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. 

Dissipating Planet

A paper by Shu-lin Li, et al. (2010) entitled “WASP-12b as a Prolate, Inflated and Disrupting Planet from Tidal Dissipation” describes some peculiar properties of an extrasolar planet. WASP-12b is an extrasolar gas giant planet that has 1.4 times the mass of Jupiter and it is located so remarkably close to its parent star that it takes only a little over an Earth day to orbit the star. In fact, WASP-12b orbits its parent star at a distance of just 2 stellar radii from the star’s surface and the planet is distorted by the star’s gravity into a prolate shape, similar to that of a rugby ball.

The nonzero orbital eccentricity of WASP-12b makes it very susceptible to the strong tidal effects from its parent star which heats the planet’s interior and causes the planet to expand. WASP-12b has an orbital eccentricity of about 0.05 and this is odd because orbital circularization should have already circularized its orbit into a zero eccentricity orbit. Another planet with a mass of a few Earths is probably responsible for perturbing WASP-12b to maintain its nonzero orbital eccentricity. WASP-12b is extremely “bloated” and it has a diameter that is 80 percent larger than Jupiter’s. The atmospheric temperature of WASP-12b is estimated to be a scorching 2500 degrees Kelvin.

WASP-12b has ballooned so much that its own gravity is unable to retain its mass from the gravitational pull of its parent star. Gas from WASP-12b is flowing towards the parent star through a nozzle that is located at the L1 Lagrangian point, a region that is situated between the planet and the star. WASP-12b is losing mass to its host star at a rate of a few billion metric tons each second. The material that is pulled off from WASP-12b forms an accretion disk around the parent star and gradually spiral inwards into the star.

Intergalactic Space

The Local Group contains dozens of galaxies contained within a volume about 10 million light years across and its two largest galaxies are the Andromeda galaxy and the Milky Way galaxy. Both galaxies account for over 80 percent of the visible light of the Local Group. The third most prominent galaxy in the Local Group is the Triangulum galaxy and it has approximately one-fifth the luminosity of the Milky Way Galaxy. The rest of the galaxies in the Local Group are irregular galaxies, dwarf irregular galaxies, dwarf elliptical galaxies and dwarf spherical galaxies. Many of these smaller galaxies are either in orbit around the Andromeda galaxy or the Milky Way galaxy. Within the Local Group, many more tiny galaxies are still probably waiting to be discovered.

The mutual gravitational attraction from matter within the Local Group dominates over the expansion of the universe. The galaxies in the Local Group range in size from the Andromeda and Milky Way galaxies which contain hundreds of billions of stars each to tiny galaxies which hold fewer than a million stars. The Andromeda galaxy and the Milky Way galaxy are separated by a distance of 2.5 million light years and they are approaching each other at a rate which will most probably result in a merger over the next few billion years. Such a merger will lead to the formation of a giant elliptical galaxy. It is very unlikely that stars will collide when both galaxies merge as stars in galaxies are typically spaced extremely far apart from each other.

Located 700 million light years away, in the vicinity of the constellation Boötes as seen from the Earth is one of the largest known voids in the Universe and it is called the Great Void or Boötes Void. This region of empty space is estimated to be 400 million light years across. For comparison, the luminous disk of the Milky Way galaxy is 100000 light years across and you will need 4000 Milky Way galaxies placed end to end to cover the span of the Boötes Void. Within this incredibly vast void, several galaxies have been detected to extend in a rough tube-shape through the middle of the void. Astronomer Greg Aldering once mentioned: “If the Milky Way had been in the center of the Boötes void, we wouldn’t have known there were other galaxies until the 1960s.”

Evolved Binaries

NASA’s Kepler space telescope was launched on 6 March 2009 with the primary objective of detecting Earth-like planets orbiting other stars. Amongst Kepler’s first major discoveries are two small objects which are hotter than the stars they orbit and both objects are likely to be very low mass white dwarfs. KOI-81b is estimated to be 40 percent as luminous as the Sun with a surface temperature of 13000 degrees Kelvin while KOI-74b is estimated to be 3 percent as luminous as the Sun with a surface temperature of 12000 degrees Kelvin. These objects are definitely not planets as they have surface temperatures an order of magnitude higher than would be consistent with stellar heating alone.

A paper by Rosanne Di Stefano (2010) entitled “Transits and Lensing by Compact Objects in the Kepler Field: Disrupted Stars Orbiting Blue Stragglers” describes the prospects of Kepler in discovering a large number of such objects as described above. These hot compact objects are most likely the cores of stars that have evolved to their present state through a process of stable mass transfer with their current stellar companions. Kepler offers a unique opportunity to study a large sample of such white dwarfs and the role of mass transfer in the evolution of binary star systems.

