Collapsing Schwarzschild 's Cat

 kw: article reactions, black holes, primordial black holes, musings

A recent article at Space.com is titled, "Are planet-killing black holes hiding inside your cat?" I suppose the meme behind the title is Schrödinger's dead/not dead cat. The author, Robert Lea, quotes researcher Dejan Stojkovic as saying,

"But don't worry about a primordial black hole shooting through your cat, or you, for that matter. The team behind these findings says such an event would be non-lethal!"

The article includes an illustration of several sizes of black holes, from supermassive (a billion suns) to sub-proton size, which is in the range of theorized primordial black holes. In particular, a black hole with the "mass of an asteroid" is stated to be smaller than a proton. I suppose that depends on the asteroid; the term "asteroid" covers material ranging in size from a sand grain to a few hundred km.

It is stated that primordial black holes, if they exist, would be zipping about at near-light speed (nobody ever says why), so one would pass through you, or your cat, or Earth, very quickly; about a nanosecond, on your case. I thought of two ways a tiny black hole can cause harm. Firstly, the intense gravitational field "nearby" (we'll try to define that soon) could disrupt tissue; and the Hawking radiation that, we have learned, will eventually result in any black hole "evaporating" by emitting radiation and thus losing mass, could cook (or evaporate!) tissue it passes through.

I would expect these two phenomena to be significant in different regimes, viz:

1. A really small black hole, weighing, say less than a million metric tons (tonnes), will have a smaller reach, gravitationally, but its Hawking radiation will be stronger. If you are "near" such an object long enough, you may not suffer damage from the gravity, but you could get cooked.
2. A larger black hole will have much less Hawking radiation, but its gravitation reach will be greater. If you are "near" such an object long enough, its gravity can do great damage, but its radiation could be beneath notice.

Calculation time! I made much use of Victor T. Toth's Hawking Radiation Calculator. Here are relevant parameters for three possible black holes, one the size of a proton, one 100 times larger, and one 100 times smaller (in radius). The proton's radius is about 0.84 fm (femtometers), or 0.84x10^-15 m; we'll call this Rp.

• Radius in Rp:              100   1.0     0.01
• Mass, Million Tonnes:   56,600   566     5.66
• Temperature, Billion K:   2.17   217   21,700
• Heat, Billion Watts:  0.000111  1.11   11,100

Note that these all are really, really hot! To get a feel for their masses: Iron has a density of 7.9 Tonne/cubic m. A cube of iron weighing 5.66 million Tonnes would be 89.5 meters on a side; for 566 Tonnes, the size is 415 m, and for 56,600 million Tonnes, the size is 1,930 m, or more than a mile. That's getting to substantial asteroid size.

To illustrate how small a proton is in relation to a typical atom, atom radii are in the range of a tenth of a nanometer, or 100,000 fm. A black hole with a radius or 100,000 fm (a little smaller than an iron atom, for example) has these parameters:

• Mass, Million Tonnes:   67 million → 67 trillion Tonnes
• Temperature, K:        1.8 million
• Heat, Watts:               0.079

Note that this "bigger" black hole may be super-hot, but its radiation is negligible. Let's first focus on Gravity. For reference, "1 G" is 9.8 Nt/kg (Newtons per kilogram) at the surface of the Earth. The proton-sized black hole, weighing 566 million Tonnes, would exert a force of 378 Nt on a mass of one gram (such as a BB) at a distance of 1 cm. That's 38,600 G. Gravity scales as the square of 1/r, so within 1 mm of the black hole, anything there (cells in your body as it passes through?) would experience a force of 3.86 million G. Here, duration is everything. If the black hole's velocity is, say a third of the speed of light (or roughly 0.1 m per nanosecond), the time it takes to move one millimeter is about 10 picoseconds. That means that a random cell that is 1 mm off the center of the black hole's path will "see" a spike in force that rapidly changes direction through a 180° arc in the space of about 0.1 nanosecond, reaching nearly four billion G's.

