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How Extra Dimensions May Be Creating Wormholes in Our Universe?

In the brane-world model, our four-dimensional universe is embedded in a higher-dimensional space known as the bulk. This setup suggests that gravitational effects from extra dimensions can influence our universe, potentially creating phenomena like wormholes. Juliano Neves, using the Nakas-Kanti approach, explored how wormholes like the Morris-Thorne and Molina-Neves types could exist in this framework. These wormholes are induced on the brane (our universe) by the gravitational influence of the bulk, without requiring any exotic matter or fields on the brane itself. The Nakas-Kanti approach starts with a five-dimensional bulk spacetime and derives solutions for the brane. This method reveals that certain wormhole geometries can emerge naturally, supported by the bulk's energy, not by matter on the brane. This work shows that regular solutions, like the Morris-Thorne and Molina-Neves wormholes, could exist without violating physical laws. Additionally, this framework may help explain mysterious phenomena like dark matter and dark energy, which are often attributed to unseen particles or fields. Instead, these effects might be caused by the extra-dimensional influence on our four-dimensional brane, offering a new perspective on the cosmos.


The concept of wormholes, often popularized in science fiction, has a deep theoretical basis in modern physics. Traditionally, wormholes are imagined as tunnels or shortcuts through spacetime that could potentially allow for faster-than-light travel or even time travel. But what if these exotic structures weren’t just figments of imagination? What if they could actually exist in the universe, guided by the laws of physics? This is where the brane-world context comes into play.

In a brane-world scenario, our four-dimensional universe (the familiar 3D space and time) is embedded within a higher-dimensional space. This higher-dimensional space—often called the "bulk"—contains more than the usual four dimensions, and these extra dimensions can have profound effects on the way gravity, black holes, and even wormholes behave. In this article, we explore how recent theoretical work, including Juliano Neves’ research, has led to new insights into the possible existence of wormholes within this framework.

What is a Brane-World?

Before diving into wormholes, it’s essential to understand the brane-world model. The idea is rooted in string theory and higher-dimensional physics, particularly in theories where additional spatial dimensions beyond the familiar three are posited. The Randall-Sundrum models (RSI and RSII) are two such theories that have garnered significant attention.

  • RSI Model: This model involves two branes—our universe being one of them—and an extra dimension that helps explain certain puzzles in particle physics, like the hierarchy problem.
  • RSII Model: This builds on the RSI model by assuming a single brane and an infinite extra dimension. It is particularly useful when studying gravitational phenomena in a higher-dimensional context.

The key takeaway is that the universe we experience is not an isolated system, but rather a "brane" within a larger, higher-dimensional "bulk." The gravitational effects from this extra dimension can influence our four-dimensional spacetime, and this is where things get interesting for wormhole research.

Wormholes in a Brane-World Context

In a brane-world, the bulk spacetime is typically described by a higher-dimensional geometry. In this setting, wormholes can be induced on the brane—meaning they are not necessarily created by the normal matter and energy we observe in our universe. Instead, these wormholes are the result of the influence of the extra dimension on our brane.

Juliano Neves, in his recent work, applied a technique known as the Nakas-Kanti approach to explore how wormholes might appear in the brane-world scenario. This approach begins by considering a regular five-dimensional spacetime (the "bulk") and then deriving solutions that can be "induced" on the four-dimensional brane.

Neves’ work focused on two key types of wormholes that could emerge from this approach: the Morris-Thorne (MT) wormhole and the Molina-Neves (MN) wormhole.

  • Morris-Thorne Wormhole: This is perhaps the most famous type of theoretical wormhole, first proposed by Kip Thorne in the 1980s. It is often described as a traversable wormhole that could, in theory, allow for time travel.
  • Molina-Neves Wormhole: This is an asymptotically de Sitter wormhole, meaning it behaves like a wormhole in a universe that is expanding at an accelerated rate, similar to what we observe in the current cosmological model.

What’s fascinating is that these wormholes are induced on the brane without the need for any exotic matter or energy in the four-dimensional universe. The cause of these wormholes lies in the gravitational influence of the bulk, which acts upon the brane, creating the curvature of spacetime needed to form the wormhole.

The Nakas-Kanti Approach: Unveiling New Spacetime Solutions

The Nakas-Kanti approach is a powerful tool for studying brane-world scenarios. It starts by looking at a five-dimensional spacetime geometry (the bulk), then uses this bulk solution to derive the four-dimensional geometry that appears on the brane. This allows researchers to find new spacetime solutions that could exist in our universe, even though they originate from higher dimensions.

For instance, Neves used this approach to show that the Morris-Thorne and Molina-Neves wormholes could be induced on the brane. These wormholes, according to Neves, are supported by an exotic fluid in the bulk, but they don’t require any matter or fields on the brane itself. The bulk’s gravitational influence is enough to induce these wormholes in our universe.

One of the most important aspects of the Nakas-Kanti approach is that it allows for regular solutions. This means that, unlike some other higher-dimensional models (like the black string solutions), the spacetime geometry in this case does not exhibit any singularities or other unphysical features. It’s a regular, well-behaved solution that could potentially describe real, observable phenomena.

How Do Wormholes Work in the Brane-World Context?

To understand how these wormholes work, it’s important to consider the nature of the bulk. In the Randall-Sundrum II model, the bulk is an infinite space with extra dimensions. The brane—our universe—is a four-dimensional hypersurface embedded within this bulk.

