Ball lightning is spherical in shape and ranges in size from a centimeter to 10 meters. It is luminous and exhibits various colors such as white, yellow, red, or blue. It is associated with lightning strikes. It is a transient phenomenon that usually exists for several seconds. However, it can occasionally persist up to 10 minutes. Finally, we note it is an extremely rare phenomenon [1] - [3] . [4] cites only 5 - 15 reliable reports of ball lightning events per year.

Although ball lightning has been known for many centuries, it is one of the most mysterious atmospheric phenomena. There are many theories of ball lightning (50 - 100), but there is no consensus on which of these theories is correct if any of them is correct.

Theoretical understanding of ball lightning employing well known physics is so poor that particles have been invoked to explain ball lightning that have never been observed in laboratories such as magnetic monopoles [5] [6] , black holes [7] [8] , axions [9] and dark matter [10] . In addition, exotic proposals such as nuclear reactions [11] and antimatter [12] have been made. Here we do not present a model of the structure or formation of ball lightning; instead, we discuss only why it does not fall as normal physical bodies do.

The motion of ball lightning is highly enigmatic because it appears to defy gravity, that is, it does not fall, rather its motion is horizontal. [13] suggests this lack of vertical motion is caused by the earth’s electric field, [14] by an electric discharge that continuously varies on a microsecond time scale, [15] through trapped electromagnetic waves inside the plasma that create outward radiation pressure sufficient to counteract gravity, [16] [17] maintain a plasma contained within a force-free magnetic field, [18] electrostatic attraction between similarly charged clusters that supports ball lightning preventing it from falling, [19] a plasma-microwave structure that prevents falling, [20] a microwave-trapped plasma cavity, [21] a self-contained spherical current/radiation circuit, where energy is stored outside the ionized core that creates electromagnetic-balancing forces that allow the structure to float and [22] a phase-locked electromagnetic wave packets within plasma, which lead to stable motion without falling.

In contrast to all the above theories, we employ General Relativity, which is Einstein’s theory of gravitation [23] , to explain ball lightning’s lack of falling motion. This theory predicts that not only mass but also energy gravitates. Specifically, we employ the circumstance that the electrostatic field energy associated with charged particles gravitates repulsively [24] to explain the observational fact that ball lightning does not fall.

We base our theory on just two fundamental assumptions:

1) Ball lightning is charged as [13] [14] [18] [25] - [27] assume.

2) Ball lightning is a physical body, meaning that it obeys the laws of physics. Therefore, it is not a hallucination or caused by sensual perception as some maintain [28] [29] . Observations show that ball lightning moves as a whole and we therefore assume that it responds to gravitational forces as a whole. Consequently, if only Newtonian gravity were present and no other forces, ball lightning would fall.

Instead of Newton’s theory of gravitation we employ Einstein’s theory of gravitation, which is more commonly referred to as General Relativity, to explain why ball lightning does not fall as normal physical bodies do. According to Einstein, energy gravitates, therefore, the electrostatic field energy associated with charged particles must gravitate. It gravitates repulsively [24] .

The basic equation we employ in our analysis of the motion of ball lightning is [30] :

$g_E=\frac{n^2}{m}{g}_e$(1)

$g_E$ is the contribution of the electrostatic field energy to the gravitational acceleration of ball lightning. m is the mass of the matter in ball lightning in units of electron mass. n is the number of electrons in the ball lightning that predominantly originated in the lightning strike that caused the phenomenon. Technically, n should include charged particles in the atoms or ions that may be a part of ball lightning, but we have shown [30] that their effect is extremely small, because their masses are so much higher than those of electrons. So we do not include them in n.

$g_e$ is the contribution of the electrostatic field energy of a single electron to the gravitational acceleration of ball lightning. The effect of electrostatic field energy of an electron of mass, $m_e$, on the surface of the earth, on the gravitational acceleration is [24]

$g_e=-\frac{e^2}{m_e{c}^{2}r}{g}_N=-4.4\times {10}^{-22}{g}_N=-\frac{g_N}{n_0}$(2)

which is the classical electron radius divided by the radius of the earth, r, multiplied by $g_N=-\frac{GM}{r^2}$, the Newtonian acceleration of gravity. c is the speed of light and e the charge of an electron. For convenience we introduce: $n_0=\frac{1}{4.4\times {10}^{-22}}$. Below we will give a physical interpretation of $n_0$.

