5 Things You Know Wrong About Black Holes!

Popular science books and physics education articles on black holes usually focus on analyzing the properties of these objects, but pay little or no attention to the misconceptions associated with them. Analyzing these misconceptions is particularly important nowadays, given the great interest that black holes arouse among non-specialists, which was recently heightened by the first image of a black hole spread all over the world by the mass media. This is especially true for physics teachers, both at school and university level, who, among other challenges, have the responsibility to correct their students' scientific misconceptions.

In our opinion, the most common misconceptions about black holes are the following:

1. Black holes are formed when stars collapse;

2. Black holes are very large;

3. Black holes are very dense;

4. The gravity of black holes absorbs everything;

5. Black holes are black.

This last misconception is perhaps the most surprising, because it contradicts the definition of a black hole. The aim of this paper is to analyze and correct these misconceptions. Given the educational purpose of this article, we will adopt an intuitive approach based on an introduction to physics.

Theoretically, there are three classical external observables that define a black hole: mass, electrical charge and angular momentum. The simplest black hole, then, is the black hole that has no spin and is electrically neutral. This object is a static black hole, also called a Schwarzschild black hole, and its mathematical description depends only on its mass. We will focus here on the simplest black hole, known as a static black hole. These simplifications will not affect the validity of the results and will allow us to avoid the complex concepts of Einstein's general theory of relativity, which is the appropriate framework for a technical analysis.

Myth-1: Black Holes are formed when stars collapse!

The concept of a black hole was born within the framework of general relativity, the theory of gravity proposed by Einstein in 1916 to extend and perfect Newton's law of universal gravitation. A black hole is a region of space-time bounded by a closed surface called the "event horizon", where the mass-energy density is so high that nothing, including light, can escape its gravitational pull. In the framework of Newtonian gravity, the horizon can be intuitively visualized as a spherical surface with a radius:

For historical reasons it is called the Schwarzschild radius; Here G=6,67x 10⁻¹¹ N · m² · kg⁻² gravitational constant, c=3x10⁸ m · s⁻¹ the speed of light in vacuum and MBH for the value of RS says it has value. This means that in principle there are no restrictions on the mass a black hole can have.

So, while it is certainly true that a black hole can form from a star, theoretically a black hole can also form from a planet, an asteroid or a grain of sand. As long as the raw material for the formation process is eventually trapped in the relevant horizon. However, only at the beginning of the Universe (when the average mass-energy density was very high) were there favorable conditions for the formation of black holes from relatively small concentrations of matter, such as those equivalent to an asteroid or a grain of sand.

Under the conditions currently prevailing in the Universe, a black hole needs at least as much mass as a star to form. But a star cannot spontaneously form a black hole because its high internal temperature prevents it. In essence, what happens is that the compressive force of gravity is balanced by the expanding thermal pressure produced by the thermonuclear reactions occurring in the center of the star. However, if the star is massive enough, the gravity exerted on it is so strong that when the nuclear fuel is exhausted and the thermal pressure drops, a gravitational collapse occurs that no force in nature can stop, resulting in the formation of a stellar-mass black hole.

The minimum mass required for an object not subject to nuclear re-motion for gravity to impose itself on all other forces is estimated to be ~3M⨀, where M⨀=1.99x10³⁰ kg is the mass of the Sun. This number is known as the Tolman-Openheimer-Volkoff limit (TOV) in honor of the physicists who first calculated it. Thus, an object that does not undergo a nuclear reaction and has a mass exceeding ~3M⨀ can gravitationally collapse into a black hole. (More precisely, the TOV limit is an upper limit on the mass of stars composed mainly of degenerate neutrons (neutron stars). This limit is subject to uncertainty because the equation of state for hadronic matter subjected to high densities is still not well known.)This number is known as the Tolman-Openheimer-Volkoff limit (TOV) in honor of the physicists who first calculated it. Thus, an object that does not undergo a nuclear reaction and has a mass exceeding 3 can gravitationally collapse into a black hole. (More precisely, the TOV limit is an upper limit on the mass of stars composed mainly of degenerate neutrons (neutron stars). This limit is subject to uncertainty because the equation of state for hadronic matter subjected to high densities is still not well known.)

Table 1 shows the Schwarzschild radius and other quantities expressed in powers of 10 for different objects. The same procedure is used in the tables in the following sections.

Myth-2: Black Holes are Very Big!

Table 1 reveals that black holes can have a wide range of masses and therefore do not necessarily have to be massive. As mentioned in the previous section, what characterizes a black hole, whether small or large, is that its mass is confined within a horizon. Technically, a black hole can be said to be a compact object, a property different from density, which we will analyze in the next section. Compactness depends on the quotient of mass and radius, not on the mass taken alone. Specifically, the compactness of a spherical object with mass M can be defined as the quotient of its Schwarzschild radius RS and its true radius R:

The closer this quotient is to 1, the more compact the object is. If we take RS as the measure of the size of a black hole, the expression 2GM/c²R=1 will be true for these objects. This means that black holes are the most compact objects in the universe, and it is intuitively obvious that all other objects must satisfy this relationship:

This result is known as the Buchdahl inequality. More precisely, Buchdahl's inequality states that under certain technical conditions, a sphere of static fluid of mass M and radius R satisfies the relation 2GM/c²R<8/9. This inequality is rigorously derived from general relativity. Table 2 shows the compactness (expressed as a ratio of RS/R) of different objects:

Myth-3: Black Holes are Very Dense!

