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Quasinormal spectra of a wormhole family: overtone features and a parameter-controlled redshift

Abhisek Barman Maji, Sayan Kar

Abstract

Though investigated extensively in the past, we take a detailed relook at the study of quasinormal modes (QNM) in a known family of wormholes (ultrastatic ($g_{00}=-1$), as well as spacetimes with different, non-constant $g_{00}$), which includes the familiar Bronnikov-Ellis spacetime as a special case. Our focus here is to go beyond the fundamental mode and obtain some of the QNM overtones using a suitable numerical scheme. Scalar and axial gravitational QNMs including two or three overtones are obtained for the family of ultrastatic geometries and their parameter dependencies are shown explicitly. Further, we comment on how (a) the overtones may influence the time-domain profile in a perturbation and (b) in what sense, the use of overtones may help in distinguishing between different geometries within the family. Finally, we show how an effect somewhat similar to the so-called `environment induced redshift' of QNMs, introduced recently (Phys. Rev. D \textbf{111}, 064026 (2025)), may be obtained for spacetimes with non-constant $g_{00}$, via an appropriate tuning of available metric parameters which systematically modify the shapes of the effective potentials arising in the perturbation equations.

Quasinormal spectra of a wormhole family: overtone features and a parameter-controlled redshift

Abstract

Though investigated extensively in the past, we take a detailed relook at the study of quasinormal modes (QNM) in a known family of wormholes (ultrastatic (), as well as spacetimes with different, non-constant ), which includes the familiar Bronnikov-Ellis spacetime as a special case. Our focus here is to go beyond the fundamental mode and obtain some of the QNM overtones using a suitable numerical scheme. Scalar and axial gravitational QNMs including two or three overtones are obtained for the family of ultrastatic geometries and their parameter dependencies are shown explicitly. Further, we comment on how (a) the overtones may influence the time-domain profile in a perturbation and (b) in what sense, the use of overtones may help in distinguishing between different geometries within the family. Finally, we show how an effect somewhat similar to the so-called `environment induced redshift' of QNMs, introduced recently (Phys. Rev. D \textbf{111}, 064026 (2025)), may be obtained for spacetimes with non-constant , via an appropriate tuning of available metric parameters which systematically modify the shapes of the effective potentials arising in the perturbation equations.

Paper Structure

This paper contains 19 sections, 47 equations, 47 figures, 11 tables.

Table of Contents

  1. Introduction and summary
  2. A brief review on the family of wormhole geometries
  3. The ultra-static wormhole family
  4. Bronnikov--Ellis wormhole with asymptotic mass
  5. Bronnikov--Ellis geometry with a chosen redshift function:
  6. Effective potentials for scalar and axial perturbation
  7. Results: quasinormal spectra (fundamental and overtones for the ultra-static case)
  8. Inferences drawn from the QNM spectra: emphasis on overtones
  9. Approximate Analytic Fit
  10. Detectable Modes
  11. Redshift
  12. Bronnikov--Ellis geometry with asymptotic mass:
  13. Bronnikov--Ellis geometry with a chosen redshift function:
  14. Remarks and future directions
  15. Methods used to find the QNMs
  16. ...and 4 more sections

Figures (47)

  • Figure 1: For $n=8$ geometry: [left] $\rho$; [middle] $\rho+\tau$; [right] $\rho+p$. Blue solid line denotes $M=0$ and orange dashed line represents $M=0.25b_0$ (here $b_0=1$). In all the images, the x-axis represents the proper coordinate $l$.
  • Figure 2: For Bronnikov--Ellis wormhole with redshift function: [left] $\rho+\tau$; [right] $\rho+p$. Blue line denotes $M=0.2b_0$ and red line represents $M=0.4b_0$. (here $b_0=1$)
  • Figure 3: Effective potential (Scalar) for Bronnikov--Ellis wormhole with $n=2$.
  • Figure 4: Effective potential (Axial) for Bronnikov--Ellis wormhole with $n=2$.
  • Figure 5: QNMs for n = 2 (Scalar) case. The results of SM and Prony fit are represented by circles and plus signs, respectively. (Table: \ref{['tab:qnm_scalar_axial_2']})
  • ...and 42 more figures