Tag Archives: #wormholes

Could 3-Form Wormholes Be Black Hole Mimickers? (Cosmology)

Mariam Bouhmadi-Lopez and colleagues have constructed a symmetric wormhole solution in General Relativity (GR), which is supported by a 3-form field with a potential that contains a quartic self-interaction term. They hint towards the possibility that, the 3-form wormholes could be potential black hole mimickers, as long as the coefficient of the quartic self-interaction term (Λ) is sufficiently large, precisely when NEC is weakly violated. Their study recently appeared in Arxiv.

General Relativity (GR) is a well-tested theory, so it would be interesting to find traversable wormhole solutions in GR with “physically reasonable” matter field to support the throat. Such a matter field should preferably possess a correct sign for its kinetic energy though necessarily still violate some energy conditions. It would be even better if such a matter field is in some sense natural (e.g., it can also be applied to explain cosmological puzzles such as the accelerated expansion of the Universe). One natural candidate is the 3-form field which is ubiquitous to string theory within a cosmological framework and beyond.

FIG. 1: (a) The embedding diagram of the wormhole spacetime supported by the 3-form field. The red curve indicates the wormhole throat. (b) This schematic plot shows the evolution of the 3-form field on the potential in the wormhole spacetime. The shaded regions represent the regions where the NEC is violated. © Mariam Bouhmadi-Lopez et al.

Now, Mariam Bouhmadi-Lopez and colleagues numerically constructed a symmetric wormhole solution in pure Einstein gravity supported by a massive 3-form field with a potential that contains a quartic self-interaction term.

They found that, the wormhole spacetimes have only a single throat and they are everywhere regular and asymptotically flat. Furthermore, their mass and throat circumference increase almost linearly as the coefficient of the quartic self-interaction term Λ increases.

The amount of violation of the null energy condition (NEC) is proportional to the magnitude of 3-form, thus the NEC is less violated as Λ increases, since the magnitude of 3-form decreases with Λ.

In addition, they have investigated the geodesic equations for null particles and timelike particles moving around the wormhole. It is found that the unstable photon sphere/orbit, on which photons can undergo circular motions around the wormhole, is exactly at the wormhole throat.

In addition, they have investigated the geodesics of particles moving around the wormhole and found that the unstable photon orbit is located at the throat. They also found that the wormhole can cast a shadow whose apparent size is smaller than that cast by the Schwarzschild black hole, but reduces to it when Λ acquires a large value.

Moreover, they also discussed the behavior of the innermost stable circular orbit (ISCO) around this wormhole and found that the radius of ISCO deviates from the Schwarzschild counterpart when Λ is small, but reduces to it for a larger Λ. Thus, their wormholes can be a black hole mimicker when Λ is large, precisely when NEC is less violated.

“Of course, most astrophysical black holes rotate, so it remains to be seen if this mimicry still holds when rotation is considered.”

— authors of the study.

“Future investigation will look into the radial perturbation on the background metric and the form field to check stability, among other considerations. Indeed, the wormhole solutions supported by the complex phantom scalar field are found to be unstable against linear perturbations. It would be interesting to check whether our wormholes suffer from the same instability, and if so, for which range of Λ.”, they concluded.

Reference: Mariam Bouhmadi-López, Che-Yu Chen, Xiao Yan Chew, Yen Chin Ong, Dong-han Yeom, “Traversable Wormhole in Einstein 3-Form Theory With Self-Interacting Potential”, Arxiv, pp. 1-12, 2021.

Note for editors of other websites: To reuse this article fully or partially kindly give credit either to our author S. Aman or provide a link of our article

What Leads To Factorization Problem? How Half Wormholes Can Fix It? (Maths / Cosmology / Quantum)

Wormholes not only play a key role in understanding the nonperturbative physics of quantum black holes, for instance: the eternal traversable wormhole; the long-time behavior of the spectral form factor and correlation functions, the Page curve etc. but also, it leads to puzzles, in particular the factorization problem. Imagine two decoupled boundary systems in the AdS/CFT context, labelled L and R. From the boundary perspective, if one evaluates a partition function in the combined system the result is just the product of the results for the two component systems:

It factorizes. But, if the bulk calculation of ZLR includes a wormhole linking L and R then superficially at least ZLR ≠ ZLZR. It fails to factorize. Some of the phenomena recently explained by wormholes, in particular the spectral form factor and squared matrix elements, are described by decoupled boundary systems and so the wormhole explanation give rise to a factorization puzzle.

