[jeffreyH]

For those interested in studying the subject the following answer on quora discusses some of the considerations to take into account when choosing a text.
https://www.quora.com/What-is-the-best-self-study-book-on-differential-geometry-for-a-beginner

[guest45734]

I have a question for you. Do you have any understanding of differential geometry?

What part of differential geometry do you suspect I do not understand. I assume you talking about grads divs and curls or more simply http://scienceblogs.com/startswithabang/2010/01/22/translating-math-geek-into-eng/ .

I have a couple of technical degrees(sadly not physics) that I would not have passed if I was not numerate however these were a few years ago (years soon turn into decades and rust sets in ).

I am intrigued, if you can raise the game to a higher level please do, I am literate and still have my textbooks.

[PmbPhy]

What part of differential geometry do you suspect I do not understand. I assume you talking about grads divs and curls

No. That's vector calculus. The basics of differential geometry are described here:
http://www.newenglandphysics.org/physics_world/ma/ma.htm

[PmbPhy]

I’d try @PmbPhy, he was a research student of Alan’s and they keep in touch.

That's incorrect. We're just friends. We talk physics a lot but I was never a student of his. I did my graduate work at Northeastern University, not MIT.

[Bill S]

http://scienceblogs.com/startswithabang/2010/01/22/translating-math-geek-into-eng/

One thing I found in the past was that Ethan Siegel often explains things in a way that even I can understand.  For example:

Well, one math geek statement is as follows: the curl of the gradient of a scalar field is always zero. What does this mean, in terms of our water? It means that I can take any topography I can find, invent, or even dream up.
I can drop a tiny droplet of water on it anywhere I like, and while the water may roll downhill (depending on the gradient), and while the water may spread out or narrow (depending on the divergence of the gradient), it will not start to rotate. For rotation to happen, you need something more than just a drop starting out on a hill, no matter how your hill is shaped! That’s what it means when someone says, “The curl of the gradient is zero.”

I must try to return to following him.

[guest45734]

It seems Einstein is proven right yet again https://phys.org/news/2018-06-einstein-galaxy.html?utm_source=nwletter&utm_medium=email&utm_campaign=daily-nwletter .

The white hole is a part of his field equations, and is worth looking at. An ER bridge would require exotic matter to keep it open which has the opposite effect of gravity ie it is something like dark energy which is driving the expansion of the universe.  The expansion is explained by Guth https://en.wikipedia.org/wiki/Alan_Guth .

What I am thinking is that we may not be viewing the output from an ER bridge correctly.

Inside an ER bridge space is not defined. Why would an exit from an ER bridge be local to one point in space, except in star trek?

Dark Energy and Gravity can be regarded as differences in potential energy of space.

A number of theories suggest that gravity is caused by the absorbance of quantum fluctuations and dark energy is caused the appearance of quantum fluctuations in space, this would imply in a BH all Quantum fluctuations are absorbed. Equally other theories argue that gravity is caused by the contraction of space and the expansion of space is caused by dark energy, in this instance space is absorbed by a BH.

Space time does not exist without quantum fluctuations. Before any quantum fluctuations ever existed we would have a singularity, and a none defined area of space. This would represent a BH which if White holes can expand using Dark energy, Einstein may be right yet again.

Space may have evolved from a nothing to an infinity because it was inevitable. Could expansion of Space be being driven by the output of a wormhole connected to all points in space time.

[Colin2B]

Could expansion of Space be being driven by the output of a wormhole connected to all points in space time.

Could you explain your idea of how this might work.

[guest45734]

Could you explain your idea of how this might work.

Since this has been moved to new theories I will take a few days and dream up a response for my general amusement, which I may post. Space is not fully understood by science so it does allow a little room for speculation, when asking questions one often gets contradictory answers or answers from nutters. I noted someone quoting Dr Chris Baird on other topics so I asked him for his opinion ref white holes. The following is his response

"Spacetime is a bit hard for us humans to understand intuitively in its complete form because it is different from other objects that we are used to in every day life. First of all, spacetime is literally a physical object. Before Einstien's theories were presented and verified, scientists could make the argument that spacetime itself is not an object, but rather is just a convenient way to describe the relationship between real objects. However, Einstein's discoveries force us to acknowledge spacetime as an independent, fundamental physical object. An object has an independent physical existence when it has a state and properties that can change and can be measured. Spacetime has curvature, which can be measured. You might say that spacetime curvature can only exist in the presence of mass/energy, and therefore is just a manifestation of the effect of one mass on another. However, this is not true. Spacetime curvature can exist in the absence of mass, energy, and any other object. One example is a gravitational wave. A gravitational wave is a traveling, fluctuating, curvature of spacetime. A mass is needed to create the gravitational wave, but once it is created, the wave travels away and becomes self-sustaining. Such a wave continues to exist millions of miles away from any other object. Gravitational waves are predicted by Einstein's equations and have been verified experimentally. Again, once created, they exist independent of any mass, energy, or electromagnetic field. It is spacetime itself that is waving, and therefore spacetime is a physical object.

