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• W3145604857 abstract "Using the modified Kunstatter method, which employs as proper frequency the imaginary part instead of the real part of the quasinormal modes, the entropy spectrum and area spectrum of the modified Schwarzschild black holes in gravity’s rainbow are investigated. In the current study, two cases of modified dispersion relations concerning energy dependent and energy independent speed of light are considered. The entropy spectra with equal spacing are derived in these two cases. Furthermore, the obtained entropy spectra are independent of the energy of a test particle and are the same as the one of the usual Schwarzschild black hole. Also, the same area spectrum formulas are obtained in these different dispersion relations. However, due to the quantum effect of spacetime, the obtained area spectra are not equally spaced and are different from the one of the usual Schwarzschild black hole. Besides, in these two cases, the same black hole entropy formulas with logarithmic correction to the standard Bekenstein–Hawking area formula are obtained by the adiabatic invariant. The form of area spacing formulas and entropy formulas are independent of the particle’s energy, but the area spacing and entropy can have energy dependence through the area. In 1972, considering black holes emitting or absorbing quanta, Bekenstein proposed that black hole entropy is proportional to horizon area and the area is quantized [1]. It was proposed that the minimum increase of horizon area can be obtained by the absorption of a test particle and expressed as [1] ( A)min = eG , (1) where e is an undetermined dimensionless constant and the unit of c= kB = 1 is used. Motivated by this proposal, many researches have been made to derive the quantum spectrum a e-mail: czlbj20@yahoo.com.cn of black holes and different spectra with different e have been presented [2–28]. Bekenstein put forward that e = 8π [2–5], that is, the black hole area quantum was ( A)min = 8πG . (2) Therein, by considering the horizon area as an adiabatic invariant, the black hole quantization was implemented and the area spectrum (2) was presented [3–5]. In addition, the quantization of black holes was also posed from the quasinormal modes (QNMs) of black holes. The QNMs is a set of complex frequencies that describe the response of black holes to a perturbation (see [29] for a review). Based on Bohr’s correspondence, Hod argued that [6, 7], the highly damped QNMs of black holes should be identical to the quantum transition of the corresponding systems and the real part of the asymptotic QNMs should be equal to the quantum transition frequency. Then, letting the radiation energy ωc equal the energy change of black holes, the QNMs were related to the quantization of black holes. Later, the proposal of black hole horizon area being an adiabatic invariant and the method of relating the QNMs to black hole quantization were united by Kunstatter [8]. It was shown that, for a system with energy E and vibrational frequency ω(E), there is a natural adiabatic invariant, I = ∫ dE ω(E) . Further, as a semiclassical limit, a black hole with transition frequency can be considered as a classical system of periodic motion with the vibrational frequency equal to the real part of the QNMs. Then, following the Bohr–Sommerfeld quantization rule I = n and considering the black hole energy as the ADM mass, Kunstatter obtained an adiabatic invariant formula for the Schwarzschild black hole as [8]" @default.
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• W3145604857 date "2012-01-01" @default.
• W3145604857 modified "2023-09-27" @default.
• W3145604857 title "Black hole spectroscopy via adiabatic invariant in a quantum corrected spacetime" @default.
• W3145604857 hasPublicationYear "2012" @default.
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