I don't know how to describe the effect on the cell. It is unlikely to survive. It probably doesn't have time to be sucked into the black hole, but a cell that is "brushed by" (say, 1/100th mm) most certainly will be. The result will be a thin "soda straw" hole through the body, much less than 1 mm in diameter, but I don't know how much less.

How about the mass with a size of 100 proton radii? At 1 cm distance, the force would be 3.86 million G's. It is very likely that such a mass passing through you (or your cat) will leave a hole a substantial fraction of a cm across. It is similar to being hit by a 30 caliber rifle bullet, just much, much faster. If either of these masses were moving a lot more slowly, such as an orbital speed in the range of 30 km/sec, rather than 100,000 km/sec (1/3 of light speed), the breadth of destroyed tissue would be dozens to hundreds of times greater, and the diameter of the "soda straw" …? It's hard to comprehend. So let's not bother checking the atom-sized black hole, weighing in at 67 trillion Tonnes! If any exist, they could explain rare cases of disappearance, perhaps.

How about temperature? The hottest black hole is the smallest, and has an incredibly tiny surface area to radiate heat, but radiates 10,000 times as much heat as the proton-sized one. It can do so for a quarter of a million years. Its radiation, mostly X- and gamma rays, amounts to 11 trillion watts. If any of these were anywhere within a few light-years, we'd see them. Let's back off to the 100 Rp radius black hole, which radiates (still in X-rays and higher) 111,000 watts. If it is traveling at 1/3 c, it passes through you in 3-4 ns, leaving behind about 4 milliJoules, or some 4,000 ergs. Spread that out along the length of the path through your body, and it isn't much heat.

Now consider the middle mass, the proton-sized one. It radiates 1.11 billion watts. In the time given, it deposits around 4 Joules, or close to one calorie. Again, not much heating. So there is little "cooking" expected from really fast-moving primordial black holes. However, if their speed is closer to orbital speeds, the "dwell time" is several thousand times greater, and 4 joules becomes more than 10,000 joules, equal to a kilowatt for ten seconds. That'll burn a hole through you! It's not quite as powerful as a lightning strike, but it's getting in that range.

I started out thinking I could debunk the idea that primordial black holes aren't much danger. In certain circumstances they aren't, that's true, but what grounds to we have to assume they are going fast enough to pass through you, or me, or the nearest cat, without swallowing up a hurtful amount of stuff, and cooking much of what isn't sucked in?

Whatever speed they are moving, the smaller ones ought to be visible as sky-blue items that emit lots of X- and gamma radiation. With current instrumentation, we'd be hard pressed to determine their actual temperature. "Millions of degrees" just begins to describe it. So, I've actually presented a challenge to the idea that primordial black holes weighing less than about a half billion Tonnes exist at all.

The Roach Motel for everything

kw: book reviews, nonfiction, physics, black holes, history of science

In 1905 Albert Einstein published four small monographs in scientific journals. Their subjects were

• The Photoelectric Effect, in which the color of the light, and thus its frequency, were directly related to the voltage of electrons emitted from a sensitive surface, and depending on the "activation potential" of various surfaces, there was a threshold below which no emission could occur. This proved that light is quantized as particles now called Photons.
• Brownian Motion, in which tiny, lightweight items such as pollen grains, suspended in water and viewed through a microscope, are seen to jiggle continuously. He showed that this is a statistical effect of jostling by molecules of water, the first empirical evidence for the existence of atoms and molecules.
• Special Relativity, in which he established that the speed of light and all effects of the interaction of light with spacetime are the same as measured in any non-accelerating reference frame, regardless of that frame's velocity with respect to any other. This implies that everything except light is variable when measured between reference frames moving at differing velocities, particularly mass, length, and the passage of time.
• Mass-Energy Equivalence, expressed in the formula E=Mc², in which he showed that Maxwell's laws imply that as energy is added to a system its mass increases. The parameter c is a large number, 300,000 km/s, and its square is thus so huge that simply heating a kg of iron, for example, between 0°C and the melting point of the iron, will only increase its mass by something like a few billionths of a billionth of a gram. But the equation as stated provides a hint, later well defined by the scientists of the Manhattan Project, that nuclear reactions which confer a reduction of mass yield enormous energy release.

