According to Einstein's theories, as anything having a mass in the universe, the Sun bends space-time basically in two ways (as far as I've understood) : by stretching it towards its center of gravity, and by dragging it along the direction of its rotation (Lense-Thirring / frame-dragging). Basically, it means that flying towards a massive celestial body (planet, star...) will increase your speed and dilate time, and if the mass is extreme (black hole / cf. "Interstellar" movie), it will strech your body ("spaghettification") and somehow send your "slender-self" in the future of the universe.

The gravitational field of the Sun extends far beyond the limits of the solar system, up to 1 light-year, that is 2104 times the distance between the Sun and Neptune, the closest star, Proxima Centauri, being located at 4,2 ly from the Sun.

Some 3d fanciful/artistic representations of the Sun and the curved space-time :

Wonderful, Erik...I do hope you have an exhibition planned in the near future (in space-time ), or, perhaps, a book.

The link between science and art is truly intertwined - one feeding off the other.

John Moore

Thanks John, there's so much to say and to show about the universe, I guess you can see creation as some living art

Here's the vestige of a collapsed star, a black hole, that is some highly concentrated matter bending spacetime (grid's peak on the picture) to the point that nothing, even light, can't escape it, and forming then a black spherical region delimited by what astrophysicists call the event horizon/Schwarzschild radius; at its very center may lie a gravitational singularity, a region where the spacetime curvature and time dilatation tend toward infinity.

A black hole can be detected by observing the phenomenons that happen in its surroundings due to the extreme curvature of spacetime: diverted light (distorted Milky Way on the picture), and orbiting around: stars or a bright accretion disk made of matter/gas when the black hole is "dining"...

Nice visualizations, but this is not related to solar robotic exploration and doesn't seem to fit anywhere else. Moved to Chit-Chat.

Nice, Erik. I have to ask: what exactly are you plotting? Constant surfaces for some invariants or curvature components? Is this using custom software?

Hi fredk, what do you mean ?

Sorry, I missed the words "fanciful/artistic". Nicely done!

Thank you.
Indeed, I'm not a mathematician but can you try to explain the concept in few words in this context...

There are lots of ways to accurately represent the curvature of spacetime (the simple rubber sheet not being one!). The curvature is described mathematically by several numerical values (components of the metric or curvature tensors) that vary over space and time. So there are all sorts of ways to plot these. Eg, plot surfaces where one of these values (components) take constant values, eg the three surfaces where some "x" takes the value 1, 2, and 3. These would be akin to isoclines/isotherms/isobars/etc. The tricky part is choosing the surfaces to reveal useful information about the spacetime.

An example of a technical approach is in this paper, which includes lots of plots for inspiration (like the lawn sprinkler spacetime!).

thanks fredk for your explanations and link, will check it out