Clouds and Extrasolar Planets

A paper by Daniel Kitzmann, et al. (2010) entitled “Clouds in the Atmospheres of Extrasolar Planets. I. Climatic Effects of Multi-layered Clouds for Earth-like Planets and Implications for Habitable Zones” studies the impact of clouds on the surface temperatures of Earth-like planets orbiting different types of stars. Clouds play a vital role in determining the climatic conditions of planetary atmospheres by reflecting incident stellar radiation back into space via the albedo effect and by trapping infrared radiation in the atmosphere via the greenhouse effect. For the Earth, low-level clouds cause cooling via the albedo effect and high-level clouds cause heating via the greenhouse effect. For mid-level clouds, the albedo effect and greenhouse effect generally balance each other.

In this paper, studies were done for Earth-like planets orbiting F, G, K and M-type stars. Note that our Sun is a G-type star and for this range of stellar types, F-type stars are the hottest while M-type stars are the coolest. With respect to a clear sky model, a planet with a higher percentage of high-level clouds will have a higher surface temperature while a planet with a higher percentage of low-level clouds will have a lower surface temperature. This characteristic applies to all Earth-like planets orbiting F, G, K and M-type stars.

For the Earth, the presence of clouds creates a net cooling effect with respect to the clear sky model and the mean value of the Earth’s surface temperature is 288.4 degrees Kelvin. Using just low-level clouds for maximum cooling effect, planets can be located up to 15 percent closer to their parent star compared to a clear sky planet to achieve the same average Earth’s surface temperature of 288.4 degrees Kelvin. On the contrary, using just high-level clouds for maximum heating effect, planets can be located up to 35 percent further from their parent star compared to a clear sky planet to achieve the average Earth’s surface temperature.

Dark Stars

The first stars that form in the early universe can be powered by dark matter instead of conventional nuclear fusion and these stars are conveniently termed dark stars. These hypothesized dark stars still remain to be discovered and future telescopes such as the James Webb Space Telescope (JWST) may have the sensitivities required to detect such stars. The term ‘dark’ does not mean that these stars appear dark, but rather it means that the energy from the annihilation of dark matter particles is the primary mechanism keeping these stars shining in hydrostatic equilibrium. A paper by Katherine Freese, et al. (2010) entitled “Supermassive Dark Stars - Detectable in JWST” basically describes such stars and their possible detection by the JWST.

Weakly Interacting Massive Particles (WIMPs), an excellent candidate for dark matter, may be their own antiparticles and this allows them to annihilate among themselves. Wherever the density is sufficiently high, the annihilations of WIMPs can generate enough energy to power such dark stars for millions to billions of years. The WIMP annihilation products thermalize within the star which provides the power required to keep the star shining and prevents the star from gravitationally collapsing. Dark stars are composed primarily of hydrogen and helium, with only a fraction of a percent of their mass in the form of dark matter. Due to the high efficiency of energy production via the annihilation of WIMPs, a small proportion of it is sufficient to sustain the star against its own gravity over astronomical timescales.

The much cooler surface temperatures of dark stars is the primary reason which allows darks stars to grow to become so much more massive than ordinary fusion-powered stars, as long as the annihilation of dark matter persists. Ordinary fusion powered stars produce ionizing photons that provide a variety of feedback mechanisms that cut off further accretion of baryonic matter. On the other hand, dark stars with their cooler surface temperatures allow the continued accretion of baryonic matter all the way up to colossal stellar masses. Dark stars can grow up to millions of times the mass of the Sun and exceed billions of times the luminosity of the Sun. Such massive stars can lead to the formation of supermassive black holes when they run out of dark matter fuel to sustain them. When the production of energy from dark matter annihilation dwindles, it causes the star to contract, heat up and undergo a brief phase as a fusion powered star before collapsing into a massive black hole.

Runaway Star

A hypervelocity star is a type of star which travels at a sufficiently high velocity with respect to its host galaxy’s rest frame that its velocity exceeds the galaxy’s local escape velocity. This places the star on a trajectory which removes it from its host galaxy. Gravitational interactions and supernova explosions in binary systems are two possible mechanisms that can produce hypervelocity stars. A paper by Andreas Irrgang, et al. (2010) entitled “The Nature of the Hyper-Runaway Candidate HIP 60350” explains the nature of one such hypervelocity star.

Kinematical observations of HIP 60350 show that it has a velocity which exceeds the local escape velocity of the Milky Way galaxy. This places HIP 60350 on a trajectory that will remove it from the Milky Way galaxy. Tracing its origin back to the plane of the Milky Way galaxy, the estimated travel time of HIP 60350 is about 14 million years. Given an estimated age of 45 million years for the star, a shorter travel time is consistent with the runaway nature of the star. So far, neither gravitational interaction nor a supernova explosion in a binary system can be strictly confirmed or rejected for HIP 60350.

In addition, a neutron star formed from an asymmetric supernova explosion can have sufficient ‘kick’ imparted to it for it to become a hypervelocity star. One such neutron star is RX J0822-4300 and it is measured to travel at a remarkable speed of over 1300 kilometres per second.