Micro Black Holes

A black hole is an object that is so dense and compact that within a certain distance from it, its gravitational pull becomes so strong that it does not let even light to escape. This distance is where the event horizon of the black hole is located and anything which crosses the event horizon, including light, can never escape. If the entire Earth is crushed to form a black hole, its event horizon will have a diameter of only 1.8 centimetres. In comparison, the black hole version of the Sun will have an event horizon that is 5910 meters in diameter.

In this article, I will explore the theoretical possibilities of using micro black holes as energy generators, antimatter factories, propulsion for interstellar space travel and gravity wells for artificial planets. These ideas are just theoretical possibilities that could be possible in the distant future. The micro black holes that I’m referring to are those with masses at or below the planetary mass regime. Unless a micro black hole can be found naturally, forming such a black hole will first require compressing a large amount of mass into an incredibly tiny volume of space. After the creation of an initial black hole, additional matter can be thrown into the black hole to increase its mass.

Hawking radiation is a form of radiation that is predicted to be emitted by black holes due to quantum effects and it is named after the physicist Stephen Hawking who theorized its existence in the 1970s. Since the emission of Hawking radiation allows black holes to lose mass, black holes that lose more mass than they accrete will eventually disappear. An isolated black hole will eventually vanish by emitting all of its mass in the form of Hawking radiation and the lifespan of a black hole is directly proportional to its mass. The amount of Hawking radiation and the mean energy of the radiation particles being emitted by the black hole are both inversely proportional to the mass of the black hole. For this reason, smaller black holes are expected to emit much more Hawking radiation than their more massive counterparts.

The first area to be investigated is the use of micro black holes as antimatter factories. Compared to ordinary matter particles, antimatter particles have the same mass but opposite charge. For example, the antimatter counterpart of an electron is a positron and it has a positive charge instead of a negative charge. On its own, antimatter is stable. However, when an antimatter particle meets an ordinary matter particle, they will annihilate with total conversion of matter to energy. The amount of energy produced when one gram of matter annihilates with one gram of antimatter is about 3 times the amount of energy produced from the detonation of the Hiroshima atomic bomb.

A micro black hole can be used as an antimatter factory since matter and antimatter are expected to be produced in equal quantities as the black hole evaporates via the emission of Hawking radiation. Since the mean energy of the radiation particles being emitted increases as the mass of the black hole decreases, the production of more massive particles will require a smaller black hole. For example, a black hole with a mass of 65 billion tons is optimal for the production of electrons and positrons. For heavier particles such as protons and antiprotons, a black hole with a much smaller mass of 35 million tons will be required.

Black holes of planetary mass can be used to create artificial planets by providing the source of mass necessary to generate the required amount of gravity. An artificial planet can be created by constructing a large spherical shell with the black hole in the center. For example, a spherical shell that is 12760 kilometres in diameter can be constructed around an Earth-mass black hole to form an artificial planet with Earth-like gravity on the external surface of the shell. In another example, a spherical shell that is 227000 kilometres in diameter can be constructed around a Jupiter-mass black hole to form an artificial planet that has over 300 times the surface area of the Earth, with Earth-like gravity on its external surface.

Such artificial planets with Earth-like environments can range from hundreds of kilometres to hundreds of thousands of kilometres in diameter. This concept can be especially useful in planetary systems with insufficient silicate and metallic elements to build solid planets. Hence, hydrogen and helium from the gas giant planets or from the local star can be used as a source of mass to form the black hole. In addition, energy can be generated by dropping mass into the black hole located at the center of such an artificial world as the accretion of even a small amount of mass into the black hole is expected to generate a tremendous quantity of energy.

Now, I shall describe the evaporation of a micro black hole with an initial mass of a billion metric tons and the amount of energy emitted by the black hole as it evaporates via the emission of Hawking radiation. The event horizon of this billion metric ton black hole is about the same size as the atomic nucleus of a hydrogen atom and it will have a luminosity of 356 million watts due to the emission of Hawking radiation, which is approximately twice the power output of a Nimitz-class aircraft carrier. This black hole will have a lifespan of over 2 and a half trillion years, which is much longer than the current age of the Universe.