But, you can remove this factorization puzzle by averaging the L and R systems over the same ensemble, denoted by (·), with the help of the SYK model. The factorization puzzle solves because (ZLZR) need not to be same as (ZL) (ZR). And infact this link between wormholes and ensembles is not a new one, it dates back to the 1980s. However, it has been recently applied in AdS/CFT context.

We can create a new form of factorization puzzle in such ensembles by asking what happens to the wormholes connecting decoupled systems when we focus on just 1 element of the ensemble. Now, Phil Saad and colleagues addressed this question in the SYK model where instead of averaging the L and R systems they picked a fixed set of couplings between the fermions.

These pictures represent saddle points of the SYK path integral, associated to the sketched bulk topology by the pattern of correlation. As the wormhole contribution is self-averaging, they have depicted it with a small red “x” to indicate the small amount of randomness. The half-wormhole contributions are not self-averaging, so they have depicted them as “half” of a wormhole with a jagged red boundary to indicate the large amount of randomness. They have included a red line linking the pair of half-wormholes on the LHS, to remind them that the LR collective fields are present, but set to zero, distinguishing this contribution from the unlinked pair of half wormholes on the RHS. © Phil Saad et al.

After averaging over fermion couplings, SYK model has a collective fields called G and Σ, that sometimes has “wormhole” solutions. Phil Saad and colleagues studied the fate of these wormholes when the couplings are fixed.

Working mainly in a simple model, they found that the wormhole saddles persist, and the dependence on the couplings is weak. The wormhole is “self-averaging”. But, that new saddles also appear elsewhere in the integration space, which they interpret as “half-wormholes.” The half-wormhole contributions depends sensitively on the particular choice of couplings.

Finally, they showed that, the half-wormholes are crucial for factorization (or restore factorization) of decoupled systems with fixed couplings, but they vanish after averaging, leaving the non-factorizing wormhole behind.

Reference: Phil Saad, Stephen H. Shenker, Douglas Stanford, and Shunyu Yao, “Wormholes without averaging”, Arxiv, pp. 1-34, 2021.

Note for editors of other websites: To reuse this article fully or partially kindly give credit either to our author/editor S. Aman or provide a link of our article

Can A Massive Star Collapse Into A Wormhole? (Cosmology)

The gravitational collapse of a massive star is a natural process that can produce a black hole. But, have you ever thought, that a massive star can also gravitationally collapse into a wormhole. Yeah, thats what Chakrabarti and Kar considered in their recent paper. They proposed a non-singular model of gravitational collapse and explored a possibility of the formation of wormhole. They showed that a time-dependent/Lorentzian wormhole geometry can arise in gravitational collapse and this wormhole structure is very similar to the recently proposed Simpson-Visser vacuum solution. Their study recently appeared in Arxiv.

Simpson-visser solution is a modification of the standard Schwarzschild spacetime, with an additional parameter ‘a’ being introduced in the metric, which controls the interpolation of the metric between a standard Schwarzschild black hole and a Morris-Thorne traversable wormhole.

In other words, for different values of the parameter ‘a’, the metric can yield different geometric structure such as:

  • When a = 0, you will get the standard Schwarzschild geometry.
  • When a ≠ 0, you will get a regular black hole.
  • If a > 2m, you will get a two-way traversable wormhole geometry.
  • If a = 2m, you will get a one-way wormhole with an extremal null throat.

Chakrabarti and Kar studied the time evolution of the collapsing wormhole geometry, which is very similar to the Simpson-Visser vacuum solution.

They investigated the behavior of geodesic congruences and confirmed that no zero proper volume singularity is reached at any time.

From a suitable boundary matching condition, they have also given an exact collapsing solution, which slowly evolves into a spherical wormhole geometry at a non-zero minimum radius.