Guess which of these discoveries led to Einstein receiving the Nobel Prize in 1922? It is the Photoelectric Effect, which laid a foundation for Quantum Physics, by effectively discovering the Photon, the first quantum particle to be so defined.

Ten years later, Einstein published articles on his General Theory of Relativity, usually just called General Relativity, which extended Special Relativity to accelerating motion and, in particular, to motions in a gravitational field. The set of equations at the core of the theory show that gravity is a consequence of curvature in spacetime caused by mass. As John Wheeler states it, "Mass tells Spacetime how to curve, and Curved Spacetime tells Mass how to move."

It wasn't long before scientists, striving to find exact solutions to the theory's equations, determined that the end point of gravitational collapse was a singularity. This had been hinted at by scientists as far back as 1783, when John Mitchell first calculated the mass needed for a Sol-sized star to prevent the escape of light, and thus be rendered invisible to a (safely) distant observer.

The events along the way between 1783 and 1915, and those since, form the structure of Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved by Marcia Bartusiak. The author's aim is not to discuss the physics of black holes to any great extent—though a certain amount is necessary—but to trace the history of the idea, from an idea that made classical physicists queasy to the modern understanding of the way black holes have shaped the universe. That "queasiness" led to general relativity being neglected for most of fifty years. Finally, improvements in astronomical instruments and methods forced recognition that such "supercollapsed" objects as black holes might indeed be real.

The first astronomical object to be generally accepted as a black hole is Cyg X-1, in the constellation Cygnus (the Swan), which weighs about 15 times as much as the Sun. It and a blue supergiant star orbit one another closely, with a period of 5.6 days. The supergiant sheds mass in irregular fashion, and some of the gas is drawn into an accretion disk circling the black hole, where frictional and compressional heating raise temperatures to millions of degrees and cause flashing and flickering at primarily X-ray wavelengths. Such a black hole is called a "stellar black hole" because it formed from the collapse of a single star.

A much larger event or series of events must underlie the formation of the very large black holes at the centers of galaxies. It is very likely that a "supermassive black hole" is at the core of every galaxy. The stars in our own galaxy, the Milky Way, orbit a black hole with a mass of about 4 million Suns, or about 270,000 times the mass of Cyg X-1. Larger galaxies, or galaxies with larger central bulges, and large elliptical galaxies which are all central bulge, have central black holes up to several billion Suns in mass.

Do these galactic black holes also shine or flash like Cyg X-1? Whenever they have a source of infalling matter, they do. Quasars are extremely bright and very tiny (compared to a galaxy) objects that are seen in light, radio, and X-rays caused by large amounts of matter in their accretion disks. "Active galactic nuclei" are dimmer than quasars, from our perspective, but are probably quasars when seen from a special perspective, because the emissions of black holes are directional.

Black holes all spin, and they all have magnetic fields. This is because they were formed from spinning matter (and accretion adds to their spin), and all plasmas in space are magnetic; the magnetic field is retained after collapse within the event horizon. Accreted matter, heated to a plasma, is spun by the spinning magnetic field and is compressed into a pair of jets which emit primarily along the spin axis of the black hole. A quasar is what we see when we are looking "down the barrel" of one of these jets. An active galactic nucleus is seen when we are off to the side. Cyg X-1 is apparently also pointed right at us.

When we read of a quasar that has an apparent brightness of trillions of stars, we must remember that the "trillions" figure is calculated by assuming equal brightness in all directions. The actual beam is a degree or two across, and a sphere has an angular area of more than 41,000 square degrees. So the "trillions" become "billions" or "hundreds of millions", nearly all concentrated into those two beams and so amplified from our viewpoint. That is still really, really bright!