Combining Equations (1) and (2) leads to:

$g_E=-\frac{n^2}{m{n}_0}{g}_N$(3)

It is most important to understand the following. Because $g_N<0$, that is, physical bodies fall downward, according to the above equation $g_E$, the gravitational acceleration of the electrostatic field energy, is upward. Thus, the energy of the electrostatic field gravitates repulsively [24] .

In general, n and m of ball lightning on the right side of Equation (1) are not known. However, we do know the value of $g_E$ on the left side of Equation (1). Since ball lightning does not fall it means that:

$g_E=-g_N$(4)

This equation means that the upward gravitational acceleration caused by the electrostatic field energy of the electrons, which came chiefly from the lightning bolt that created the ball lightning, balances the normal Newtonian gravitational acceleration.

Combining these last two equations yields:

$\frac{n^2}{m}=n_0=2.3\times {10}^{21}$(5)

So, even though we generally do not know the values of n and m, we do know the ratio of $\frac{n^2}{m}$. We now turn to employing the above equation to explore the relationship between the values of n and m under various circumstances.

Equation (8) leads to the conclusion that the minimum number of electrons required to achieve the equality of downward Newtonian gravitational force and upward gravitational force of the electrostatic field energy is $n_0=2.3\times {10}^{21}$. $n_0$ is the value of $n$, when $\mu =0$. That is it corresponds to a pure electron body. But, out of all the models proposed so far that suggest ball lightning is charged, the model with the highest estimate of the value of the charge is [18] with 0.1 C that is 6.24 × 10¹⁷ electrons. $n_0$ is orders of magnitude larger than this value, which suggests that none of these models is correct in their current form.

Does $n_0$ fit estimates of the energy in ball lightning? A lightning bolt containing $n_0$ electrons has an estimated energy of 3.68 × 10¹⁰ joules. This energy fits well with the estimated energy density, 10¹⁰ J/m³ of ball lightning [46] .

How frequent are lightning strikes with $n\ge n_0$? [47] estimate that 0.1% of lightning strikes transport a charge > 350 C. $n_0$ corresponds to 368.5 C so they are roughly 0.1% of the total number of lightning strikes. They are therefore rare, about 1 in 1000 strikes. Nevertheless the total number of such strikes is appreciable. There are worldwide about 100 lightning strikes/s that is 3.15 billion/year. So every 10 s or about 3 × 10⁶ per year is an estimate of the frequency of superbolts with $n\ge n_0$.

However, only a small faction of these strikes, which may lead to ball lightning, are reported. This is because of geographical constraints: 1) Only a small fraction of the earth’s surface at any instance is visible to humans. 2) reporting is more likely to take place in developed countries. [4] cites 5 - 15 reliable reports of ball lightning events per year. Considering these constraints we suggest this number is explained by the frequency of superbolts with $n\ge n_0$.

Experiments have been performed to create ball lightning. [38] simulated a lightning strike in the lab by applying a 10 - 20 kV direct current (DC) discharge to a 3-mm layer of soil, transferring up to 3.4 coulombs of charge. [48] reproduced ball-lightning-like “plasma fireballs” using a combination of air-gap electrical discharge and microwave radiation. [49] - [51] produced glowing plasma formations generated by discharges with polymer and metal materials. [52] created microwave-sustained plasma fireballs under atmospheric conditions, which exhibited some features of natural ball lightning. None of these experiments created ball lightning. However, they all possessed some features of ball lightning.

Observations show that ball lightning does not fall. It therefore appears to defy gravity. We invoke Einstein’s theory of gravitation instead of Newton’s theory of gravitation to explain these observations. Our theory rests on the circumstance of Einstein’s theory that the electrostatic field energy associated with charged particles (in our case electrons) gravitates repulsively.

We suggest electrons chiefly from the lightning strike that caused the formation of the ball lightning remain in the ball lightning. If the number of electrons is greater than 2.3 × 10²¹ then it is possible for the upward gravitational acceleration of the electrons to equal the downward gravitational force of Newtonian gravitational theory. The exact number of electrons required to achieve this equality depends upon the mass of uncharged matter in the ball lightning as Figure 2 shows.

In addition to explaining why ball lightning does not fall, our theory also explains why the reporting of ball lightning sightings is so rare. This circumstance is due to the rarity of superbolts coupled with geographical and reporting constraints. We have therefore explained two major aspects of the phenomenon of ball lightning.

We conclude that ball lightning does not defy gravity. It indeed obeys the laws of gravitation, however, not Newton’s law of gravitation rather Einstein’s theory of gravitation.

Many thanks to Dr. and Mrs. William McCormick, whose generous support has provided the prerequisite financial basis and most importantly the necessary time to complete this project.