Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-01-09
Int.J.Mod.Phys.A23:1613-1626,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, LaTeX, to be published in Int. Jour. Mod. Phys. A
Scientific paper
10.1142/S0217751X08039463
The Klein-Gordon and Dirac equations are considered in a semi-infinite lab ($x > 0$) in the presence of background metrics $ds^2 =u^2(x) \eta_{\mu\nu} dx^\mu dx^\nu$ and $ds^2=-dt^2+u^2(x)\eta_{ij}dx^i dx^j$ with $u(x)=e^{\pm gx}$. These metrics have non-constant scalar-curvatures. Various aspects of the solutions are studied. For the first metric with $u(x)=e^{gx}$, it is shown that the spectrums are discrete, with the ground state energy $E^2_{min}=p^2c^2 + g^2c^2\hbar^2$ for spin-0 particles. For $u(x)=e^{-gx}$, the spectrums are found to be continuous. For the second metric with $u(x)=e^{-gx}$, each particle, depends on its transverse-momentum, can have continuous or discrete spectrum. For Klein-Gordon particles, this threshold transverse-momentum is $\sqrt{3}g/2$, while for Dirac particles it is $g/2$. There is no solution for $u(x)=e^{gx}$ case. Some geometrical properties of these metrics are also discussed.
Alimohammadi Masoud
Baghjary A. A.
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