“The term responsible for a wormhole structure comes from the g11 component of the metric”

Finally, they discussed that this singularity-free nature of the spacetime lies within its wormhole-like structure (called collapsing sphere), which also leads to a violation of the Null Convergence Condition.

Reference: Soumya Chakrabarti, Sayan Kar, “A wormhole geometry from gravitational collapse”, Arxiv, pp. 1-14, 2021. https://arxiv.org/abs/2106.14761

Note for editors of other websites: To reuse this article fully or partially kindly give credit either to our author/editor S. Aman or provide a link of our article

Are Casimir Wormholes Possible In 3D Spacetimes? (Cosmology)

Oliveira and colleagues carried out study on the existence of Traversable Casimir Wormholes in arbitrary dimensions. They showed that, Casimir energy can be a source of the Morris-Thorne wormhole for all spacetime dimensions (D) greater than 3. Their study recently appeared in Arxiv.

In 2019, Garattini showed that, in four dimensions, only the standard negative Casimir energy density and the radial pressure are able to form a Morris-Thorne Wormhole. On another hand, in a recent paper, Alencar and colleagues showed that in three dimensions the same is not true, thus, this inspired Oliveira and colleagues to investigate the influence of dimensionality of spacetime on the Casimir wormhole, in order to generalize both results.

In order to investigate the influence, they first analyzed Einstein’s equation in D dimensions static and spherically symmetric spacetime and considered the Casimir energy and pressure as sources. They found that the solution depends only on the redshift and shape functions.

They also showed that the boundary and flare-out conditions can be satisfied for any dimensions. Therefore, these conditions do not impose any restrictions for Casimir wormholes in D dimensions.

In addition, it has been shown, why for 3D spacetimes it is not possible to form wormholes. They showed it, by obtaining a general condition which was satisfied by the state parameter wD. It is given by

This expression revealed that for D= 3 we must have w3 = 0, this eliminates the possibility of Casimir source and thus, the formation of wormhole in 3D spacetimes.

Finally, by computing the integrand (Φ(r)), they showed that, for every spacetime of dimension greater than 3, it is possible to construct a traversable Morris-Thorne wormhole by using casimir energy as a source.

“We should point that this must have consequences for the physics of extra dimensions, particularly related to the newly discover humanly traversable wormhole. It would be interesting to generalize the above result to backgrounds that are not asymptotically flat. This is the topic of our future works.”

— concluded authors of the study

Reference: P.H.F. Oliveira, G. Alencar, I.C. Jardim, R.R. Landim, “Traversable Casimir Wormholes in D Dimensions”, Arxiv, pp. 1-6, 2021.

Note for editors of other websites: To reuse this article fully or partially kindly give credit either to our author/editor S. Aman or provide a link of our article

This Part Of Wormhole Try To Remain In Thermal Equilibrium (Cosmology)

Kim and Lee studied the thermodynamic equilibrium of matter in a wormhole ‘station’ which connects various distinct asymptotic regions of a spacetime.

An example of the ‘station’ is a traversable wormhole connecting two distant regions. We all know that, a wormhole is a physical object which connects two distinct regions of a spacetime. We can imagine a wormhole as a three-dimensional space with two spherical holes (‘mouths’) in it. These holes are connected to each other by means of a ‘handle’ having a ‘throat’ in it. Usually, it is assumed that the length of the ‘handle’ does not depend on the distance between the ‘mouths’ in an external space. The wormhole can be used to travel through the space if it is stable or lives long enough.

Figure 1. Characteristic plot of a space-like section of a wormhole spacetime. One of the angle direction is contracted. © Kim and Lee

In the presence of a traversable wormhole, various interesting phenomena happen which are beyond ordinary physical sense. Kim and Lee illustrated a few of them. First, the geometry is not symmetrical under the reflection with respect to the ‘throat’. Therefore, the size of the ‘mouths’ may not be the same in general. Secondly, the Arnowitt-Deser-Misner (ADM) mass of the wormhole measured by an asymptotic observer reside in the upper half is not the same as that in the other half. If you are an observer who is travelling through a wormhole, the proper time may not flow with the same speed in the upper/lower half. A time travel was shown to be possible when the two asymptotic regions are adjoined. Now, Kim and Lee, focused on a ‘static’ (traversable) wormhole based on general relativity in the absence of cosmological constant and studied the thermal equilibrium of self-gravitating matters in the wormhole spacetime.

