One day, we find ourselves standing on a very interesting planet.  This planet is far, far from Earth, and orbits VERY close to a black hole.  As such, their perception of time and energy is very different from the rest of the universe. Being close to such a large mass, time on that planet actually runs much slower than it does on Earth.

To solve their world’s energy problem, the people on this planet launched a very special satellite in a highly-eccentric orbit.  This satellite comes very close to the planet during a small part of the year, and quickly slingshots far away for the rest of the year.  It is in its own stable orbit and requires no additional energy once launched.

When the satellite is close, they charge its internal capacitors with almost no losses.  The satellite receives over a megajoule of energy.

As the satellite moves away from the planet, it experiences a strong relativistic effect.  Because it is leaving the gravitational well of the black hole, the rate-of-time on the satellite changes, and from the point-of-view of the planet, it appears to speed-up substantially.   While from the point-of-view of the satellite, everything on the planet appears to slow down.

When the satellite is finally a long way from the planet, it begins beaming a tightly-focused microwave beam toward the planet at 10ghz.

Due to the nature of special relativity, these waves become refracted as they approach the planet.  This causes an upshift in the frequency many-fold.  The formerly 10ghz microwaves are refracted all the way to 500thz, where they are received on the planet as visible light.

Because this blue-shift refraction has increased the energy of the incoming waves, the planet is now able to use much more power than it transmitted to the satellite in the first place.

Naturally, the planet sets aside a small amount of power to recharge the satellite when it is back nearer to the black hole.

This process worked so well that the planet eventually launched dozens of these satellites, and they now provide all of the power and light they will ever need.

Some crazy inventors on that planet still are hard at work trying to recreate the same effects with simple circuits, since refractive shifts in frequency are much easier to create using coils and capacitors as opposed to the expensive, bulky satellites.  One of them was heard muttering that frequency is energy and another went insane rambling about kings and electrons…

Earthlings trying to reach them are not likely to ever make contact with this civilization.  You see, while that planet uses the exact same radio frequencies we use on Earth, the relativistic redshift means Earth receives them at 1-100hz.   And while the black-hole planet received every one of our SETI transmissions, they cannot decipher them as the radio waves get upshifted to gamma-ray bursts as they approach the planet.

References

• Charles Steinmetz on Reaction Machines