The first quasar had a spectrum too weird to fathom, at first, until it was finally realized that the spectral lines were those of hydrogen, shifted far toward the red end, implying a cosmological distance of about 2 billion light-years. The distance to a quasar is actually rather tricky to calculate, because of three effects (this is just me now; the second and third factors are not mentioned in the book):

1. The cosmological red shift caused by the expansion of space.
2. The gravitational red shift caused by the tremendous gravitational potential close to the event horizon (where the gravitational red shift would be infinite!). This increases the total red shift and by itself will cause us to over-estimate the distance to the quasar.
3. A blue shift caused by the relativistic velocity of the superheated matter beam, which might be as much as 0.2c to 0.5c pointed toward us, and perhaps even more. This counteracts some of the red shift from expansion and gravity.

Of these three factors, it is generally considered that the first is the greatest, but I have not read a definitive analysis of the second and third factors for any particular quasar…and I've been looking.

The book is fascinating and enjoyable. A timeline in an appendix helps tie events together, and traces the contributions of many scientists to the understanding of general relativity and gravitational collapse and its implications. A well-researched and well-written book, it rounds out the scientific story into a fascinating human story.

Governors of universal evolution

kw: book reviews, nonfiction, cosmology, astronomy, black holes, kerr black holes

Chandra X-ray Observatory image of Centaurus A and its X-ray jet. Centaurus A, at a distance of 11 million light years, is the nearest powerful active galaxy. Credit: NASA/CXC/CfA/R. Kraft et al. The more visible jet is more than a million light years in extent, but only about half of it is clear in this x-ray image. The "bubble" on the opposite side is quite a bit larger than the galaxy as seen in visible light.

This image is much better than any amount of words to describe the subject of Gravity's Engines: How Bubble-Blowing Black Holes Rule Galaxies, Stars and Life in the Cosmos by Caleb Scharf. In a synthesis of discoveries about the formation and growth of black holes, a subject of continued and avid study, the author shows how some of the physically smallest objects in the universe govern the development of stars and galaxies on the largest scales.

Black holes are indeed small. The Event Horizon radius is a simple function of mass: r = 2.95km/Ms, where Ms refers to solar masses. Physicists like to use radius. The rest of everybody thinks in diameter. So I'll primarily use diameter when writing of an object's size. If the Sun were squeezed into a black hole, its diameter would be 5.9 km, which is about 3.7 miles. That is the size of a small city.

Black holes come in two ranges of size, so far as we know. Stellar-mass black holes range from about 2 to 20 or so (probably not exceeding 100) solar masses. Their diameters thus range from 12 to 120 km, to perhaps 300 km. Galactic black holes are much, much heavier and larger. Those so far known range from about 1 million to 20 billion solar masses. The diameter of their event horizon is thus anywhere from 6 million km to 120 billion km. An average one, if that makes any sense, would be about the size of the Solar System, but weigh a billion times what the Sun does. On the scale of a galaxy, that is tiny!

It is not known how mass is distributed inside the event horizon of a black hole, but in a non-rotating black hole, it may indeed all be concentrated at the center, in a "singularity" of zero size. Physics really cannot describe it.

I have used the term "event horizon" a few times already. Its radius is also called the Schwarzchild Radius, the point from which the escape velocity is equal to the speed of light. Let's think about that. An object falling from far away toward a black hole would approach the speed of light as it approached the event horizon. As it crossed the event horizon, would its velocity really exceed the speed of light? I have read descriptions that state that space itself gets dragged in, so that the object falling is exceeding the speed of light relative to "outside", but not relative to the infalling space. Such descriptions imply that space is a kind of something, which makes no sense. Whatever is really happening near and within an event horizon, we cannot describe it with any known science.

Two paragraphs earlier I mentioned a non-rotating black hole. Actually, no such thing exists. Every object we have observed, from moons and planets and galaxies and clusters of galaxies, is rotating. A huge rotating star that collapses into a black hole when its fusion fuel runs out will keep rotating, and its RPM's will increase dramatically. Dr. Scharf writes that black holes probably start out rotating near their maximum rate, at which any matter just inside the event horizon will have a speed just below that of light. For stellar black holes, that can be a million times per second, while for galactic black holes, the rotation rate is in the range of one RPM.

