Building a Gravitational Wave Transmitter · Imagine that Kardashev 2 or 3 technologies can find or make black holes of Earth-scale mass—which is about the size of the tip of your

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My rule is there is nothing so big nor so crazy tha t one out of a million technologica lsocieties may not feel itself driven to do, provided it is physica lly possible.

—Freeman Dyson“The Search for ExtraterrestrialTechnology,” 1965

* * *In the last few years, physicists have thrown open a grand new window on our universe. Thereare now two detectors of the ripples in space-time called gravitational waves. The f irst wasLIGO (Laser Interferometer Gravitational-Wave Observatory), and the copy of it in Italy, VIRGO,went online this year. They now sense black holes and neutron stars merging by the gravita-tional waves (gravwaves) they emit.Pulling a good signal out of the vast sea of noise effects demanded filtering from the many

sources of noise—trucks on highways, earthquakes, even footsteps. But suppose there are sig-na ls to be heard, too?A similar possibility emerged in the nineteenth century, after Maxwell predicted electromag-

netic waves moving at the speed of light. Hertz, in a simple experiment using electrical circuits,detected them in radio wavelengths. Hertz thought sending signals would never happen; hiswaves were too weak and diffuse in spectrum, he thought. An Italian teenager heard of Hertz’sremarks and thought of sending messages with the waves and made it so, along with others.

Science Fact

Building aGravitational

WaveTransmitter

Albert Jackson & Gregory Benford

That resolve by Marconi provoked a world we now enjoy. Today we listen for electromagneticsignals from other minds among the stars. In the future, gravitational wave astronomy will combat the many noise sources with ever-

more detailed methods to tease out even fainter signals. Perhaps, for motives we cannot wellimagine, other smart beings will even encode messages in the gravitational waves that washthrough our space-time every moment.Making such messages is a very hard task. Space-time is stiff! Producing the slightest ripples in

space-time demands moving enormous amounts of mass-energy. Even with today’s state-of-the-art LIGO equipment, two ordinary stars orbiting each other don’t emit gravitational waves at ameasurable level. To see gravitational waves demands the close grazing of large masses at rela-tivistic or near relativistic speeds. (The f irst LIGO detection was the merger of two approxi-mately thirty-solar-mass black holes.)Perhaps very advanced intelligences elsewhere can command huge energies and send possi-

ble gravitational wave messages to civilizations such as ours. (Note that the extinction rate ofgravitational waves in the interstellar medium, unlike photons, is nearly zero.) We cannot knowtheir motives, though see below for possibilities. To do this they will be vastly wealthy, so theymight prefer to speak to those who have mastered the far more difficult task of sensing gravita-tional waves, compared to the simpler detection of electromagnetic signals in a myriad of pos-sible wavelengths, which we now have.Our study stands in the tradition of Dysonian ideas. More than a half-century ago, Freeman

Dyson proposed that SETI agendas should look at technologies for harnessing an entire star’s en-ergy, building on ideas of the legendary writer Olaf Stapledon. Dyson suggested that we shouldlook not only for signals, but also for side effects like infrared emission, on scales that do not con-tradict physical law, but are beyond conceivable human engineering. We do similarly here lookfor signals in gravitational waves emitted for a purpose, following on the SETI ideas evolved sincethe 1950s.1 Besides a command of vast energies, a very advanced civilization should be able to fi-nesse super-sophisticated engineering physics, within the limits of the basic facts of the Universe.The amount of energy produced can be related to the quantity of energy by a parameter specifiedby the Russian scientist Nikolai Kardashev, which relates the amount of energy available to a civ-ilization. Energy types are characterized by scales such as Type 1 “planetary,” Type 2 “stellar,” andType 3 “galactic.” Let Kardashev 1, 2, and 3 denote these civilizations in what follows.

* * *Tiny Engines

If a civilization sends signals using gravitational waves, there are two problems to be solved:the transmitter and the receiver. The energies in a gravwave transmitter are huge, but its core issmall—so let’s begin there. The entire radiating center can be the size of your living room.Let’s say we start by injecting a smaller mass (m) into a grazing orbit around a large mass (M).

