An infinitely large napkin, if made of any sort of normal matter, would have infinite mass. It's gravitational pull would propigate, at c IIRC, out from the instant of its creation across all of space/time, sucking all objects (including itself) towards it's center of mass at the speed of light (OK, just under. Literally c-0.000...1m/s). It not only would create a black hole, it would signal the end of the entire universe. The destruction of any point in space would depend simply on the distance from the napkin. For every 299,792,458 meters away from napkin center, that object would have one second of existance left. When the gravitational pull hits anything, the acceleration would be so strong, again 0-c in 0 seconds, that some crazy subatomic fusion would occur.
Any physicists out there able to flesh this out? I find the thought experiment fascinating and am sure I'm missing/misrepresenting something.
How can an infinitely large napkin have a center of mass? It seems to me that all everything would get sucked on a trajectory normal to the napkin's surface. Any horizontal force would get cancelled by an opposite force, at an opposite point on the napkin. Also, force of gravity drops off with the inverse square of distance, so the force would have a finite value, depending on the density of the napkin. Similar idea to a common homework problem for introducing electrostatics: calculate the electric field generated at some point by an infinitely long wire with some charge density.
Interesting to note, the napkin creates a uniform gravitational field above and below it. Meaning that the force applied to an object is the same regardless of how far away it is from the napkin! That force is 2pi * G * m * rho where rho is the mass density of the napkin.
It is the same result as infinite planar light sources or infinite planar electrostatic charges. Move the test particle a small delta above or below the napkin, and the result will become apparent.
Indeed, if it wasn't flat it would not perfectly cancel.
The drop off applies because the force of gravity is proportional to 1 / distance^2, so in this case the napkin would still have infinite mass, but it would not have infinite density, so if you took a surface integral of the gravitational force provided by each point in the napkin, over the whole napkin, it would converge on a finite value, as each point contributes less and less force as you get father away.
Any physicists out there able to flesh this out? I find the thought experiment fascinating and am sure I'm missing/misrepresenting something.