In order to understand whether a wormhole station remains in thermodynamic equilibrium or not. We have to consider a space-like section of the wormhole station which are connected to 4 asymptotic regions (or you can consider any number of asymptotic regions but yes, it must be more than 2). Just refer fig 2 given below:

Figure 2. Characteristic plot of a space-like section of the wormhole station connecting four asymptotic regions. © Kim and Lee

As you can see in figure above, the ‘station’ consists of a ‘core’, N-‘mouths/outsides’, and N-‘branches’ which connects a ‘mouth’ with the ‘core’, where each ‘mouth’ plays the role of a gate to/from an outside. The station may consist of combinations of ordinary+exotic selfgravitating matters in thermal equilibrium. A typical example of N = 2 case is a traversable wormhole in which two outsides are connected by a wormhole ‘throat’ (an example of ‘core’). The wormhole ‘handle’ is made of two ‘branches’+‘core’. A ‘mouth’ Mn, which is a border between the station and the outside An, is assumed to be hard enough to prevent matter inside from spilling out (where, n =1, 2, 3…N).

Now, lets consider two regions A1 and A2, which are disjointed. Well, when they are disjointed the two regions have unequal temperature, and authors showed that, this difference does not cause any problem. However, when they are adjoined, the difference of the asymptotic temperatures seems to cause a trouble mainly because of the transitive relation between the objects in thermal equilibrium, called “zeroth law of thermodynamics”, which states that if two systems have the same T, then the two are in thermal equilibrium.

“This pathology actually comes from the incompleteness of the previous mentioned coordinates which originates from the multiply connected property of the space.”

“Still there remain a few important questions. First, what is the first law of the thermal system in the wormhole? Specifically, what is the entropy of the system consisting of matter plus wormhole? Second, does the equilibrium is stable or not? In other words, what happens when a mass falls in a wormhole in thermal equilibrium. Further studies are required to answer these questions.”

— concluded authors of the study

For more: Hyeong-Chan Kim, Youngone Lee, “Thermodynamic Equilibrium of a Wormhole Station”, Arxiv, pp. 1-13, 2019. https://arxiv.org/abs/1902.02957

Note for editors of other websites: To reuse this article fully or partially kindly give credit either to our author/editor S. Aman or provide a link of our article

How Can You Distinguish Kerr Wormholes From Kerr Black holes? (Astronomy /Cosmology)


⦿ Oasuya and Kobayashi in their recent paper considered throat effects on shadows of Kerr-like wormholes and showed that existence of the throat alters the shape of the shadow of Kerr wormholes significantly.

⦿ They also showed that the radius of the unstable circular photon orbits is smaller for the Kerr-like wormhole than that of the Kerr black hole with the same mass.

⦿ Atlast they manifested that even if you don’t know the mass of the object, you can determine whether the object is Kerr wormhole or black hole just by throat effects.

A wormhole is a spacetime bridge connecting two separate points in spacetime. Astrophysically, it is plausible to regard that wormholes are rotating. One of the metric for the rotating wormhole is the Kerr-like wormhole proposed. It is important to distinguish this wormhole from the Kerr black hole, and one such way is to study shadows of the Kerr-like wormholes. Remarkable attention to shadows cast by compact objects grows recently, since the Event Horizon Telescope observed the black hole shadow at the center of the galaxy M87.

Now, Oasuya and Kobayashi have revisited to investigate the shadow cast by the Kerr-like wormhole. They determined the boundary of the shadow by unstable circular photon orbits and have found that, in certain parameter regions (like larger wormhole spin ‘a’ and larger deviation parameter λ), the orbit is located at the throat of the Kerr-like wormhole (as shown in Fig 1), which was not considered in the literatures.