But these masses are physically small, a centimeter or two across, yet massive—because theyare black holes.Gravwave radiation depends on the mass of objects; so small yet massive ones are best for en-

gineering a transmitter.Imagine that Kardashev 2 or 3 technologies can f ind or make black holes of Earth-scale

mass—which is about the size of the tip of your index finger. Take that smaller mass and put anelectrical charge on it. That lets you accelerate and guide it.Slam the smaller mass into a tight grazing orbit. Here general relativity helps enormously. Figure 1 comes from online site Rela tivity 4 Engineers, plotted with a new line for every full

orbit. The orbit “whirls” around the black hole a few times and then “zooms” out and backagain—a so-called zoom-whirl orbit. This happens when the mass grazes very close to the moremassive black hole. This inner edge is between two to three times the event horizon radius. Ifthe orbiting mass comes much closer, it will either fall into the black hole, or it will escape com-pletely, depending on its total orbital energy. The point is these zoom-whirl orbits emit powerful gravwaves. A unique feature of this sys-

tem is how tiny it is! Black hole M (the central mass) is almost a centimeter, and black hole m

SEPTEMBER/OCTOBER 2019

37BUILDING A GRAVITATIONAL WAVE TRANSMITTER

(exciter mass) is a millimeter. The whole orbital configuration is about one meter—the length ofyour arm. The emitted gravwaves are a few centimeters, the orbit size. Our present detectorssee waves tens of kilometers in length, so they can’t see such a gravwave transmitter.Making this happen demands delicate control of the orbit and energy, using methods like

those in our big particle accelerators—strong electric and magnetic fields. Putting charges andmagnetic f ields onto the two black holes helps this along. So does hole spin. Energy f lowsthrough the whole strongly-coupled system. The central hole’s spin adds to the incoming hole’sangular momentum, boosting the orbit back out. Zoom-whirl behavior is characteristic of strong relativity and high velocities. It radiates har-

monics in the gravitational waves—the key to imposing high-bit-rate signals on the outgoinggravwave train.

* * *To keep the mechanism going, the small mass has to be artif icially extracted, accelerated

anew, and fresh velocity and spin must be added electromagnetically. Then it returns to orbitaround the big mass about ten times, then escapes again. The civilization must array accelera-tors and guiders that precisely aim for the sweet spot orbits. It can’t let the small mass fall intothe big mass black hole.

38 ALBERT JACKSON & GREGORY BENFORD

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Figure 1: Nonlinear zoom-whirl orbits, shaded for each pass. They are nested sets.

Generally, injecting the small mass into an eccentric orbit around a black hole means thoseorbits decay in a flash. These tiny objects on the scale of centimeters might be controlled elec-tromagnetically, through their charges and magnetic moments. A small mass m with the rightimpact parameter can come in from infinity and go into winding orbits.The energetics are enormous. Kardashev 2 or 3 civilizations might manage it. As an example, consider a 0.1 Earth mass m forced into an orbit around a 1.0 Earth mass cen-

tral body, M, both black holes of size less than a centimeter. The smaller mass m is injected intoa nearly radial trajectory toward the central mass M. With a suitable angular momentum embed-ded into the smaller m, the mass twists into a class of zoom-whirl orbits, approaching no closerthan five centimeters. This is safely beyond the critical radius from which it cannot be recov-ered, about three cm. The zoom-whirl orbits emit gravitational radiation at frequency ~1 GHz while executing orbits in

less than a millionth of a second. The zoom-whirl orbits extend the total emission time to a mi-crosecond. This means at least a thousand bits of information can be emitted before the smaller massreturns to the energy source to be resupplied. That’s about sixty words.This accelerator must be large, but the emitting staccato “ticker” is quite small: the size of

your hand. One might envision a number of small masses as the “exciters” orbiting in a compli-cated convoy to make a more intense, signal-rich ensemble. These can then emit in concert, in-suring a longer message.Of course, managing the black hole and gravwave stresses in the central region of the emitter

is crucial. The emitter sits at the core of a relatively low-mass surrounding structure that mustflex and endure severe stresses. The wave stretches one transverse direction while the othercompresses. Because of potential accident, the entire assembly should orbit well beyond any in-habited zones—say, far out beyond the planets of a solar system. The total gravwave energy emitted to be heard across the galaxy (about 100,000 light-years) is

equivalent to about a tenth of an Earth mass. How can such a machine energy be replenished? Obvi-ously, a culture able to handle such masses and thus energies must have sources we do not know.The precursor to any such project must be using black holes to extract energy. Such energy sources



Figure 2: The emitter and its engine, circling its host star. The “Superradiance machine” is inward of thegravitational wave machines, though it could be even further out. Energy gets beamed between them all.

Image credit: Douglas Potter

might be essential in mining operations throughout an outer solar system, where large, sporadic en-ergies are useful in mass processing for industrial use.Our calculations show that the power radiated by this transmitter is a million million times

the output of our sun. Where would this energy come from? Here’s a diagram of the whole she-bang, with ideas about the power source, too.

The Kerr BombTo make such energies, now suppose the advanced civilization has three small black holes.

