Draft version August 12, 2024
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ILLUMINATION OF A PLANET BY A BLACK-HOLE MOON AS A
TECHNOLOGICAL SIGNATURE
Abraham Loeb1

1

Astronomy Department, Harvard University, 60 Garden St., Cambridge, MA 02138, USAABSTRACT
I show that Hawking radiation from a mini black hole with a mass of ∼ 1011 g in alow orbit around an otherwise frozen rogue planet, can supply the energy needs of acivilization on the surface of the planet. Maintaining this furnace for more than a fewyears requires a modest accretion rate of ∼ 2 kg s−1 . The associated technosignature
is detectable as a gamma-ray source occulted by a warm planet every 1-2 hours, withno stellar-mass companion.

2Loeb
1. INTRODUCTION

In this paper, I consider the possibility that an advanced civilization would choose
to manufacture a furnace that returns clean energy from the matter fueling it, with aconversion eﬃciency of mass to energy of nearly 100%, two orders of magnitude above
the most eﬃcient nuclear fuel. Once the fuel enters the furnace, it gets consumed anddisappears from view. This enclosure of this ideal furnace is the event horizon of amini black hole.
Advanced civilizations could satisfy their energy needs by processing matter throughan accretion disk around a mini black hole that orbits their planet like a moon.
The main technological challenge in producing a mini black hole involves the enormous mass density required to make it. If it is possible to manufacture a mini blackhole and keep it as a luminous moon around the planet, then this artiﬁcial furnace
could replace a star in illuminating and warming a rogue planet that is otherwise
frozen and uninhabitable. Rogue (free-ﬂoating) planets without a host star to warmthem up were recently discovered by gravitational microlensing (Mróz et al. 2020;Sumi et al. 2023; Mróz et al. 2024; Kunimoto et al. 2024; Rektsini & Batista 2024).
For the past half century, cosmologists conjectured that mini black holes might havebeen produced in the infant Universe, when the radiation energy density was highenough (Carr & Hawking 1974; Carr & Green 2024). It is possible that the dark matter is made of primordial black holes in the mass range ∼ 1017 -1022 g (Carr & Kuhnel2021; Green 2024). Here, we consider a diﬀerent possibility that a suﬃciently advanced technological civilization might have been able to trap a primordial black holeor manufacture a mini black hole in order to satisfy its energy needs.
Stephen Hawking realized in 1974 that a mini black hole would shine on its own,even without an external supply of fuel (Hawking 1974). The associated Hawking
radiation is brighter for smaller black holes, causing them to evaporate over a shorttime. Given the Hawking relations, we identify below the optimal black hole mass forproviding the solar energy ﬂux on an Earth-size planet. For simplicity, we focus thediscussion on non-spinning (Schwarzschild) black holes.

2. DESIRED PARAMETERS OF THE BLACK HOLE

To obtain speciﬁc numbers, consider a mini black hole that circles a rocky planet
like the Earth at an altitude of ∼ 1.5 × 103 km, about a quarter of the Earth’s radius.
This is commonly called a Low Earth Orbit for artiﬁcial satellites and was chosen here
to obtain modest energy and mass requirements. Such a black hole would supply theenergy ﬂux of 1.4 × 106 ergs s−1 cm−2 that the Earth is currently receiving from theSun if its luminosity is L• ∼ 4 × 1023 ergs s−1 = 10−10 L⊙ .
This moon would illuminate the ground under it periodically over an orbital timeof about ∼ 90 minutes. The duration of the luminous period scales with the orbital
radius of the moon to the 1.5 power.

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In terms of fundamental constants, the Hawking luminosity is given by,~c6L• == 0.93 × 10−10 L⊙
2215360πG M•

M•1011 g−2.

(1)

The required energy ﬂux at this low-altitude orbit can be supplied by Hawking radiation from a mini black hole with a mass of M• = 0.96 × 1011 g (L• /10−10 L⊙ )−1/2 ,which is equivalent to the mass of an asteroid with a 40-meter diameter.
The Hawking evaporation time for such a black hole is,t• =5120πG2M•31.80083~c4

= 1.5 yrM•1011 g3.

(2)

In order to maintain the operation of the furnace for a period longer than a year, itis necessary to supply it with a modest accretion rate of,Ṁ =M•t•

kg= 2.2sM•
1011 g−2,(3)so as to keep its mass constant. This mass supply resembles the deposition of logs
in a wood-burning ﬁreplace. The civilization could automate the process by steadily
releasing material from a companion satellite, orbiting in the vicinity of the blackhole and feeding its accretion disk in a steady state to compensate for its Hawking
radiation loss. If the feeding ever stops, the ∼ 1011 g black hole would evaporate anddisappear within t• ∼ 1.5 years. In the regime where the black hole accretion ratebalances the Hawking mass loss rate, the accretion luminosity would make a small
fractional correction to the Hawking luminosity, of order the radiative eﬃciency withtypical values . 10%.
The Hawking temperature of the mini black hole is given by,T• =~c38πkB GM•= 1.2 × 1015K

M•
1011 g−1,(4)with the peak of the Hawking radiation emitted in γ-rays with an energy of Eγ =415 (M• /1011 g)−1 GeV. These photons would be reprocessed by matter in the surrounding accretion disk, as well as the planet’s atmosphere and rocky surface, into
low-energy radiation and heat that could supply the energy needs of the host civilization.
The Klein-Nishina cross-section for scattering of the emergent radiation on electronsis ∼ 10−30 cm2 (Eγ /415 GeV)−1 or equivalently ∼ 10−6 (Eγ /415 GeV)−1 of the Thomson cross-section. As a result, the emergent luminosity of ∼ 10−10 L⊙ is comparable
to the eﬀective Eddington limit for infalling matter onto a ∼ 1011 g black hole. This
numerical coincidence allows matter to accrete into the black hole in response to its
attractive gravity despite the repulsive radiative force from the Hawking radiation.

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The technology to produce a mini black hole of this mass must reach a mass densityof,
−2
gM•
3c3
60= 5 × 10,(5)ρ=32πG3 M•2
cm3 1011 g
near its event horizon. Whether such a technological feat was accomplished by anadvanced civilization in the Milky-Way galaxy remains to be seen. Gamma-ray andinfrared telescopes could search for an anomalous gamma-ray moon occulted every
1-2 hours by a warm, infrared-emitting planet.

3. DETECTION AS A TECHNO-SIGNATURE

If we ever detect a rogue rocky planet which is illuminated by a gamma-ray moonwith no stellar-mass companion, we would need to consider the possibility that thesource was created (or trapped as a primordial black hole) by a highly-advanced
technological civilization. There is no better marker of technological innovation thancreating a furnace out of spacetime curvature in the form of a mini black hole.
Currently, there are a large number of startup companies aiming to make compact
fusion reactors. A mini black hole would be far more eﬃcient and environmentallyfriendly.

ACKNOWLEDGEMENTS
This work was supported in part by Harvard’s Black Hole Initiative, which is fundedby grants from JFT and GBMF.

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