Deep in the center of a rotating black hole, there is not a point singularity. Instead, there is a ring. Whether it is a torus or a ring of infinite thinness is not known, but this gets us away from having all matter fall to a dimensionless point. In fact, if rotational energy is extracted from a black hole, and its RPM's decrease, the ring shrinks, but the slower it goes, the harder it is to get more energy out, so I suspect there is no such thing as a truly non-rotating black hole. Kind of like a Heisenberg Uncertainty Principle for angular momentum! (The HUP explains why temperatures of absolute zero are unattainable. This is similar.)

There is one other characteristic of a rotating black hole. There are two horizons. The inner one is spherical, just like a non-rotating event horizon. The outer one is an ellipsoid, shaped like a doorknob, and when rotation speed is the maximum possible, its outer radius is twice the radius of the inner sphere. The ellipsoid is tangent to the sphere at the rotational poles. Between these two horizons, space and time get mixed up, and matter that falls in off-center can pass through this Ergosphere and back out again, with more energy than it had going in. This is how energy is extracted from a rotating black hole. I have yet to read an explanation of these two horizons in which their size was clearly explained, but I think I understood that the outer edge of the ellipsoid is at the Schwarzchild Radius, and the polar radius is smaller. At maximum RPM, the inner sphere has half the size of the event horizon of a non-rotating black hole. I think...someone correct me if I got it backwards!

The first half or more of the book explains all this in an engaging way. It is all leading up to the explanation of the jets and bubbles seen in the image above, which requires one more parameter: magnetism. Whichever size of black hole we are talking about, the matter than came together to form it had a magnetic field. All known planets and stars and galaxies have a magnetic field. It is part of the territory, so to speak, when you have rotating mass. You may have read that Mars has no magnetic field. It's field is weaker than Earth's, by a factor of a hundred or so, but it is definitely not zero. So when a black hole is formed, the magnetic field doesn't vanish. Its total extent remains the same, but in the vicinity of the horizon, its intensity grows dramatically. A rotating magnetic field sets things up for an enormous dynamo.

I don't  pretend to know the physics of it, and even this author glides right by it, but when the spinning magnetic field gets spun up enough, it twists into a "tail" at each rotational pole. Any matter in the vicinity of the black hole will either orbit it, or fall inward. Most of this is likely to be gas and thin dust. The dynamics of this orbiting stuff and the "frame dragging" of the black hole's rotation (a mysterious effect of general relativity) will force most of it into a disk in the plane of the hole's equator. Friction within this disk will heat it to a few thousand degrees. As the innermost material gets inside the ergosphere, it gets sped up a lot, and some of it gets caught up in the twisted magnetic field and squirted out into the jet within the magnetic tail. Here, it can approach the speed of light, and temperatures of millions of degrees. This jet crashes through any gas and dust it finds surrounding the area, and blows a bubble in it. These big bubbles interfere with star formation, and also reduce the rate that stuff can reach the black hole.

What does that have to do with stellar or galactic evolution? Just about everything! A distant object that Dr. Scharf and his colleagues studied, called 4C41.17, showed that galactic black holes formed very early. Their jets and bubbles slowed down the formation of stars and guided the development of the earliest galaxies. Distant, and thus early, galaxies are seen to have active nuclei, and the ones for which we are looking down the throat of the jet we call quasars. The bottom line is that the activity of these huge black holes, tiny as they are compared to their host galaxies, regulates the rate of star formation. Without them, most of the Universe might have burned out by now, leaving just quintillions of dim red dwarfs to sputter away for the next few trillion years.

Now I'm going to leave the author a few things to say. This all is just what interested me most. There is just one thing left I wonder about. So-called dark matter is posited to react only to gravity. It seems to make up between 80% and 90% of the mass of the universe. Isn't it also being pulled into black holes of all sizes? Does it contribute to their mass and perhaps other properties?

Beyond this horizon, everything sets

kw: book reviews, nonfiction, cosmology, black holes

The book took me a long time to finish, and left me puzzled. What, and how, am I to think about these things? Beneath the notice of most of us, an intellectual war has been raging among a small number of physicists, a generally respectful war, carried out with great civility, but concerning the fundamentals of physics and the reality of our Universe.