These may be harvested primordial black holes, if they exist. Two are the orbital gravwave ma-chines, the larger central mass plus the exciter mass. The machine central and exciter blackholes form a binary system orbiting the home star. The third black hole is a rotating (Kerr) black hole—the “machine” power plant. It exploits

“superradiance,” which means radiating strongly because of coherence in the sources, like ra-dio antennas. This means extracting energy from the rotating black hole by scattering electro-magnetic radiation from it. The home star sunlight gets diverted to the big black hole, thenamplified by superradiance (see figure 2 and the references therein). Surround the powerhouseblack hole (a Jovian-mass rotating black hole, radius about two meters) with a spherical mirrorabout three hundred meters in diameter. Figure 3 shows a cut away of the “bomb transmitter-mirror” system. This scattered radiation will pick up a small amount of energy from the rotatingevent horizon. If the scattered radiation is then confined, for a very short length of time, by aspherical “mirror,” then an enormous amount of energy can be extracted.This energy comes from the rotational energy of the spinning black hole (the mechanism is

superradiance). Suppose the “powerhouse” black hole has a mass of Jupiter and the Kerr blackhole is rotating at its maximum. This means the horizon would be spinning at ~1 GHz, as long asthe impinging radiation has a frequency of less than, or of the order of, this it will be amplified.One notes an immediate problem with the mirror. If the radiation is to be contained to a level


ANALOG

Figure 3: The Kerr power plant, a pulsating black hole bomb.

Image credit: Douglas Potter

1016 times bigger than the Sun’s output, then the mirror would have to have a tensile strengthand thermodynamic characteristic stranger than neutron star material! These are magnificent machines, indeed. What does this contraption give forth? A gravwave

that even civilizations like ours could detect. A larger question is, why? We leave that to our con-clusion.

Gravitational Waves and Kardashev Civilizations

The LIGO receivers have seen gravitational radiation from natural objects. As a gravitationalwave passes through matter, it can change its geometry, namely a characteristic length. If onemeasures a length L and it responds to a gravitational wave by ΔL, the ‘strain’ is measured byh=ΔL/L. This dimensionless amplitude is very small indeed, due to the weakness of gravitationalwaves. LIGO can measure h to the value of 10-22, or in approximate physical terms, 1/1000 the di-ameter of a proton. Physically, h is related to the transmitter by h is proportional to ΔE/r where ΔE is a burst of

gravitational radiation energy and r is the distance from the transmitter. Take ΔE as theamount of energy produced in annihilation of a mass m, namely mc2, and take the distance ofthe transmitter to be ten thousand light-years. Table 1 shows a calculated correspondence be-tween dimensionless amplitude, amount of energy production, and civilization ‘scale’ for civ-ilization located at ten thousand light-years.

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Table 1: Advanced civilization transmitter located at 10,000 light-years

DimensionlessAmplitude

(h)

Mass convertedto Energy

(ergs)

Kardashev ScaleCivilization

GravitationalWave Receiver

10-22~0.1 Earth Mass

1027 grams 3.6 LIGO at 100 Hz

10-25~ mass of Ganymede

~1026 grams 3.0 Advanced GravitationalWave Detector ~1GHz

10-33~ The mass of asteroid Ida~ 1017 grams

2.4 “Planck” Length Detector

The amount of mass annihilated is given in grams and representative objects. A Type 3 pluscivilization a one hundred light years away LIGO can detect, but presently only in the frequen-cy range of ~100 Hz. A more plausible signal, we argue, may lie in the GHz range.

Gravitational Wave MachinesThe process would begin by injecting (using Kardashev 3 technology) a small mass m into an

unbound orbit about M, deep in the non-Newtonian region of the black hole. It executes sev-eral orbits—say, about ten loops, then returns to a great distance. To keep the mechanism go-ing, the small mass m has to be artificially returned to orbit about the big mass. The energeticsare enormous. A unique feature of this system is how tiny it is! Black hole M is almost one cen-timeter, and black hole m is a millimeter. The whole orbital configuration is about one meter.The civilization must array an instrumentality that can precisely aim and hit the right impact pa-rameter, as well as monitor and “trim” the stability of the “operational” orbit. The energy radi-

ated will cause decay of the circulating orbit and the small mass m cannot be allowed to fall intothe big mass black hole. The small mass must be cycled back to the big mass. The physics is al-lowed, but the engineering is beyond our mere human comprehension! Generally, injecting the small mass into an eccentric orbit around a black hole means those

orbits decay in a flash. However, a mass injected with kinetic energy can skim the knife-edge atthe photon sphere, ~3 R

swhere R

sis a Schwarzschild radius. This can still be an open orbit—

that is, returns to infinity—thus allowing a large region where the charged mass can be ener-gized again, with velocity and spin added electromagnetically in an accelerator. These tinyobjects on the scale of centimeters can be controlled electromagnetically, through their chargesand magnetic moments. A small mass m with the right impact parameter can come in from in-f inity and can go into winding orbits that circle at 3m about ten times and then escape. Thesame is true of ultra-relativistic trajectories of objects with mass. Relativistic orbits very close toblack holes precess around the black hole and form nested sets. We are positing a civilizationthat not only can command “galactic-magnitude” energies but can also craft guidance, naviga-tion and control systems of almost infinite grandeur.

