How Do You Recognise A Wormhole, Which Mimicks To Be a Black Hole? (Astronomy)

Summary:

—> According to Paul and colleagues, unlike black hole, such wormholes have accretion disks on both sides of their throat.

—> They also considered two classes of rotating wormhole geometries. The first is the Kerr worm hole and Morris-Thorne wormhole, also known as the Teo wormhole and showed with the help of algorithm and simulations that the Teo wormhole don’t have any photon sphere, (like Kerr-wormhole) it means that throat itself in this case act as an effective photon sphere.

—> They also proposed that such wormholes have very strong gravitational lensing effect, as throat itself act as photon sphere in this case.


It is believed that supermassive black holes with masses of the order of 10^6-10^10M exist at the center of most galaxies. Observational aspects of black holes, which are characterized by an event horizon, are naturally of great significance, as these might shed light on the underlying physics of the end stages of gravitational collapse, which are perhaps influenced by quantum phenomena in the regimes of very strong gravity. Indeed, recent observations of the center of the galaxy M87 by the Event Horizon Telescope have triggered a flurry of activities towards understanding and quantifying possible images of accretion disks that can be formed around the galactic center.

While the notion of the event horizon continues to attract much attention, it has become clear by now that compact objects which do not have an event horizon might mimic many of the properties of black holes. One such object is the wormhole – an exotic solution of Einstein’s equations that connect two different universes or two distant regions of the same universe by a throat. Celestial objects that are not tidally disrupted can tunnel through the throat, from one universe or one distant region to another. An important issue related to this tunneling of material objects through the wormhole throat is that of traversability, and it was shown by Fuller and Wheeler that the Schwarzchild wormhole (also called the Einstein-Rosen bridge) is not traversable in this sense. Traversable wormholes, which are of physical interest appeared first in the work of Morris and Thorne and a subsequent description of a “time machine” based on the Morris-Thorne construction appeared in Morris et al. and Nonikov et al.. Details of these can be found in the excellent book by Visser. Typically, the matter sourcing wormhole geometries violates standard energy conditions. However, several attempts have been made to evade such violations, and as is well known, dynamical scenarios or wormhole geometries in modified gravity may offer situations in which these energy conditions are not violated. Stability of wormhole geometries which is known to be related to the equation of state of the matter supporting such geometries, is also a much studied topic, although the issue is still debated. While it is known that some wormhole geometries might be stable under metric and field perturbations, others might not. However, in spite of these issues, wormholes continue to attract much attention as they are prototype examples of solutions of general relativity that can mimic black holes.

The fact that wormholes can strongly resemble black holes was noted more than a decade ago by Damour and Solodukhin, who pointed out that several features of black holes such as quasi-normal modes, accretion properties, no-hair theorems etc. can be closely mimicked by wormhole geometries as well. Indeed, after the first results on gravitational wave detection by LIGO were obtained, it was shown by Cardoso, Franzin and Pani that a class of wormholes that have a thin shell of phantom matter at the throat can exhibit an initial quasinormal ringdown mode that is entirely similar to that of a black hole, with differences emerging only at late times. Later, Konoplya and Zhidenko showed that specific classes of wormholes can in fact ring similarly or differently compared to black holes at all times. In the light of the above discussions, it is clearly important and interesting to further study the observational distinctions between black hole and wormhole geometries.

So, Paul and colleagues in their recent paper point out that one can observe dramatic differences between these objects in the context of their accretion disk images. They proceeded with two assumptions. First, they restrict themselves to thin accretion disks in wormhole geometries, which were analytically studied by T. Harko and colleagues. Second, they assumed that the accreting matter does not interact with the matter seeding the wormhole, which is a fairly standard assumption in the literature. Specifically, since the wormhole has a throat, it is possible and indeed natural to have accretion disks on either or both sides of the wormhole throat. If one only focuses on the disk on the same side of the throat as that of the observer, then the images may or may not mimic those of black hole accretion disks. However, Harko and colleagues showed in their paper that the images of the disk when it is on the side of the throat opposite to that of the observer are drastically different from the ones observed from black holes. In a related context, Sarkar and colleagues have shown recently that strong gravitational lensing from wormhole geometries might be qualitatively different from the ones in black hole backgrounds. The reason for this is two-fold. Namely, with the observer and the source both on the same side of the wormhole throat, the throat can itself act as an effective photon sphere, where light travels in unstable circular orbits and via a small perturbation can reach an observer at infinity. Also, the observer and the source might be on different sides of the wormhole throat which opens up a further possible feature of gravitational lensing that is absent in black hole geometries. In this paper, they logically continue this analysis further, and focus on the images of accretion disks of black hole and wormhole geometries.

In present work, Paul and colleagues considered two classes of rotating wormhole geometries. The first is the Kerr-like wormhole constructed and the second is the rotating version of the Morris-Thorne wormhole, also known as the Teo wormhole. They constructed accretion disk images for these wormholes numerically and considered two different numerical algorithms. The first one is a semi-analytic construction, in which separated null geodesic equations obtained by analytically integrating the second order equations once are used, and the second, in which a fully numerical ray-tracing method is used by employing a fourth order Runge-Kutta algorithm. With both these methods, they obtained the accretion disk images of the two classes of wormhole geometries they considered.

