Asymmetric wormholes may cast more than one shadow

In April 10, 2019 the Event Horizon Telescope collaboration released one of the most celebrated images of that year: a bright ring formed by the light and electromagnetic radiation that bends around a black hole with a mass that is 6500 million times that of the Sun. That image was in agreement with our expectations from what a (rotating) black hole should look like when surrounded by an accretion disk that emits electromagnetic radiation (light, heat, radio waves, ...). 

Black holes have an event horizon from which nothing can escape but they also have what is called a photon sphere, which is more external than the event horizon, and which represents a region in which photons are forced to orbit around the central object. If a photon gets sufficiently close to the black hole and crosses its photon sphere, then the photon orbit will fall following a spiral trajectory inwards until it falls within the event horizon. But if hits this boundary tangentially, then it could stay orbiting the central object for, in principle, an arbitrarily long time. Photons that get very close to the photon sphere but manage to scape after a long number of orbits will be able to reach us and provide evidence of the existence of this peculiar surface. Our detectors will perceive a (deformed) ring of intense radiation around a dark central region, which is known as black hole shadow. 

But photon spheres are not unique to black holes, and other compact astrophysical objects can also develop one. This is the case, in particular, of sufficiently compact wormholes, those hypothetical astrophysical objects that could be used to travel to distant regions of the universe by exploiting the topological properties of space-time. As a result, a wormhole surrounded by an accretion disk could also exhibit a bright ring in which radiation accumulates before escaping to reach us. 

A key difference between a wormhole and a black hole shadow is that light can scape from the wormhole, and this could make the internal region of the disk shadow brighter than in the black hole case since radiation emitted from the other side of the wormhole could reach us through it.

Like black holes, wormholes can have a mass and an electric charge. The funny thing of wormholes is that these two parameters need not be the same on both sides of these cosmic gates. As a result, the photon spheres on both sides could have different sizes and this necessarily has an impact on the properties of their shadows. In our work, we have analysed in some detail the conditions that allow for the existence of asymmetric thin-shell wormholes, formed by a thin shell of energy, and how the asymmetry affects their shadows according to observers on each side of them. 

Our analysis has been carried out in a gravitational context more general than Einstein's theory of gravity, the so-called f(R) theories of gravity in Palatini formalism. This mathematical scenario allows us to use the same external solutions as in Einstein's gravity but modifies the properties of the  energy shell that conforms the wormhole. The result is that stable configurations are possible and do not require exotic energy sources, which typically involve repulsive gravitational properties. The details can be found in a preprint posted in arXiv this week by our colleagues Mercè Guerrero, Gonzalo J. Olmo, and Diego Rubiera-García. 

Why is it important?

Our results are important because the universe contains hundreds of thousands of millions of galaxies and most of these structures are possible thanks to the existence of massive compact objects at their centres. Whether those compact objects are all black holes or more exotic entities is a matter that must be determined through observation. But in order to correctly interpret observational data, we must be able to estimate a range of different possibilities which are consistent with current theories. Observations will thus help us better understand what is physically possible and rule out theoretical alternatives.  

If the ring of light predicted by black holes is not always realised in nature and thicker structures or more than one thin ring are ever observed, then we could be facing the discovery of a kind of exotic astrophysical object that so far has only been found in the science fiction literature and movies. The implications that the existence of such objects could have for our understanding of the origin and evolution of the universe, and even for the development of future technologies are difficult to foresee. 


Our work has focused on the study of static, spherically symmetric wormholes with a certain mass and electric charge, but astrophysical objects are also rotating and may have deformations. Incorporating these new elements in the analysis will provide additional insights on new effects present in the shadows of compact objects, thus helping us refine our predictions and extract more valuable information from observational data. 

Read this paper on arXiv: e-Print: 2102.00840 [gr-qc]


Written by M. Guerrero, G.J. Olmo, and D. Rubiera-García. 

Photo by Ben Collins on Unsplash

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