Of course, scientists cannot be silent about things that deeply move them, so many publications have ensued, but mostly in journals read only by other physicists. A rare popular press article has appeared, say in Scientific American or Popular Science, about universal holograms, or information loss, or variously named "strings", or accelerating cosmological expansion.

As it turns out, the four items mentioned just above are all related, at least to Leonard Susskind and a number of contemporary physicists. In his new book, The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics, Dr. Susskind explains the central role of black holes in the controversy, and how they tie together all the important physics concepts of the late 20^th and early 21^st Centuries.

I won't go into any detail here, because I can't. Not only is the book large, more than 400 pages, but the author has already simplified his arguments a great deal in order to reach a nonmathematical public.

I do just have to express my puzzlement over his discussion that, to an outside observer, an object gets heated as it falls to the event horizon of a black hole, even if it is the only thing in the vicinity. Of course, the now-familiar accretion disk heats incoming stuff by friction. But the observed heating is based on the observation itself:

• The gravitational redshift approaches infinity for "light" that reaches us from an object that is approaching the event horizon.
• Let us remember, the event horizon is the point at which gravity stops light entirely. Any electromagnetic energy that originates or reflects from something at or below the event horizon can only proceed inward.
• Time dilation also approaches infinity in the same manner.
• For us to see it, the falling object we are watching must be emitting or reflecting radiation that began as much shorter wavelengths than what we detect. Eventually, our "camera" might record an image using visible photons that began their journey to us as gamma rays.
• These very high-energy photons (gamma rays) imply very high temperature. So the object we are observing must be very hot.

I looked and looked, but never found out what exactly is heating up the object in question, just this circular argument about high-energy photons. Thus, at the moment I counter-contend that for a freely falling object, the only source of heating is tidal friction. Start with a big enough black hole (galactic mass or so), and the tides and heating are minimal. However, suppose the object is not freely falling. Suppose it is a thermometer on a long (and very strong) rope!

Such a thermometer would be heated all right, by the photons hitting it as they freely fall into the black hole. Depending on how close to the event horizon you can get it, the thermometer could be flooded by gamma ray photons that began life as infrared or visible photons, or even the microwave background radiation. But to a freely falling object, the photons seem to have the same energy they had when both they and the object were far from the black hole.

Although I am a science junkie, there is a limit to my understanding. The point of the book is, to me, that science is a very human endeavor. It would be no fun at all were it carried out only by emotionless robots. I am not sure such robots could do science, however, because they'd at least need motivation, and the motivation, "My programmer built in a requirement to 'do science'," is cold comfort indeed.

No, scientists are human, albeit in a few cases, humans who have learned to disagree without being too disagreeable. They hold their views with the same passion that St. Francis and Billy Sunday held theirs, and evangelize with identical fervor.

As a result of the black hole war, new mathematical tools were developed to help "rewire" the brains of a few physicists so they can understand a new paradigm. Boy, I thought particle physics was confusing. Now these guys are operating in realms where the a proton is as big and empty as a galaxy (which is 99.9999% space between stars), compared to a thing called the Planck Mass.

By the way, there is a lot of hope for the LHC (Large Hadron Collider), which will get working again once it is repaired after last year's broken magnet. People fear it will produce tiny black holes that might grow larger and swallow stuff up. Those black holes are the point, and they won't grow. Any black hole that weighs less than a kilogram will evaporate, due to Hawking radiation, in less than 10^-22 seconds. It'll make bang somewhat smaller than the bang that created it, but in that slice of a second it ought to produce a ton of data for the scientists to mull over. It just might provide experimental confirmation of some of the things Dr. Susskind has written about.