Now, it becomes strange because spacetime is very different from any other type of object in the universe. Spacetime itself has no mass. However, spacetime curvature can store energy and gravitational waves do carry energy. Furthermore, spacetime is the background in which all other objects exist and interact. Although you can in principle remove all the atoms, or all the apples, or all the electrons from a certain region, you can't remove spacetime from a certain region. So when we say that spacetime is a physical object that can be measured and manipulated, we have to be careful not let this lead us into thinking it is like other physical objects.

Regarding white holes, you need to realize that at this point they are more like science fiction than solid science. The popular media and some speculative scientists love to bat around the idea of a white hole. However, most physicists do not consider that white holes actually exist in our physical universe or could exist. Yes, Einstein's field equations by themselves allow white holes, but only in toy universes that do not match our actual universe. There are several problems. First of all, there is no physical mechanism that could create a white hole. Secondly, a white hole would require spacetime to curve in a way that we have never seen before and seems at odds with everything we know about the universe (roughly speaking, it leads to repulsive static gravitational forces). If you tried to create a white hole using matter, it would have to be made out of non-sensical/exotic matter. Otherwise, the white hole must have always existed, which is not possible in a universe with a finite lifetime. Furthermore, a white hole is inherently unstable. If you managed to almost create one, it would destroy itself before you actually succeeded. White holes are the opposite of black holes. Black holes have regular spacetime curvature, can be created with regular matter, and are inherently stable. Any irregularity in a black hole's surface naturally smooths itself down, with the excess energy and spacetime curvature irregularity carried away by gravitational waves. In contrast, white holes have non-physical spacetime curvature, must be created using non-sensical matter, and are inherently unstable.

Now, I am not saying that the non-existence of white holes is 100% certain. We never know where scientific discoveries will take us. Rather, I am saying that if we stick to our actual universe (rather than playing with toy universes, which can be rewarding), an intellectually honest scientist that sticks to facts can't have much to say about them. Even if they do end up existing, they would require new physical laws, and until we have those laws, anything I say would be unhelpful speculation.

As far as we can tell, the expansion of the universe on a cosmic scale is not driven by anything. Rather it is an innate property of spacetime itself. In other words, any time you have a cosmic-scale region of space with no matter in it (or evenly-distributed matter), spacetime in this region will naturally expand on its own. That's just what spacetime does. It has nothing to do with the Big Bang and inertia. In other words, the expansion of the universe is very different from an expanding fireball caused by an explosion. Scientists call the cause of the universe's expansion "dark energy" because it acts like an energy, but it is not a literal energetic particle that fills space. It is just the nature of spacetime. Dark energy is not something you can collect and use. In other words, "dark energy" is not actually a self-existing physical object. Rather, it is a convenient way for humans to describe how spacetime behaves on the cosmic scale when filled uniformly with matter.

The laws of thermodynamics are local laws and therefore do not apply to the universe as a whole on the cosmic scale. The universe as a whole does indeed not obey thermodynamics, but this is not a problem, because it does not have to. These are difficult topics to straighten out because they involve concepts that are exotic (we don't encounter them in everyday life), and because they are at the edge of our understanding.

- Dr. Baird

"

Not everything is 100% certain in science. White holes are maybe possibly possible and they require exotic energy which repels like dark energy Space is full of dark energy and it repels like the inside of a wormhole could we be existing on the inside of a wormhole. There are a lot of things to consider about the nature of space and how it has evolved, gravity and dark energy are opposites, one absorbs the other. How an ER and EPR bridge redistributes energy in space time from a singularity is interesting.

I note no sentient responses were given to my previous post.

Edit a starting point for discussion might be the ER = EPR theory, and what that would appear like in space. https://myalberteinstein.com/2015/11/21/the-einstein-rosen-bridge-and-the-einstein-podolsky-rosen-paradox-er-and-epr-wormhole-and-entanglement/

Edit Edit both EPR and ER bridges suggest there is a way around space tie via another dimension etc