In this article we show that the asymptotic iteration method (AIM) allows one to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de Sitter (SdS) black holes. An added benefit of the method is that it can also be used to calculate the Schwarzschild anti-de Sitter (SAdS) quasinormal modes for the case of spin zero perturbations. We also discuss an improved version of the AIM, more suitable for numerical implementation. ¶ Main address from 1st of June. 1 The phrase "continued fraction" used for WKB solutions should not be confused with the type of continued fractions developed from Frobenius series for QNMs by Leaver [2]. In the rest of the paper "continued fraction" will mean those generated from Frobenius series.
We discuss an approach to obtaining black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second order ordinary differential equations.We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordström (RN) and Kerr black holes in a unified way. An advantage of the AIM over the standard continued fraction method (CFM) is that for differential equations with more than three regular singular points Gaussian eliminations are not required. However, the convergence of the AIM depends on the location of the radial or angular position, choosing the best such position in general remains an open problem. This review presents for the first time the spin 0, 1/2 & 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM, and confirms results previously obtained using the CFM.We also presents some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher dimensional generalizations and we give an example of doubly rotating black holes.
In this paper we use the conformal properties of the spinor field to show how we can obtain the fermion quasi-normal modes for a higher dimensional Schwarzschild black hole. These modes are of interest in so called split fermion models, where quarks and leptons are required to exist on different branes in order to keep the proton stable. As has been previously shown, for brane localized fields, the larger the number of dimensions the faster the black hole damping rate. Moreover, we also present the analytic forms of the quasi-normal frequencies in both the large angular momentum and the large mode number limits.
We propose a projective operator formalism that is well-suited to study the correlations of quantum fields in non-inertial frames. We generalise a Glauber model of detection of a single localised field mode that is capable of making measurements in an arbitrary reference frame. We show that the model correctly reproduces the Unruh temperature formula of a single accelerated detector, and use it to extract vacuum entanglement by a pair of counter-accelerating detectors. This latter example is a proof of principle that this approach will be appropriate to further studies on the nature of entanglement in non-inertial frames and, in general, to model experimentally feasible scenarios in quantum field theory in non-inertial frames. Finally, as further confirmation of the validity of our approach, we introduce an explicit perturbative matter-radiation interaction model which reproduces both the generalised Glauber model and the projective measurement results in the weak coupling regime. arXiv:1203.0655v2 [quant-ph] 1 Dec 2012
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.