As the black hole evaporates by emitting Hawking radiation over 2 and a half trillion years or so, it will eventually reach a mass of 10 million metric tons. At this mass, the size of the black hole’s event horizon is about 100 times smaller than the atomic nucleus of a hydrogen atom and it will have a luminosity of 3.56 trillion watts from the emission of Hawking radiation, which is roughly the average total power consumption of the entire United States in 2008. At this mass, the black hole still has a life span of another 2 and a half million years.

Now, I’ll fast forward until the black hole has just one year remaining. At this time, the black hole will have a mass of 72 thousand metric tons, an event horizon that is 15000 times smaller than the atomic nucleus of a hydrogen atom and it will shine with a luminosity of 68.5 thousand trillion watts, which is approximately 4000 times the average total power consumption of the human world in 2008. A black hole around this order of magnitude of mass can be use as a propulsive device to accelerate a spaceship to relativistic velocities, tens of thousands to hundreds of thousands of kilometres per second. This can be done by directing the high energy radiation particles emitted from the black hole to produce thrust. Ordinary matter can also be fed into the black hole to sustain it.

As the black hole gets smaller and smaller, it will lose more and more of its mass in the form of Hawking radiation at an increasing rate. When the black hole reaches a remaining lifespan of 10 seconds, it will have a mass of 492 metric tons, a diameter of 1.46E-021 meters and a luminosity of 1.47E+021 watts. At this stage, the black hole is just over a million times smaller than the atomic nucleus of a hydrogen atom and in one second, it emits more energy than the detonation of 23 million Hiroshima atomic bombs.

Finally, when the black hole reaches the final second of its existence, it will have a mass of 22.8 metric tons, a diameter of 6.78E-022 meters and a luminosity of 6.84E+021 watts. At this stage, the black hole is over two million times smaller than the atomic nucleus of a hydrogen atom and in its final second, it will emit more energy than the detonation of 300 million Hiroshima atomic bombs. To further put it into perspective, the amount of energy emitted in the final second of the black hole’s existence is over 40 times the total worldwide energy consumption in 2008. You will certainly want to be very far away during the final moments of the black hole’s existence as it disappears in an incredible burst of energy.

All the values which I have used in this article to describe black holes were calculated using a program which I have developed a few years ago. It is interesting to note that there is a possible natural source for micro black holes. A primordial black hole is a hypothetical type of black hole that is theorized to form out from the extreme densities present during the beginning of the Universe and these black holes are expected to be very low in mass. On way to detect such black holes is via their Hawking radiation, but none have been detected so far. A primordial black hole with a mass of 173 million metric tons will have a lifespan that is equal to the current age of the Universe and if such primordial black holes exist in sufficient numbers, their demise might be detectable as they emit an extraordinary burst of Hawking radiation in their final seconds. NASA’s Fermi Gamma-ray Space Telescope which was launched in 2008 might have the sensitivity necessary to detect the energetic demise of primordial black holes if they exist.

Cannonball Super-Earths

A super-Earth is an extrasolar planet with a mass between 1 to 10 times the mass of the Earth and our Solar System does not have any planets that are within this mass regime. A number of super-Earths have already been discovered around other stars. The four distinct types of materials that could make up a super-Earth with different proportions are iron alloys, silicates, volatiles/ices and hydrogen-helium gas. For a given mass, a less dense super-Earth will have a larger diameter while a denser super-Earth will have a smaller diameter. Thus, a pure hydrogen-helium gas planet will have the largest possible diameter while a pure iron planet with have the smallest possible diameter. However, the upper and lower limiting diameters for a super-Earth of a given mass are highly unlikely with regard to the physical processes involved in planet formation.

A paper by Robert A. Marcus, et al. (2010) entitled “Minimum Radii of Super-Earths: Constraints from Giant Impacts” examines the smallest possible diameter a super-Earth of a given mass can have. Therefore, volatiles/ices and hydrogen-helium gas are not considered and only rocky planets with an iron core and a silicate mantle are considered here. The only way to significantly increase the density of a planet requires the removal of the silicate mantle while preserving the iron core. An effective way to do that is by the stripping of the planet’s silicate mantle by giant impacts.