Table I: The position of the inner edge of an accretion disk for different parameter values. The positions of the wormhole throat (rth) or black hole outer horizon (r+) and the inner edge (rin) of the disk for different parameter values. Generally, the inner edge rin of the disk is at the marginal stable orbit rms. However, when there is no marginal stable orbit outside the wormhole throat, the throat itself acts as the position of the disk inner edge.

“Importantly, considering the fact that there might be accretion disks on both sides of the wormhole throat, we get an overall picture that is strikingly different from any black hole accretion
disk image obtained so far in the literature. This is the main contribution of this work.”, said Sarkar.

They showed that there might be very distinctive features of the accretion disk images from a wormhole that can conclusively prove its difference with that in the background of a black hole. Specifically, they showed that this difference arises as the wormhole might have accretion disks on both sides of its throat, so that if the observer and the disk are on opposite sides of the throat, novel images might be obtained which are not known to occur in any other geometry. Thus, any accretion disk image that contains such features might be used to distinguish wormholes from other objects. It is to be noted that the novel feature (multiple images) of an accretion disk when it is on the other side of the throat are generic to wormholes.

FIG. 1. The images of a Kerr-like wormhole with accretion disks on both sides of the throat [(a)]. (b) is the zoomed in version of (a). The outer edge of the disk is at r = 20M. The observers inclination angle is θo = 80◦. The observer is placed at the radial coordinate r = 10⁴M, which corresponds effectively to the asymptotic infinity. All spatial coordinates are in units of M.

While, the images for the Teo wormhole qualitatively differ from those of a black hole as the image of the black hole contains a thin ring image inside the direct image, whereas the image of the wormhole does not [compare between Figs. 2(a) and 2(b) and between Figs. 2(d) and 2(e)]. This thin ring image is formed by light rays which undergo strong gravitational lensing due to the photon sphere which lies outside the event horizon. For the Teo wormhole, they don’t have any photon sphere outside the throat. Although the throat in this case acts as an effective photon sphere, before a photon starts winding around the throat due strong lensing, it hits the disk as the disk extends upto the throat. As a result, they don’t have the thin ring image for the Teo wormhole. However, the images for the Kerr-like wormhole in this scenario mimic those for Kerr black hole [compare between Figs. 2(a) and 3(a) and between Figs. 2(d) and 3(d)].

FIG. 2. The images of a Kerr black hole [(a) and (d)] and a Teo wormhole [(b), (c), (e) and (f)] with accretion disks. (b) and (e) are for the case when the disk is on the observer’s side, and (c) and (f) are for the case when it is on the other side. The outer edge of the disk is at r = 20M, and the position of its inner edge for different parameters is shown in Table I. The observer’s inclination angle is θo = 80◦. The observer is placed at the radial coordinate r = 10⁴M, which corresponds effectively to the asymptotic infinity. In order to get rid of the parameters M and M˙, they have normalized the fluxes by the maximum flux observed for the Kerr black hole with a = 0. Also, they have plotted the square-root of the normalized flux and rescaled the color function for better looking. The color bars show the values of the square-root of the flux. All spatial coordinates are in units of M.

The most striking differences in the images, however, occur when they considered the disk to be on the other side of the throat. The images in this case have unique characteristic features. A single intensity map of a disk image contains multiple images [see Figs. 2(c), 2(f), 3(b), 3(c), 3(e) and 3(f)]. This unique characteristic feature of the images can in principle distinguish a wormhole background from a black hole. Here they noted that, when there are disks on both the sides of the throat, the images will be the superposition of the images of the disk on the observer’s side and those of the disk on the other side. One such example is shown in Fig. (1), where they also provided a zoomed-in version to display the features more prominently. The striking difference with the black hole example of Fig.(2(d)) is clear.

FIG. 3. The images of a Kerr-like wormhole with an accretion disk when the disk is on the observer’s side [(a) and (d)], and when it is on the other side [(b), (c), (e) and (f)]. The outer edge of the disk is at r = 20M, and the position of its inner edge for different parameters is shown in Table I. The observer’s inclination angle is θo = 80◦. The observer is placed at the radial coordinate r = 10⁴M, which corresponds effectively to the asymptotic infinity. In order to get rid of the parameters M and M˙, they have normalized the fluxes by the maximum flux observed for the Kerr black hole with a = 0. Also, they have plotted the square-root of the normalized flux and rescaled the color function for better looking. The color bars show the values of the square-root of the flux. All spatial coordinates are in units of M.

“We have considered two different examples here, but we expect that our analysis is robust, and that the features displayed in Fig. (1) will be qualitatively similar in other wormhole geometries.”, concluded authors of the study.


Reference: Suvankar Paul, Rajibul Shaikh, Pritam Banerjee, Tapobrata Sarkar, “Observational signatures of wormholes with thin accretion disks”, Journal of Cosmology and Astroparticle Physics, pp. 1-24, 2020. https://iopscience.iop.org/article/10.1088/1475-7516/2020/03/055


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