Cooking with black holes

kw: musings, black holes

A book I am about halfway through discusses black holes, and a lot of it has to do with Hawking radiation and the implications of that. See the link just above for a detailed treatment in Wikipedia. A briefer explanation is thus:

• Richard Feynmen's work on quantum electrodynamics showed that virtual particles are continually created and destroyed, in complementary pairs, everywhere and always. They provide the properties we associate with "the vacuum."
• Stephen Hawking showed that when a pair of virtual particles gets created just next to the event horizon of a black hole, during the tiny fraction of a second that the particles are physically separated, one may pass through the event horizon.
• The extreme "strain" on space-time caused by the proximity of the black hole reifies the particles, such that one is captured by the black hole and the other escapes, becoming a particle that is seemingly emitted spontaneously by the black hole's event horizon.

This means that a black hole is a black body, in the physics sense, with a temperature and a perfect black-body thermal spectrum. However, for the black holes we expect to find astronomically, this temperature is very low, and the particles emitted have very low energies. How low? The Wikipedia article I linked above has the equations to figure it out. I made a table to help wrap my mind around the concepts. First, the temperature is extremely low for stellar-mass and larger black holes, but can get rather higher for lighter ones. The table will include a 1kg mass to illustrate how high. I also use "E" notation for large and small numbers: 2e14 means 2•10¹⁴.

(I apologize in advance for Blogger's tendency to put too much white space before a table.)
Table: Black Hole Sizes and Radiation Characteristics

Object	Mass, kg	Temp, K	Radius, m	Power, W
Solar mass	2E30	7E-9	2,980	1.5E-32
Earth mass	6E24	0.0024	0.009 (9mm)	1.9E-21
Moon mass	7.4E22	0.19	1.1E-4 (0.11mm)	1.1E-17
Asteroid	1E14	1.4E8	1.5E-13	6.1
1 km3 H2O	1E12	1.4E10	1.5E-15	61,000
1 kg	1	1.4E22	1.5E-22	6.1E38

We expect black holes produced by natural processes to be the mass of the Sun or heavier. The top row of the table shows that the temperature and thermal output of such an object are too low to measure, particularly when the background temperature of the universe is, at present, about 3K. Even the temperature of a Lunar-mass black hole is in a realm that is difficult to measure, less than 1/5 of a Kelvin (Note, a Kelvin is what a degree of Centigrade size is called when the zero point is absolute zero, called zero Kelvins or 0K).

Should any black holes lighter than the Moon exist, the temperature is higher, and can get very high indeed, as seen by the last three rows of the table. I picked a mass for the asteroid to be about the size of the one that clobbered the Dinosaurs. What does a temperature of 1.4E8 degrees mean? 140 million degrees! Such an object, the mass of a mountain, the size of a proton, radiating 6 watts of mainly gamma rays and x-rays, would be a truly dangerous item. (The x-ray machine used to take a chest x-ray emits about a tenth of a watt of x-rays, but only about a tenth of that passes through your chest. A dental x-ray machine is considerably lower power than that. Six watts of such radiation is a lot!)

Comparing the data in these three rows, the regularities are clear. Temperature is exactly proportional to 1/Mass; radius is proportional to Mass; and total energy output is proportional to the square of 1/Mass.

Back to the radiation emission: A 1-kg black hole radiates so furiously, at a temperature of 14 billion trillion degrees, that all its mass would be emitted in less than 1E-21 second. Black holes in the range of a few kilograms and smaller are simply energy bombs! A 3-megaton thermonuclear weapon converts a gram of mass to energy in a microsecond or so. Imagine the conversion of a number of kilograms in less than a nanosecond.

What is my conclusion? Firstly, as to my title: a black hole that emits sufficient thermal energy to "cook" with, does so with penetrating radiation that would cut right through any lead shielding. Plus, your "stove" would tend to swallow up the food if it is put close enough to be heated!

Secondly, no black holes are currently evaporating, because thermal energy is entering them from the universe at a rate much greater than they emit their own. If the universe really does get stretched out by accelerating cosmic expansion until any large (stellar or galactic) black holes that now exist can begin to evaporate, not much will seem to happen for times so long they are hard to imagine: 10⁶⁰ to 10¹⁰⁰ years. But once a large black hole slowly evaporates down to a few million tons, things go rather faster, and the last ton will "evaporate" explosively. It would be a fatal mistake to be within a light-year or less of such an explosion!