Is it theoretically possible to create a 'time bubble', where inside the bubble time will stop or at least slow down radically? I am a layman who dabbles online in physics, I thought this would be cool and has probably been done in sci fi already, but was wondering if it were actually possible.
 A: Sure you can!  You will need:

*

*One (1) large spherical shell of ordinary matter

It can be shown that inside a spherical shell like this, the amount of time $\tau$ experienced by an observer at rest inside is related to the amount of  time experienced by an observer at rest very far away from the shell by
$$
\tau = \sqrt{1 - \frac{2 G M}{R c^2}} t
$$
where $M$ is the total mass of the shell and $R$ is its radius.
The smaller this square root factor is, the slower time will run inside the shell compared to outside the shell.  In principle, you can make this square root factor as small as you like by increasing the mass of the shell and/or decreasing its radius.  Note, however, that if the mass gets too big or the radius gets too small, the shell will collapse into a black hole, along with any hapless observers who happen to be inside.  This is undesirable in most situations.
In practical terms, a large spherical shell made out of "everyday" materials (i.e., those we have the technology to currently manufacture) will not be able to support its own weight, and it will collapse inwards on itself at a mass well below that required to form a black hole.  This may also have deleterious effects on anyone inside the shell at the time.
A: Very common and close to this is Gravitational Time Dilation.  If you are outside of a gravitational field and looking in, the things within the gravitational field are moving through time more slowly than the things far from the field.
This effect is fairly small for small planets, like the earth, but some classic examples on Earth are: 1) GPS, which uses very precise timing, needs to be corrected for this effect because we are moving through time more slowly than the satellites because we are in a stronger field; but that correction is in the nanosecond range. 2) Over the age of the earth, the core is about 2.5yrs younger than the surface.  This dilation effect is much more significant in larger gravitational fields, and gets totally warped in a black hole.
But, to be clear, wherever you are, it always feels locally like time is moving along at a normal speed.  It's only when you look at something else in a different circumstance that you would perceive a time dilation.
A: Dilating time inside a bubble (and then getting something back out of it) is possible, but you have to send the bubble on a journey. Strap a really big rocket and an unreasonably huge amount of fuel and armor to the bubble and send it on a long round trip. Either boost it up to close to the speed of light relative to the launch pad, fly in a big loop, come back, and boost back down to zero relative velocity; or fly to the nearest supermassive black hole, park in low orbit for a while, then boost back out to the original distance from the SMBH. In either circumstance, a clock in the bubble will measure much less time to have passed than does a clock at the launch pad.