Contrary to what common sense suggests, the density of a black hole is not necessarily high, and under certain conditions it can be quite low. Since the only size we can assign to a black hole is determined by its Schwarzschild radius, we can define its density (ρΒΗ) as the ratio between its mass and the volume of a sphere of radius RS:

We can interpret this quantity as the "average density", because when an object is compressed beyond the Schwarzschild radius, this compression continues without anything stopping it, meaning that the density at the center of the horizon increases without limit. If we add our initial equation to this last equation:

Table 3 shows the ρΒΗ values for the different types of black holes, including mass ranges in kg and units of M⨀ solar masses for each. In addition to the stellar-mass black hole and supermassive black hole, two hypothetical objects are also shown, the only types for which there is solid observational evidence: the intermediate-mass black hole and the micro-black hole.

Both of these two types of black holes are hypothetical, but their astronomical status is different. Although there is no evidence for micro-black holes, signs of the existence of intermediate-mass black holes have emerged in recent years. The most recent of these comes from observations made with the ALMA telescope in Chile, where there is evidence of a very compact object with a mass of 10⁴ M⨀ in the constellation Sirius. Theoretically, micro-black holes could have formed shortly after the big bang, simply because the mass-energy density was extremely high at that time.

As a basis for comparison, recall that the density of fresh water on the Earth's surface is 10³kg · m⁻³. As indicated by our last equation and Table 3, the average density of the largest observed supermassive black holes could be less than the density of fresh water on the Earth's surface.

Myth-4: The Gravity of a Black Hole Absorbs Everything Like a Vacuum Cleaner!

The gravity outside a spherical star of mass M is the same as the gravity produced by a black hole of the same mass. But we know that stars don't "suck up everything around them like a vacuum cleaner", and so this is also true for black holes. In fact, planets orbit stars in stable orbits for billions of years, which means that if the Sun were replaced by a black hole with a mass of M⨀, we wouldn't notice anything abnormal, except of course that we would lose light. In other words, the Earth would continue to maintain a stable orbit around this new black hole. In addition, there would be no change in the Earth's distance from the Sun other than that predicted by the effects of general relativity and Newtonian gravitation.

But this scenario changes dramatically when an object is very close to a black hole. In general relativity, the innermost stable circular orbit (ISCO) is the smallest orbit in which a test particle can stably orbit a black hole (see Table 4). In the case of a Schwarzschild black hole, the ISCO radius is calculated as follows:

This radius is extremely small compared to the typical size of a star. For example, if we take MBH=M⨀, we get RISCO~10³m, which represents only one hundred thousandth of the average solar radius, R⨀~10⁸m.

Below RISCO, a particle cannot maintain a stable orbit and is doomed to fall into a black hole and be "absorbed" by it. This phenomenon has no counterpart in Newtonian physics, where there is always a stable orbit. In Einstein's physics, this instability can be explained by recalling that a particle whose orbit is close to the horizon will have a relativistic velocity (close to ⅽ) that leads to a large increase in its kinetic energy; based on the equivalence between mass and energy, this implies an increase in the mass of the particle that makes the gravitational attraction more intense and causes the particle to be eventually absorbed.

Myth-5: Black Holes are "Black"!

When analyzing the misconceptions in the previous chapters, we only used ideas from General Relativity and Newtonian gravity. However, the analysis of the last misconception requires the inclusion of quantum theory. The first physicist to present a detailed description of black holes that combined general relativity and quantum theory was Stephen Hawking, in his famous work published in 1974 and expanded in 1975. More precisely, Hawking used quantum field theory, a mathematical scheme that describes elementary particles and their interactions (except gravity) and combines special relativity and ordinary quantum mechanics.

Hawking's revolutionary discovery is that an isolated black hole has a temperature and emits thermal radiation from the horizon in all directions. In Hawking's words:

The fact that the black hole is isolated is important because it means that the emission of radiation does not depend on mechanisms related to the absorption of material located outside the horizon, as in the accretion disk.

Hawking showed that the thermal radiation emitted from the horizon of a black hole of mass MBH, known as Hawking radiation, has a blackbody spectrum with absolute temperature given by the formula:

This is called the Hawking temperature. The presence of the characteristic constants of general relativity (ⅽ and G), quantum mechanics (ℏ) and thermodynamics (k) in this equation shows that this equation was obtained by combining these three theories. Here ℏ=h/2π =1.05x10³⁴ J · s is the reduced Planck constant and k=1.38x10⁻²³ J · K⁻¹ is the Boltzmann constant. According to Hawking's calculations, TH is the temperature that would be recorded by an observer far away (ideally infinitely far away) from a black hole. The inverse ratio between TH and MBH in this last equation suggests that Hawking radiation is only important for small and light black holes, such as micro-black holes. However, as we know, these objects have not been detected. Also, although there is no solid experimental evidence for the existence of Hawking radiation, due to consistency with other widely confirmed physical theories, experts agree that Hawking radiation exists.

Table 5 shows the different TH values calculated from our last equation and the corresponding radiation types and wavelengths. In the case of micro-black holes, it can be seen that TH is very high and the event horizon emits mainly gamma rays. However, for supermassive black holes and stellar-mass black holes (the only types of black holes for which there is observational evidence), TH is very close to absolute zero and Hawking radiation is not detectable.

Result

Black holes are no longer a subject of interest only to experts, and more and more people are interested in discovering their secrets, which emphasizes the importance of correcting misconceptions about them. From this perspective, we hope that the ideas discussed in this paper will contribute to a better understanding of black holes.

It is important to keep in mind that black hole physics is a very active field of research, full of questions and in a constant state of transformation. It should therefore not be surprising that in the near future, some currently accepted ideas about black holes may be refuted by theoretical or observational evidence and become misconceptions, such as the widely held belief until 1974 that black holes are black. But these new ideas will build on existing ideas, and we must be aware of today's misconceptions in order to understand and appreciate tomorrow's advances.

Source:

1. https://arxiv.org/pdf/1909.06006