In these cases, the existence of the throat alters the shape of the shadow considerably, and it will be much easier to differentiate it from that of the Kerr black hole, compared with those cases without the throat effects taken into account, where the shapes of the Kerr-like wormhole and the Kerr black hole are found to be similar figures.

We point out that the effects of the wormhole throat become prominent when the unstable circular photon orbits are located at the throat in certain parameter space. In these cases, the shape of the shadow is altered considerably, and it will be much easier for us to figure out the differences.”

— told Kobayashi, second author of the study

Also, the radius of the unstable circular photon orbits is smaller for the Kerr-like wormhole than that of the Kerr black hole with the same mass.

Fig 1. Regions where the throat affects the shape of shadow in parameter space (a/M, λ²). Red and blue lines denote rthroat = r {stat. (min), Sys. (ph) and rthroat = r{stat. (max), Sys. (ph), respectively. Unstable circular photon orbits control the shadow shapes below the red line, while the throat solely determines them above the blue line. In between, both effects forms the shapes of the shadow. © Oasuya and Kobayashi

On the other hand, they make us aware of another perspectives. Like, if there are throat effects on the shadow shape, one can figure out whether the observed shadow is cast by the Kerr-like wormhole or the Kerr black hole “even in the case” when the object mass is unknown, not determined by other observations such as by motions of objects around the wormhole/black hole.

Reference: Shinta Kasuya, Masataka Kobayashi, “Throat effects on shadows of Kerr-like wormholes”, pp. 1-6, ArXiv, 2021. https://arxiv.org/abs/2103.13086

Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us

Can We Identify Massless Braneworld Black Holes (BWBH) & Distinguish Them From Wormholes & Schwarzschild BH? (Cosmology / Astronomy)

In 2016, LIGO detected gravitational waves, which are supposed to be signals of coalescence of two black holes. In 2019, the Event Horizon Telescope (EHT) collaboration produced the first-ever image of a black hole, which lies at the center of the M87 galaxy 55 million light-years from Earth. The image showed a bright ring with a dark center, which is the black hole’s shadow. These rapid advancements in observational technologies to detect black holes will also give us a chance to discover exotic compact objects such as boson stars, gravastars, wormholes, non-Abelian black holes, and braneworld black holes.

To detect such objects, it is necessary to understand theoretical predictions for observation in advance. For this purpose, observational consequences of boson stars, gravastars, wormholes, and braneworld black holes have been studied recent years.

Among many models of braneworld black holes, massless black holes, in which the curvature is produced only by a tidal effect, are observationally important because their gravitational lensing effects are characteristic and discriminative. Now, Ohgami and colleagues studied gravitational lensing by massless braneworld black holes in more detail. Specifically, they studied their microlensing and shadows, and discussed whether we can distinguish them from standard Schwarzschild black holes and Ellis wormholes by radio or electromagnetic observations.

First, they studied defection angles of light rays that pass around those objects. Previous work showed that both deflection angles of the braneworld black hole and the Ellis wormhole are proportional to α¯2, while that of the Schwarzschild black hole to α¯1. Ohgami et al. therefore speculated that the braneworld black hole and the Ellis wormhole may exhibit similar features in microlensing phenomena.

FIG. 1: Numerical results of radiation luminosity for the Schwarzschild black hole (red), the braneworld black hole (blue), and the Ellis wormhole (green). © Ohgami et al.

To elucidate observational consequences of those microlensing phenomena, they calculated images of an optical source object behind a lens object for the three models and their light curves. They found that for the braneworld black hole as well as for the Ellis wormhole, luminosity reduction appears just before and after amplification. This means that, observations of such reduction would indicate the lens object is either a braneworld black hole or a wormhole, though it is difficult to distinguish one from the other by microlensing solely.

FIG. 2: Setup of their analysis for obtaining optical images. They put an observer, a gravity source, and dust surrounding it. The dust falls into the gravity source constantly © Ohgami et al.

