Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBTZ quasinormal frequencies as poles of Greens function
48
0
0.0
(
0
)
Added by
Alfredo Lopez Ortega
Publication date
2018
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Based on the well known fact that the quasinormal frequencies are the poles of the frequency domain Greens function we describe a method that allows us to calculate exactly the quasinormal frequencies of the Klein-Gordon field moving in the three-dimensional rotating BTZ black hole. These quasinormal frequencies are already published and widely explored in several applications, but we use this example to expound the proposed method of computation. We think that the described procedure can be useful to calculate exactly the quasinormal frequencies of classical fields propagating in other backgrounds. Furthermore, we compare with previous results and discuss some related facts.
rate research
Read More
Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger. But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure, including distant small perturbations to the potential. In what sense are quasinormal modes a property of the resulting black hole? We explore this question for the linearized perturbation equation with two potentials having disjoint bounded support. We give a composition law for the Wronskian that determines the quasinormal frequencies of the combined system. We show that over short time scales the evolution is governed by the quasinormal frequencies of the individual potentials, while the sensitivity to global structure can be understood in terms of echoes. We introduce an echo expansion of the Greens function and show that, as expected on general grounds, at any finite time causality limits the number of echoes that can contribute. We illustrate our results with the soluble example of a pair of $delta$-function potentials. We explicate the causal structure of the Greens function, demonstrating under what conditions two very different quasinormal spectra give rise to very similar ringdown waveforms.
We compute the quasinormal mode frequencies and Regge poles of the canonical acoustic hole (a black hole analogue), using three methods. First, we show how damped oscillations arise by evolving generic perturbations in the time domain using a simple finite-difference scheme. We use our results to estimate the fundamental QN frequencies of the low multipolar modes $l=1, 2, ldots$. Next, we apply an asymptotic method to obtain an expansion for the frequency in inverse powers of $l+1/2$ for low overtones. We test the expansion by comparing against our time-domain results, and (existing) WKB results. The expansion method is then extended to locate the Regge poles. Finally, to check the expansion of Regge poles we compute the spectrum numerically by direct integration in the frequency domain. We give a geometric interpretation of our results and comment on experimental verification.
Recently it has been proposed that a strange logarithmic expression for the so-called Barbero-Immirzi parameter, which is one of the ingredients that are necessary for Loop Quantum Gravity (LQG) to predict the correct black hole entropy, is not another sign of the inconsistency of this approach to quantization of General Relativity, but is rather a meaningful number that can be independently justified in classical GR. The alternative justification involves the knowledge of the real part of the frequencies of black hole quasinormal states whose imaginary part blows up. In this paper we present an analytical derivation of the states with frequencies approaching a large imaginary number plus ln 3 / 8 pi M; this constant has been only known numerically so far. We discuss the structure of the quasinormal states for perturbations of various spin. Possible implications of these states for thermal physics of black holes and quantum gravity are mentioned and interpreted in a new way. A general conjecture about the asymptotic states is stated. Although our main result lends some credibility to LQG, we also review some of its claims in a critical fashion and speculate about its possible future relevance for Quantum Gravity.
In the study of perturbations around black hole configurations, whether an external source can influence the perturbation behavior is an interesting topic to investigate. When the source acts as an initial pulse, it is intuitively acceptable that the existing quasinormal frequencies will remain unchanged. However, the confirmation of such an intuition is not trivial for the rotating black hole, since the eigenvalues in the radial and angular parts of the master equations are coupled. We show that for the rotating black holes, a moderate source term in the master equation in the Laplace s-domain does not modify the quasinormal modes. Furthermore, we generalize our discussions to the case where the external source serves as a driving force. Different from an initial pulse, an external source may further drive the system to experience new perturbation modes. To be specific, novel dissipative singularities might be brought into existence and enrich the pole structure. This is a physically relevant scenario, due to its possible implication in modified gravity. Our arguments are based on exploring the pole structure of the solution in the Laplace s-domain with the presence of the external source. The analytical analyses are verified numerically by solving the inhomogeneous differential equation and extracting the dominant complex frequencies by employing the Prony method.
We consider the equivalence of quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope. Using WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and black hole shadow radius. We verify this correspondence with two black hole families in $4$ and $D$ dimensions, respectively.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
