Spectroscopy of the Rotating Kaluza-Klein Spacetime via Revisited Adiabatic Invariant Quantity

Abstract

In this paper, we have investigated the spectroscopy of the rotating Kaluza-Klein spacetime by applying Bohr–Sommerfeld quantization rule and the first law of thermodynamics. we derived the expression of the adiabatic invariant quantity in the dragged–Painleve coordinate system. Then, via revisited adiabatic invariant quantity, we derive the area and entropy spectra of the spacetime. We obtained the area spectrum of the Kaluza-Klein spacetime is ${\Delta } A=8\pi {l_{P}^{2}}$ , and the entropy spectrum is ΔS = 2π. This result is consistent with the Bekenstein’s original result, which imply the entropy and horizon area are discrete and equidistant for the spacetime.