# Einstein's Field Equations - SF Writer needs general answer

• Ring Gate
In summary, the concept of "gates" in this novel refers to wormholes located in a region of space that is not too warped. The author is seeking a simplified ratio for the Field Equations that can provide a 2 or 3 digit accuracy for calculating the distance between two stars, in order to accurately describe the movement of these gates. The use of Newton's law for gravitation is suggested as a sufficient solution, with the caveat that the gates are not located near black holes or neutron stars. The concept of "space warping" is also discussed, with the possibility of using tidal forces to calculate the distance between stars. Additional resources on wormholes in science fiction are recommended for further research.
Ring Gate
I am working on a novel that uses 'gates' that for lack of space here let’s just call worm holes (any excuse works for this question). But these gates cannot bridge to each other if located in a region of space that is warped too much.
So I'm looking for a proportional answer, not a calculated exact one.
Example: If light (like from a star) diminishes by the inverse square law, then a similar situation of what I am looking for would be: If I arbitrarily chose the amount of light hitting the Earth to be what I want for some other planet, then if I know how bright its star is compared to the Sun I can figure the distance that planet has to be to get the same amount of light as our Earth does. So a star four times as luminous would require its planet to be twice as far from it as the Earth is from the sun. Looked at this way, I don't need to know units in lumens, distances in meters, etc. Just arbitrary general units and a quick ratio.
NOW
If I were to say for instance that a gate could work if it orbited the Sun at a distance like that of earth, which is 1 AU (only an example) is there a simplified ratio that the Field Equations can be roughly equal to for at least 2 or 3 digit accuracy to be able to say another star of so many solar masses would equal some minimum distance away then for a gate at that star?
I do know that it is simpler for calculations outside of a massive object rather than inside, but it is still too complicated for this Sci-Fi writer. I hope that some rough proportion can be used for distances several times the radius of the sun, again only 2 or 3 digits at least, but if 4 or more, fantastic! The story is NOT a dry textbook to be checked for accuracy, but I do not want to write in things that to someone knowledgeable would laugh at as clearly off.
Thank you very much for any help provided.

Ring Gate said:
I am working on a novel that uses 'gates' that for lack of space here let’s just call worm holes (any excuse works for this question). But these gates cannot bridge to each other if located in a region of space that is warped too much.
So I'm looking for a proportional answer, not a calculated exact one.
Example: If light (like from a star) diminishes by the inverse square law, then a similar situation of what I am looking for would be: If I arbitrarily chose the amount of light hitting the Earth to be what I want for some other planet, then if I know how bright its star is compared to the Sun I can figure the distance that planet has to be to get the same amount of light as our Earth does. So a star four times as luminous would require its planet to be twice as far from it as the Earth is from the sun. Looked at this way, I don't need to know units in lumens, distances in meters, etc. Just arbitrary general units and a quick ratio.
NOW
If I were to say for instance that a gate could work if it orbited the Sun at a distance like that of earth, which is 1 AU (only an example) is there a simplified ratio that the Field Equations can be roughly equal to for at least 2 or 3 digit accuracy to be able to say another star of so many solar masses would equal some minimum distance away then for a gate at that star?
I do know that it is simpler for calculations outside of a massive object rather than inside, but it is still too complicated for this Sci-Fi writer. I hope that some rough proportion can be used for distances several times the radius of the sun, again only 2 or 3 digits at least, but if 4 or more, fantastic! The story is NOT a dry textbook to be checked for accuracy, but I do not want to write in things that to someone knowledgeable would laugh at as clearly off.
Thank you very much for any help provided.

For this level of question, other than that you are proposing a wormhole, the rest of your question is just about strength of gravity = curvature in Newtonian sense. In which case, you have an inverse square law, just like your light example. The same reasoning would apply for the ballpark level you seek.

You might want to ask questions like this also in the Science Fiction writing subforum of Science Fiction and Fantasy, under PF lounge.

Oh, Welcome to Physics Forums!

Why thank you very much PAllen! I hoped it might have been that simple or maybe some square to cube ratio like orbital periods. Excellent, and thank you for mentioning the subforum too. I was unaware of it.

Thanks again!

As long as nothing's moving near the speed of light (and you're not near anything like a black hole or a neutron star), Newton's law for gravitation will suffice. So if you have a star which is four times as massive as another, the gravitational fields are equivalent when you're twice as far away from the larger star.

One could also make a case for "space warping" being tidal forces. In which case they'd fall off faster - M/r^3 But you can make up pretty much anything you want -- As far as I know, GR wormholes don't really mind being in curved space-time.Which leads to some interesting features, which you may or may not want to know about. I'd suggest reading Cramer's SF column on wormholes from Analog just for background.

http://www.npl.washington.edu/av/altvw33.html

is one, there are more

Ring Gate:

Technical question - how do your gates move in relation to the rest of universe? Do they orbit their stars? Or luckily just float nearby, untouched by any gravity, so for most of their time they should are in empty space, far from stars? (just curious)

## What are Einstein's Field Equations?

Einstein's Field Equations are a set of ten non-linear partial differential equations that make up the basis of Einstein's theory of general relativity. They describe the relationship between the curvature of space-time and the energy and matter present in the universe.

## Why are Einstein's Field Equations important?

Einstein's Field Equations are important because they provide a mathematical framework for understanding the fundamental nature of space, time, and gravity. They have been extensively tested and have been shown to accurately predict the behavior of objects in the universe.

## How did Einstein come up with these equations?

Einstein developed his theory of general relativity by building on the work of Isaac Newton and other scientists. He spent years studying and refining his ideas about the nature of gravity and space-time before finally publishing his famous equations in 1915.

## What is the significance of the equation E=mc^2 in Einstein's Field Equations?

The equation E=mc^2 is not actually part of Einstein's Field Equations, but it is a consequence of his theory of general relativity. It shows the relationship between mass and energy, and is often used to explain the immense amount of energy released in nuclear reactions.

## How have Einstein's Field Equations been tested and confirmed?

Einstein's Field Equations have been tested through various experiments and observations, including the bending of starlight by the sun's gravitational field, the precession of the orbit of Mercury, and the detection of gravitational waves. All of these have provided evidence that supports the predictions of general relativity and Einstein's equations.

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