* * *Why do this?

The great equalizer in all communication across vast ranges is the speed of light andgravwaves alike. This leads to motives, once societies achieve Kardashev 2 level technologies.With such enormous effort to create a gravwave emitter, why not do something simpler, like aradio transmitter? This gravwave machine violates the KISS rule—Keep It Simple, Stupid. The simplest reason to build a gravwave emitter is a desire to avoid the mere Kardashev 1 so-

cieties such as ours, who use electromagnetic signals. A Kardashev 2 will have mastered a solarsystem, which implies long-term stability and cultural calm. Spacecraft velocities are around tenkilometers per second, which makes them deadly missiles. Handling them demands careful con-trol. This may well mean they are not aggressive and will not want to attract the attention ofyoung, violent aliens. They may not wish to be known at all to mere electromagnetic civiliza-tions. This isn’t a crazy motive—look at all the alien invasion films we create!Further, gravwave communities may wish to discuss dangerous technologies with distant,

long-lived societies, without being overheard by electromagnetic snooper ears. (For what thosecould be, consult Glorious, a Larry Niven and Gregory Benford novel out next year.) Or theremay be motives we cannot imagine—yet.The broad, grand goals of alien minds can be imagined, though. Briefly, they can be:

* * *• Kilroy Was Here—memorials�to dying societies.• High Church—records of a culture’s highest achievements. The essential message is thiswas the best we did; remember it. A society that is stable over thousands of years may in-vest resources in either of these paths. The human prospect has advanced enormously inonly a few centuries; the lifespan in the advanced societies has risen by 50% in each of thelast two centuries. Living longer, we contemplate longer legacies. Time capsules and ever-proliferating monuments testify to our urge to leave behind tributes or works in (literally)concrete ways. The urge to propagate culture quite probably will be a universal aspect ofintelligent, technological, mortal species.

• The Funera l Pyre: A civilization near the end of its life announces its existence. Considerthe poem Ozymandias: the ancient motivation is sheer pride. A grand society may be ex-tinct, their gravwave the beacon tended by robots.

• Help! Quite possibly societies that plan over timescales of thousands of years will foreseephysical problems and wish to discover if others have surmounted them. An example is acivilization whose star is warming, as ours is. They may wish to move their planet outwardwith gravitational tugs. Many other environmental problems are possible. �

• Join Us: Religion may be a galactic commonplace; after all, it is here. Seeking converts is com-mon, too, and electromagnetic preaching fits a frequent meme. Other motives for joining


ANALOG

might be sending a signal to younger civilizations to initiate contact. This echoes the StarTrek criterion for joining the Federation: having a warp drive.

* * *These motives may well persist into cultures vastly more powerful than ours, who prefer

gravwave signals to the easier electromagnetic ones. LIGO has opened a window that perhapsfew societies in our galaxy could manage, or wish to. It may show us more than astronomers ex-pect.Possibly we have overestimated the technical difficulties. Received power can be enhanced in

transmissions if sources are made coherent. In gravitational radiation, this would mean resonantparalleling of trajectories in the smaller masses, as they orbit the central mass. This might be pos-sible, but will greatly complicate matters, as the zoom-whirl orbits are already highly nonlinear;adding a coherence constraint makes their management more difficult. But the output could befar higher, making the whole machine simpler, with smaller masses to move. One can also imagine an array of more than one m/M system. This would mean spacing the

large mass elements in order for their emissions to align. Such an array then can direct emissionsin a narrower spatial and perhaps frequency band, just as in electromagnetic systems. Some ef-ficiency improvements seem possible this way. If so, the threshold of gravwave emitters may below enough to make it a commonplace of truly long-lived societies.

* * *We thank James Benford, Allen Steele, David Brin, and Michael Brotherton for useful ideas.

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References1. A Gravitational Wave Transmitter, A. Jackson, Gregory Benford,https://arxiv.org/abs/1806.02334http://www.einsteins-theory-of-rela tivity-4engineers.com/rela tivistic-orbits.html



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Building a Gravitational Wave Transmitter · Imagine that Kardashev 2 or 3 technologies can find or make black holes of Earth-scale mass—which is about the size of the tip of your