Does Black Holes And Worm Holes Have Same Absorption Spectra? (Quantum / Maths)

Summary:

  • Crispino and colleagues studied the absorption of massless scalar waves in a geometry that interpolates between the Schwarzschild solution and a wormhole that belongs to the Morris-Thorne class of solutions.
  • Their results showed that black holes and wormholes present distinctive absorption spectra.
  • They concluded that, wormhole results are characterized by the existence of quasibound states which generate Breit-Wigner-like resonances in the absorption spectrum.

Crispino and colleagues investigated the propagation of massless scalar waves in the geometry proposed by Simpson and Visser. The line element of this geometry depends on a parameter. Depending on the values of a parameter, this geometry describes a Schwarzschild black hole (BH), a regular BH, or a wormhole spacetime belonging to the Morris-Thorne class. Their study recently appeared in the Journal Physical Review D.

Within General Relativity (GR) , BHs are solutions of the Einstein’s field equations that posses an event horizon. The first exact solution of Einstein’s equation is known as Schwarzschild geometry, which describes a spherically symmetric, electrically uncharged and non-rotating BH. The spherically symmetric, electrically charged and non-rotating BH geometry is known as the Reissner-Nordström solution. The first exact uncharged rotating BH solution was obtained by Kerr, while the charged rotating BH was presented in Newman and colleagues. Such standard BH solutions of GR are cursed with singularities, where geometrical quantities diverge and physics predictability breaks down. Later, regular BHs, i.e. non-singular BH solutions, were proposed as an alternative to avoid the singularity problem. While, wormholes are solutions that connect two asymptotically flat regions by a throat.

Absorption of matter and fields is of great interest in GR, for instance, in explaining the role of accretion by BHs in active galactic nuclei. There have been many studies on the absorption of scalar waves by black holes. But, in comparison to BHs, few results for the absorption of scalar waves by wormhole spacetimes are available.

Thus, Crispino and colleagues now carried out the study on the scalar absorption for Schwarzschild and regular BHs, as well as for Morris-Thorne wormholes, considering the simpson-Visser line element. They used the partial wave approach to compute the scalar absorption cross section in this geometry.

“We found that the absorption spectrum of this geometry presents interesting features. For instance, the wormhole solution can show imprints of quasibound states around the throat, leading to narrow peaks (or Breit-Wigner-like resonances) in the absorption spectrum.”

— told Crispino, one of the author of the study

TABLE I. Trapped modes frequencies for a=2.1M. © Crispino et al.

They found that the BH and the wormhole configurations can be quite distinctive concerning the absorption of scalar waves. The distinction is due to the presence of trapped modes around the wormhole’s throat (as shown in table 1) and to the different values of the total absorption cross section in the low- and high-frequency limits (as shown in fig 1 below). The absorption cross section of the wormhole branch of interpolation can present narrow resonant peaks due to a potential well at the throat of the wormhole (refer fig 4 and 6 below). Moreover, these peaks become broader as they increase the parameter ‘a’, due to the decreasing of the depth of the potential well around the wormhole throat.

“Due to the shape of the potential of the wormhole case, the results are, in general quite different from the BH ones. Such differences arises due to the presence of potential well. This potential well allows quasibound states to exist around r = 0. These quasibound states are similar to the trapped modes and are associated to stable null geodesics at the wormhole throat in the eikonal limit. These trapped modes have complex frequency and the imaginary part is usually small i.e. they are long-lived modes. “

— told Crispino, one of the author of the study

They also reported similar resonance effects in the absorption cross section for extreme/exotic compact objects (ECOs) and for BH remnants, where the partial transmission amplitudes also present Breit-Wigner-type resonances, analogously to the phenomenon present in nuclear scattering theory.

FIG. 1. Total absorption cross sections of massless scalar waves for wormholes with different values of ‘a’, compared with the geometric cross section (horizontal lines). In Figs. 1 (a), 1 (b), and 1 (c), they have set a = 2.5M, a = 3M and a = 4M, respectively. © Crispino et al.
FIG. 2. Total absorption cross section of massless scalar waves for regular BHs (with different values of a), compared with the geometric cross section (horizontal dashed line). In this figure, they also showed the total absorption cross section of massless scalar waves for the Schwarzschild BH, for comparison. © Crispino et al.
FIG. 3. Effective potential, for null geodesics in the BH case, as a function of the radial coordinate ‘r’. In this figure, they have selected different values for the parameter a (0 ≤ a < 2M). © Crispino et al.
FIG. 4. Effective potential for null geodesics in the wormhole case, as a function of the radial coordinate ‘r’. In this figure, they have selected different values for the parameter a (a ≥ 2M). © Crispino et al.
FIG. 5. Effective potential for the massless scalar field φ in the BH case, as a function of the radial coordinate ‘r’ in units of the event horizon ‘rh’. In this figure, they have selected different values for the parameter ‘a’, obeying 0 ≤ a < 2 M. © Crispino et al.
FIG. 6. Effective potential for the massless scalar field φ in the wormhole case, as a function of the radial coordinate ‘r’ in units of M. In this figure, they have selected different values for the parameter ‘a’ , obeying a ≥ 2 M. © Crispino et al.

Featured image: Total absorption cross section of massless scalar waves for the wormhole with a = 2.1M, compared with the geometric cross section (horizontal line). The narrow peaks, associated to the vertical black dashed lines arise due to the potential well, which imply in the existence of the trapped modes. They also exhibit, below the plot, an absorption band composed with the results for the total absorption cross section. © Crispino et al.


Reference: Haroldo C. D. Lima Junior, Carolina L. Benone, and Luís C. B. Crispino, “Scalar absorption: Black holes versus wormholes”, Phys. Rev. D 101, 124009 – Published 5 June 2020. DOI: https://doi.org/10.1103/PhysRevD.101.124009


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