Thus, they next analyzed the optical images of the braneworld black hole surrounded by optically thin dust and compared them with those of the Ellis wormhole. Because the spacetime around the braneworld black hole possesses unstable circular orbits of photons, a bright ring appears in the image, just as in Schwarzschild spacetime or in the wormhole spacetime. This indicates that the appearance of a bright ring does not solely confirm a braneworld black hole, a Schwarzschild, nor an Ellis wormhole. However, they found that only for the wormhole the intensity inside the ring is larger than the outsider intensity. Their results mean that observations of shadows would distinguish black holes from Ellis wormholes.

They therefore concluded that, with future high-resolution very long baseline interferometry observations of microlensing and shadows together, we could identify the braneworld black holes if they exist.

Reference: M. Kuniyasu, K. Nanri, N. Sakai, T. Ohgami, R. Fukushige, S. Koumura, “Can we identify massless braneworld black holes by observations?”, Phys. Rev. D 97, 104063 – Published 29 May 2018. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.104063

Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us

At Ultra High Densities, Which Kind Of Wormholes You May Find? (Quantum / Physics)

The quark structure of baryonic matter is the central paradigm of the present-day elementary particle physics. At very high densities, which can be achieved in the interior of neutron stars, a deconfinement transition can break the baryons into their constitutive components, the quarks, thus leading to the formation of the quark-gluon plasma. Moreover, the strange quark matter, consisting of a mixture of u, d and s quarks, may be the most energetically favorable state of matter.

The existence of a large variety of color superconducting states of quark matter at ultra-high densities has also been suggested and intensively investigated. At very high densities, matter is expected to form a degenerate Fermi gas of quarks in which the quark Cooper pairs with very high binding energy condense near the Fermi surface. This phase of the quark matter is called a color superconductor. Such a state is significantly more bound than ordinary quark matter. This implies that at extremely high density the ground state of quark matter is the superconducting Color-Flavor-Locked (CFL) phase, and that this phase of matter rather than nuclear matter may be the ground state of hadronic matter.

The thermodynamic properties of the quark matter are well-known from a theoretical point of view, and several equations of state of the dense quark-gluon plasma have been proposed in the framework of a Quantum Chromodynamical approach, such as the MIT bag model equation of state and the equations of state of the superconducting Color-Flavor-Locked phase.

Motivated by these theoretical models, Harko and colleagues now explored the conditions under which wormhole geometries may be supported by the equations of state considered in the theoretical investigations of quark-gluon interactions. Since quark-gluon plasma can exist only at very high densities, the existence of the quark-gluon wormholes requires quark matter at extremely high densities. In these systems the basic physical parameters describing the properties of the QCD quark-gluon plasma (bag constant, gap energy, quark masses) become effective, density and interaction dependent quantities. It is this specific property of the strong interactions they have used to generate specific mathematical functional forms of the bag function and of the gap function that could make possible the existence of a wormhole geometry supported by a strongly gravitationally confined normal or superconducting quark-gluon plasma.

In our paper, we investigated the possibility that wormhole geometries can be realized by using quark matter, in both normal and superconducting phases. To describe quark matter we adopt the Massachusetts Institute of Technology (MIT) bag model equation of state, while for the investigation of the superconducting quark matter we consider the equation of state obtained in a first order expansion of the free energy of the system.

— told Harko, lead author of the study.

In the case of the normal quark-gluon plasma, wormhole solutions can be obtained by assuming either a specific dependence of vaccum pressure (B) on the shape function b, or some simple functional representations of B. In both cases in the limit of large r the bag function tends to zero lim_(r→∞) B = 0, and in this limit the equation of state of the quark matter becomes the radiation type equation of the normal baryonic matter, p = ε/3. Therefore, once the density of the quark matter increases after a deconfinement transition, a density (radial coordinate) dependent bag function could lead to the violation of the null energy condition, with the subsequent generation of a wormhole supported by the quark-gluon plasma. A high intensity electric field with a shape function dependent charge distribution could also play a significant role in the formation of the wormhole.

“By appropriately choosing the forms of the bag and gap functions several wormhole type solutions of the gravitational field equations are obtained, with the matter source represented by normal and superconducting quark matter, respectively.”

— told Mak, author of the study.

