordon Equation ◽  
Square Root ◽  
Klein Gordon ◽  
Math Phys ◽  
Klein Gordon Equation

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 Killing Tensor and Carter Constant for Painlevé–Gullstrand Form of Lense–Thirring Spacetime

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 473
Author(s):  
Joshua Baines ◽  
Thomas Berry ◽  
Alex Simpson ◽  
Matt Visser
Keyword(s):  
Jacobi Equation ◽  
Gordon Equation ◽  
Rotation Parameter ◽  
Slow Rotation ◽  
Square Root ◽  
Killing Tensor ◽  
Constant Of Motion ◽  
Klein Gordon ◽  
Hamilton Jacobi Equation ◽  
Klein Gordon Equation

Recently, the authors have formulated and explored a novel Painlevé–Gullstrand variant of the Lense–Thirring spacetime, which has some particularly elegant features, including unit-lapse, intrinsically flat spatial 3-slices, and some particularly simple geodesics—the “rain” geodesics. At the linear level in the rotation parameter, this spacetime is indistinguishable from the usual slow-rotation expansion of Kerr. Herein, we shall show that this spacetime possesses a nontrivial Killing tensor, implying separability of the Hamilton–Jacobi equation. Furthermore, we shall show that the Klein–Gordon equation is also separable on this spacetime. However, while the Killing tensor has a 2-form square root, we shall see that this 2-form square root of the Killing tensor is not a Killing–Yano tensor. Finally, the Killing-tensor-induced Carter constant is easily extracted, and now, with a fourth constant of motion, the geodesics become (in principle) explicitly integrable.

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation
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