The bulk geometry is not just any five-dimensional space; it is specifically an asymptotically anti-de Sitter space (AdS). This means that, far from any mass or energy, the spacetime behaves in a way that is similar to a negatively curved space (like a hyperbolic surface). The presence of this curvature in the bulk affects the brane, leading to the formation of spacetime structures like black holes and wormholes on the brane.

The Nakas-Kanti approach explains how these structures are induced without needing additional matter or energy on the brane itself. In other words, the gravitational influence from the bulk is enough to create the geometry needed to form wormholes, even though no particles or fields live directly on the brane.

The Effective Four-Dimensional Field Equations

How can we be sure that the wormholes described by Neves are valid solutions on the brane? The answer lies in the effective four-dimensional field equations, which describe how the gravitational field behaves on the brane. These equations are derived from the energy-momentum tensor of the bulk, which describes the distribution of matter and energy in the higher-dimensional space.

The Nakas-Kanti approach generates a bulk energy-momentum tensor that can give rise to the desired solutions on the brane. By using these field equations, Neves was able to demonstrate that the Morris-Thorne and Molina-Neves wormholes are valid solutions that can exist in a brane-world context.

Wormholes and the Search for Dark Matter and Dark Energy

One of the most intriguing aspects of this research is its potential to provide new insights into dark matter and dark energy. These two mysterious phenomena are thought to make up most of the universe's mass-energy content, yet we have no direct evidence of their existence in the form of particles or fields in our four-dimensional universe.

In the brane-world context, however, the effects of extra dimensions could explain the phenomena attributed to dark matter and dark energy. For example, the effective four-dimensional cosmological constant obtained in Neves’ work could account for the accelerated expansion of the universe, which is usually attributed to dark energy.

Additionally, the influence of the bulk could explain gravitational effects that we observe in galaxies and galaxy clusters, which are often attributed to dark matter. These effects could be the result of higher-dimensional interactions that we cannot directly perceive on the brane, but which still have real effects on our universe.

Conclusion

The study of wormholes in the brane-world context opens up exciting possibilities for understanding the structure of the universe. By considering how extra dimensions influence our four-dimensional universe, we can uncover new insights into the nature of gravity, black holes, and even dark matter and dark energy.

Juliano Neves’ work, using the Nakas-Kanti approach, demonstrates that wormholes like the Morris-Thorne and Molina-Neves types can be induced on the brane due to the gravitational effects of the bulk. These wormholes don’t require exotic matter or energy in our universe, but rather emerge from the influence of higher-dimensional spacetime.

As we continue to explore the brane-world context and its implications for cosmology and gravitational theory, we may one day uncover even more surprising results—perhaps even finding real-world evidence for wormholes and other exotic phenomena. The universe may be far more mysterious and complex than we ever imagined, and the brane-world context offers a promising avenue for unraveling these cosmic secrets.

Reference: Juliano C. S. Neves, "Wormholes from beyond", Arxiv, 2024. https://arxiv.org/abs/2412.11947


Technical terms 

  1. Brane-World: Imagine our universe as a 3D sheet (called a brane) floating in a higher-dimensional space. This concept comes from theories like string theory, where there could be more dimensions (extra dimensions beyond the 3D space and 1 time dimension we experience). Our universe is just one of these "branes" in a larger, higher-dimensional space.

  2. Bulk: The bulk is the higher-dimensional space outside our 3D universe. If our universe is a 3D sheet (brane), the bulk is like the larger container or higher-dimensional "world" in which our universe exists. Think of it as the "container" for our universe.

  3. Randall-Sundrum Models (RSI & RSII): These are theories that explain how extra dimensions could exist.

    • RSI has two branes (one is our universe), and an extra dimension that explains certain problems in particle physics.
    • RSII assumes there is only one brane (our universe) and an infinite extra dimension, which is useful for studying gravity and cosmology.
  4. Morris-Thorne Wormhole: A theoretical shortcut or tunnel through spacetime, first proposed by physicists Morris and Thorne. This wormhole could allow faster-than-light travel or even time travel, but it’s just a theoretical idea so far. The wormhole is supported by "exotic matter," which has strange properties (like negative energy).

  5. Molina-Neves Wormhole: A specific type of wormhole that behaves like a tunnel in a universe with an expanding space (similar to our universe's accelerated expansion). It’s named after the researchers Molina and Neves who studied it.

  6. Nakas-Kanti Approach: A method used to study brane-world models. It starts by looking at the higher-dimensional "bulk" and then calculates how the effects of this higher dimension show up in our four-dimensional universe (the brane).

  7. Exotic Fluid: This is a type of fluid with strange properties, like negative energy. It’s needed to keep wormholes open and prevent them from collapsing. Exotic fluids are often part of theoretical models, but we haven’t observed them in reality.

  8. Effective Field Equations: These are mathematical equations that describe how gravity and other forces work in our universe. They tell us how energy, mass, and the shape of spacetime interact with each other. In the brane-world context, these equations help us understand how higher-dimensional effects show up in our four-dimensional universe.

  9. Asymptotically Anti-de Sitter Space (AdS): A type of spacetime that curves negatively, kind of like the surface of a saddle. This negative curvature affects the gravitational behavior in that space. In the brane-world model, the bulk spacetime is assumed to have this kind of geometry, which influences our universe's gravitational effects.

  10. Cosmological Constant: A term in physics that represents the energy density of empty space, also called "dark energy." It’s responsible for the accelerated expansion of the universe, which we observe today. In the brane-world scenario, the bulk could influence this, explaining the effects we attribute to dark energy.

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