While, in the case of the superconducting quark matter the gravitational field equations can be solved by assuming that both the bag function and the gap function are shape function and s quark mass dependent quantities. However, in the large r limit, in order to reobtain the standard baryonic matter equation of state, the condition of the vanishing of the mass of the s quark is also required, lim_(r→∞) m_s = 0. The assumption of a zero asymptotic u, d and s quark mass is also frequently used in the study
of quark star models.

Reference: Tiberiu Harko, Francisco S. N. Lobo and M. K. Mak, “Wormhole geometries supported by quark matter at ultra-high densities”, International Journal of Modern Physics D, Vol. 24, No. 01, 1550006 (2015). https://doi.org/10.1142/S0218271815500066

Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us

Microscopic Wormholes As A Theoretical Possibility (Cosmology / Quantum)

Oldenburg physicists deal with hypothetical tunnels in space-time

Wormholes play an important role in many science fiction films – as a shortcut between two distant places in space. In physics, however, these tunnels in spacetime have so far been purely hypothetical structures. An international team led by Dr. Jose Luis Blázquez-Salcedo from the University of Oldenburg is now presenting a new theoretical model in the journal Physical Review Letters that makes microscopic wormholes appear less exotic than previous theories.

Like black holes, wormholes appear in the equations of general relativity that Albert Einstein established in 1916. An important assumption of the theory is that the universe has four dimensions – three dimensions of space and time as the fourth dimension. Together they form what is known as spacetime. It is curved by heavy objects like stars, similar to a rubber blanket into which a metal ball sinks. The curvature of spacetime determines how objects such as spaceships and planets, but also light, move. “In theory, space-time could be bent and curved without heavy objects,” explains Blázquez-Salcedo, who has meanwhile moved to the Spanish Universidad Complutense de Madrid. A wormhole would therefore be an extremely strongly curved area of ​​spacetime, which resembles two connected funnels and connects two distant places like a tunnel. “Mathematically speaking, such an abbreviation is possible, but no one has ever observed a real wormhole,” says the researcher.

Such a wormhole would also be unstable: if a spaceship were to fly into it, for example, it would immediately collapse into a black hole, i.e. an object in which matter disappears forever. The connection to other places in the universe would be cut. In order to keep the wormhole open, previous models require an exotic, only theoretically conceivable form of matter that has a negative mass, i.e. weighs less than nothing.

Blázquez-Salcedo and his colleagues Dr. Christian Knoll from the University of Oldenburg and Eugen Radu from the Universidade de Aveiro in Portugal now show in their study that wormholes can be passable even without this assumption. The researchers chose a comparatively simple, “semiclassical” approach, as they write: They combined elements of relativity theory with elements of quantum theory and the classical theory of electrodynamics. They considered certain elementary particles such as electrons and their electrical charge to be the matter that is supposed to pass through the wormhole. As a mathematical description they chose the Dirac equation, a formula that describes the probability of a particle’s location according to quantum theory and relativity theory as a so-called Dirac field.

As the physicists report in their study, it is the consideration of the Dirac field that allows the existence of a wormhole that can be traversed by matter in their model. The prerequisite is that the ratio between the electrical charge and the mass of the wormhole exceeds a certain limit. In addition to matter, signals – such as electromagnetic waves – could also cross the tiny tunnels in space-time. The microscopic wormholes that the team envisions would probably not be suitable for interstellar travel. In addition, the model would have to be further refined in order to find out whether the strange structures could actually exist. “We suspect that the wormholes can also exist in a complete model,” says Blázquez-Salcedo.

The work was developed within the graduate school “Models of Gravity”, which the Oldenburg physicist Prof. Dr. Jutta Kunz together with Prof. Dr. Claus Lämmerzahl from the Center for Applied Space Technology and Microgravity (ZARM) at the University of Bremen. In addition to the University of Oldenburg, other universities and research centers are also involved.

Original article: Jose Luis Blázquez-Salcedo, Christian Knoll and Eugen Radu: “Traversable wormholes in Einstein-Dirac-Maxwell theory”, Physical Review Letters, journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.101102

Provided by University of Oldenburg