Does the flat spacetime soultion of spacetime tell us that wormholes with no enegry holding them open should close?

General Background

 

Introduction to General Relativity

 

General Relativity can be explained as a theory of space and time, combined into spacetime.

 

Spacetime is a 4th dimensional manifold. You can imagine it similar to a 3 dimensional piece of flat fabric. It has 3 dimensions of space and 1 of time. Spacetime is the plane that events happen on.

 

Curvature of Spacetime

 

General relativity explains that gravity is the curvature of spacetime. The curvature of spacetime is caused when something with mass or energy enters it, causing spacetime to warp around it. Similar to when you place a ball on a piece of fabric, the fabric will bend from the weight of the ball, except this happens in 4 dimensions instead of 3. 

 

We often use the 3 dimensional diagram to visualive to warping of spacetime because it is easier to comprehend. The 4 dimensional diagram is actually just 3 dimensional as well, this is because we live in 3 spatial dimensions and it is impossible to show the 4th dimension (time), so instead it's 3 more in a cube shape than a square shape. That's why the 4th dimensional diagram is sometimes confusing to look at, and that's also why we use the square 3 dimensional diagram instead. Both diagrams convey the same information, one is just in a higher dimension.

 

When visualised, the warping looks like this;

 

3 Dimensional spacetime warping:

Credit: European Space Agency

 

4 Dimensional spacetime warping:

Credit: Sketchfab 

 

It is also important to note that when nothing is inside spacetime, its called asymptotically flat spacetime. Asymptotically flat spacetime is similar to how the curves of Earth disappear because Earth is so large. This is because we do not yet know if spacetime itself curves, like a squiggly line. But as long as there is no mass or energy influencing the curvature of spacetime, it is asymptotically flat.

 

Spacetime will also warp more or less depending on the mass of the object, just like how fabric will bend more if there you place a heavier ball on it. This is easy to visualise with a 3D diagram.

 

Credit: Sciencenews.org

 

The curvature of spacetime also affects the path of travel lights takes and causes time dilation.

 

The curvature of spacetime caused by a massive object causes light to follow the bent path of spacetime, causing the light to seemingly bend. We can view this phenomena ourselves, but it takes an extremely dense object to have a noticeable effect on the path light will travel, such as a blackhole. Less massive objects such as the sun or earth will not have a noticeable impact on the path of light.

 

Blackholes will often be depicted where we can see the front and back of the accretion disc at the same time, this is caused by the curvature of spacetime bending light to the other side. This is even noticeable in our first ever photo of a blackhole.

 

Credit: Event Horizon Telescope

 

Here’s a scientific diagram on what a detailed photo of a blackhole is hypothesised to look like;

 

Credit: NASA

 

Notice how we can see the back and front of the accretion disc. That's the result of spacetime changing the path of light.

 

Spacetime can also cause time dilation as mentioned. Since spacetime is the combination of space and time, the curvature of it also has an effect on the 1 time dimension. Just like how space gets warped around a massive object causing light to change its path, time also does too.

 

The more stretched out spacetime is, the stretched space and time will be. And for time this means time slows down. Time travels slower on earth than it does in interstellar space because earth is a massive object and it bends spacetime, causing time to slow down. This is epically noticeable around blackholes, where time hypothetically nearly stops at the centre of it. We cannot know for sure if it nearly stops at the centre because we have never been to the centre of a blackhole, but according to general relativity, it should.

 

Bending of Spacetime into Extra Dimensions

 

Outside of the regular curvature of spacetime from massive objects, spacetime is able to bend into other dimensions. This is often difficult to explain without the aid of visualisations.

 

Credit: https://medium.com/swlh/the-physics-of-wormholes-654facefd2ea

 

Pay attention to how spacetime bends over itself in the diagram above. It is bending without a massive object influencing it. These folds in spacetime can be compared to the folds in fabric.  

 

When spacetime hypothetically folds over itself it can create what we call “hyperspace”. Hyperspace is often seen as a fictional concept, but astrophysics explains it as the space between spacetime. If spacetime can hypothetically fold, there has to be an empty space where it is not, because inorder for something to fold like this there has to be a negative space where it is not. That is what hyperspace is.

In science fiction, you can travel through hyperspace, but as far as we know you can only travel along spacetime, so you can travel through hyperspace with wormholes, but you cannot fly straight through it. Of course, we would never know unless there was a tear in spacetime, but hyperspace theory states we wouldn’t be able to.

 

Einstein Rosen Bridges

 

 

 

Einstein Rosen Bridges, or also known as wormholes, are theoretical bridges connecting two regions of spacetime. 

 

There are two main kinds of wormholes, inter-universe wormholes and intra-universe wormholes. Inter-universe wormholes are wormholes that connect two separate universes. Intra-universe wormholes connect two regions in spacetime in one universe. Summed up, inter wormholes connect two separate universes and intra connect the same one. 

 

Focusing on intra-universe wormholes, wormholes are caused by the bending of spacetime. When a wormhole forms, spacetime has to bump into itself, causing it to form a wormhole. The most popular theory of how this happens is via two massive objects on either side of spacetime. The bending in spacetime caused by these objects would push spacetime into itself. 

 

 

The diagram above shows the formation of an intra-universe wormhole. ‘A’ shows the importance of spacetime bending over itself so that the wormhole can form; this is required for this method of formation of a wormhole. Two masses in the two different parallel regions of spacetime are also required. 

 

When the two masses are in the two different areas of spacetime they cause spacetime to warp, and if the masses are dense enough they can cause spacetime to bump into itself resulting in a wormhole.

 

Other theories state that the massive objects can attract to each other from across completely different regions of spacetime or spacetime bumping into itself while bending without a massive object. All these theories share one thing that is common, that spacetime has to bump into itself one way or another..

 

It is important to note that there is not yet a realistic model for the formation of wormholes, however, these are the most accurate models that physicists have in modern day. 

 

Quantum wormholes are much easier to develop a model for because it overcomes one of the challenges that wormholes on a much larger scale face, which is negative energy. Quantum wormholes have local negative energy to create a wormhole. Large wormholes on an astronomical scale dont have the same properties as quantum wormholes, so it's not as simple as just increasing the model to a larger size. 

 

 

The methods of wormhole formation that was previously discussed all use the classic model of gravity, which is normal gravity caused by the bending of spacetime without the aid of quantum mechanics. It's also important to note that we currently don't have a solution to how spacetime joins together smoothly to create a wormhole, but we do have an idea of why and how. There are also equations to explain wormholes. All these models are still theories, but again, the best idea we have about how they should form.