An example of mantle stripping via collision in our own Solar System is the planet Mercury. By mass, Mercury is 70 percent iron and 30 percent silicate, while the Earth is one-third iron and two-thirds silicates and other materials. Proportional to its mass, Mercury has a higher iron content than any other planet in the Solar System. It is currently theorized that Mercury was initially over twice its current mass with an iron core and a substantial silicate mantle. A large object, roughly one-third Mercury’s current mass, struck the planet and stripped away much of the planet’s original crust and silicate mantle, leaving behind the iron core together with a thin layer of the original crust and silicate mantle.

The conclusions derived from this paper show that the collision stripping of mantle material is an effective mechanism in producing a super-Earth with a higher mean density by increasing the iron mass fraction. It is easier for the collision stripping of mantle material for a lower mass super-Earth to produce a large iron mass fraction as compared to a higher mass super-Earth.

However, even with the most extreme impact conditions, the collision stripping of mantle material from a super-Earth is still unable to produce anything close to a pure iron planet. The maximum mass of a super-Earth with over 70 percent iron by mass is most probably 5 Earth masses since its formation via the stripping of its silicate mantle by a giant impact requires an initial object of 10 Earth masses. The maximum mass of a super-Earth is expected to be around 10 times the mass of the Earth since a more massive planet will probably undergo runaway growth via accretion of hydrogen-helium gas and become an even more massive gas giant planet.

NASA’s Kepler space telescope is expected to find a few hundred planets in the super-Earth mass regime and a sample of them will probably have masses too large for their observed diameters based on standard planet formation. The formation of such dense “cannonball” super-Earths can then be explained by the collision stripping of mantle material to produce a larger iron mass fraction.

Alien Earths

Earth-size and probably even Earth-like planets are expected to be common throughout the galaxy; orbiting stars not too different from our Sun. How will such Earth-like worlds differ from our own? A paper by Courtney D. Dressing, et al. (2010) entitled “Habitable Climates: The Influence of Eccentricity” examines how factors such as obliquity, spin rate, orbital eccentricity, orbital distance from host star and the fraction of surface covered by ocean might affect the habitability of Earth-like extrasolar planets. In this paper, regions of a planet that are at temperatures between 273 to 373 degrees Kelvin are considered habitable while regions outside that temperature range are considered uninhabitable.

Obliquity refers to the tilt of a planet’s axis, spin rate refers to the time required for a planet to complete one rotation about its axis, orbital eccentricity refers to how much a planet’s orbit around its star deviates from a perfect circle and orbital semimajor axis refers to the mean distance of a planet from its host star. An orbital eccentricity of zero denotes a perfect circle and an orbital eccentricity of one denotes a parabola. The Earth for example, has an obliquity of 23.4 degrees, a spin rate of 24 hours, an orbital eccentricity of 0.0167 and an orbital semimajor axis of 149.6 million kilometres. In addition, the surface of the Earth is 70 percent ocean and 30 percent land.

Of all the extrasolar planets with measured orbital eccentricities, a large fraction of them have significant orbital eccentricities and this suggests that Earth-like planets in near circular orbits, like ours, probably represent only a small subset of potentially habitable worlds. This paper basically studies the numerous possible types of Earth-like planets and many of the models of Earth-like planets presented are particularly interesting.

Take for example, a desert planet with an obliquity of 90 degrees, an orbital semimajor axis of 1.225 AU and an orbital eccentricity of 0.2. Winter at the southern hemisphere of this planet occurs when the planet is furthest from its star and during this long winter, the southern pole freezes and reaches an incredibly cold temperature of minus 120 degrees Centigrade. For this planet, the southern pole becomes transiently habitable only during northern winter when the planet is closest to its star. The southern pole of this planet experiences the most extreme temperature variations. During southern winter, the planet is furthest from its star and the southern pole experiences perpetual darkness. During southern summer, the planet is closest to its star and the southern pole experiences perpetual daylight.

This paper can be obtained at http://arxiv1.library.cornell.edu/abs/1002.4875 and it investigates the many types of possible Earth-like worlds that can exist. Notable examples described in this paper include:

- An Earth-like planet whose spin axis is tilted 90 degrees, such that the entire northern hemisphere can be in constant daylight while the entire southern hemisphere can be in constant darkness and vice versa, during specific points of the planet’s orbits around its host star.

- A planet where one day has a length of 8 hours or another where one day has a length of 72 hours.

- An Earth-like planet whose highly eccentric orbits around its host star brings it from a distance where most of its surface is scorching hot out to a distance where most of the planet’s surface plunges into a deep freeze.