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Abstract The gravitational perturbations of a rotating Kerr black hole are notoriously complicated, even at the linear level. In 1973, Teukolsky showed that their physical degrees of freedom are encoded in two gauge-invariant Weyl curvature scalars that obey a separable wave equation. Determining these scalars is sufficient for many purposes, such as the computation of energy fluxes. However, some applications—such as second-order perturbation theory—require the reconstruction of metric perturbations. In principle, this problem was solved long ago, but in practice, the solution has never been worked out explicitly. Here, we do so by writing down the metric perturbation (in either ingoing or outgoing radiation gauge) that corresponds to a given mode of either Weyl scalar. Our formulas make no reference to the Hertz potential (an intermediate quantity that plays no fundamental role) and involve only the radial and angular Kerr modes, but not their derivatives, which can be altogether eliminated using the Teukolsky–Starobinsky identities. We expect these analytic results to prove useful in numerical studies and for extending black hole perturbation theory beyond the linear regime.
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Modeling a Strain and Piezo Potentials in an InAs/GaAs Quantum Dot
We investigated the single-electron spectrum of an InAs/GaAs quantum dot (QD) using an effective potential model developed in previous studies. Our objective was to explore the limits of applicability of this model. We conducted numerical simulations, introducing a piezoelectric potential as a perturbation to the effective potential. The profile of this additional potential was derived from theoretical numerical studies presented in the literature. We analyzed the impact of variations in this profile within the framework of the perturbation theory. Our findings indicate that within a variation range of 25%, the effective potential model remains applicable.
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- PAR ID:
- 10588535
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Processes
- Volume:
- 12
- Issue:
- 11
- ISSN:
- 2227-9717
- Page Range / eLocation ID:
- 2524
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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