Noname manuscript No.(will be inserted by the editor)

Black Holes and Dark Matter Must Come First

Without them galaxies and stars would never form

Douglas Leadenham

Received: date / Accepted: date

Abstract Following Einstein's 1916 general theory of relativity, the black hole con-

cept came soon after. Since the 1930's, dark matter has been the explanation for the

motion of galaxies in clusters, and subsequently the rotation of stars around the centers

of galaxies. The timing of black holes and dark matter in the evolution of the universe

has not yet been explained. Now that black holes are known to lie at the centers of

galaxies, and that rotating pairs of stellar black holes are required to make gravita-

tional wave events, it would seem that they are common in the universe. If both play

major roles in galactic and stellar evolution, it would also seem that they must be

among the earliest objects to form. Here is explained the appearance of fundamental

particles, dyons or Dirac monopoles, as the universe underwent exponential expan-

sion prior to the cosmic background radiation. Dyons carry both electric and magnetic

charges, the magnetic ones vastly stronger than the electric, and the dyons aggregate.

In exponential expansion energy density decreases proportionally, and dyon aggregates

could evaporate or dissociate to form the particles observed in accelerator experiments.

Herein the process in which dyon aggregations become black holes and dark matter is

described.

Keywords Black holes · Dark matter · Black strings · Quarks

PACS 04.70.Bw · 95.35.+d · 98.80.Cq

Mathematics Subject Classi�cation (2010) 83C57

1 Introduction

The physical universe began with exponentially increasing size from a tiny cosmic egg

of energy density de�ned by the Planck energy. This idea may have begun with the

D. Leadenham675 Sharon Park Drive, Menlo Park, California 94025Tel.: 650-233-9859

E-mail: douglasleadenham@gmail.com

2 D. Leadenham

observation that the light up- and down-quarks have energies lying on an exponential

curve starting from the electron energy, and that higher energy mesons have energies

lying on an exponential curve starting from the proton energy.1 These higher energy

particles are unstable at present day terrestrial ambient energy, but when the universe

was just beginning, its energy density was very high and such particles would remain

stable for a short time until the ambient energy decreased enough for them to decay to

a lower energy state. Analogous metaphors are evaporation from a liquid or sublima-

tion from a solid. Pressure and temperature are key to those processes, but when the

universe had just begun temperature was not well de�ned. Temperature is a property

of matter in our de Sitter space, and temperature measurements are de�ned by stable

particles, electrons and protons, that later dominated the matter in the universe.

In the early universe one works with energy as the working variable.

De�nition 1 Planck energy EP :

EP =

√~c5G

Equivalence of energy and mass is known to all.

De�nition 2 Einstein's formula:

E = mc2

In general relativity mass and length are also equivalent.

De�nition 3 Schwarzschild's gravitational radius formula:

rg =2Gm

c2

The fundamental particles of matter are the electron and proton. Calculate the gravi-

tational radius of each and get:

rge = 1.35× 10−57m

and

rgp = 2.48× 10−54m

Compare these to their respective interaction radii, the Compton radius and proton

radius.

rC = 3.86× 10−13m

rp = 8.77× 10−16m

Clearly, the mass-energy of these is contained in �elds covering some 40 orders of

magnitude in size. One sees that mass is not a nut with a �eld around it; rather, it is the

energy in the �eld inside the interaction space. The recent observations of gravitational

waves showed that merging black holes give up energy on the order of a solar mass

or more in these waves. Energy can't escape from inside the Schwarzschild radius of

either black hole. Instead, this energy comes from the �eld around the pair of holes as

the �eld smooths from a rapidly rotating dumbbell to a single rotating sphere.

1 http://pdg.lbl.gov/2015/listings/contents_listings.html

First matter 3

2 Energy density

Elementary textbooks give the energy density formulas for electric and magnetic �elds,

but rarely if ever give the energy density in a gravitational �eld. That may be because

the de�nition of mass, its energy equivalent, and the energy in the �eld around the

mass are not well de�ned. Use Earth as an example.

De�nition 4 Energy density in the �eld of a mass where the surface gravity is known:

ug =g2

8πG

For Earth

g =GM⊗R2⊗

From Def. 3 as applied to Planet Earth

M⊗ =Rg⊗c

2

2G

Modeling the �eld with all the mass inside the gravitational radius, we get

ug =R2g⊗c

4

32πG

1

r4

which is the energy density as a function of distance from the gravitational radius,

an inverse 4th power of radius relationship, as expected. In the case of black holes,

nothing is known for certain of the state inside the gravitational radius, because it

is the event horizon. Later in this paper will be shown what can be expected inside,

based on current knowledge. So, it is useful here to calculate the total energy in the

�eld around a mass.

Efield =

∞̂

Rgm

um (r) dV =

∞̂

Rgm

R2gmc

4

32πG

1

r44πr2dr =

Rgmc4

8G

Now form the ratio of this to the mass-energy.

ratio =

Rgmc4

8G

mc2=

2Gmc2

8Gmc2=

1

4

This result tells us that the total energy of a mass is partly the gravitational or inertial,

known as mc2, and 14 more in the �eld around it. This result is one of classical general

relativity. For fundamental particles, their gravitational radius is so small that all of the

energy can be taken as �eld energy, and this is correctly treated in quantum relativity

where energy density is the working variable. The exact nature of the �elds containing

the masses or mass-energies of electrons and quarks is not yet known, although string

theory provides clues.

4 D. Leadenham

Table 1 Fundamental Particle Energies

Fundamental particles Energy, E, MeV Energy, E, MeV Particle Data Groupmodel, E2 = exp(aE1) coupling, a = 0.9801, MeV−1 as observed current mass measurementelectron, e− 0.511 0.511 baseline particleup-quark, u 1.65 2.3 stable nuclear componentdown-quark, d 5.04 4.8 stable nuclear componentcharged pion, π± 139.62 139.57 virtual nuclear component

3 Field energy expanded the nascent universe

Before there were any electrons and quarks the universe expanded exponentially. The

energy density decreased, and as it did the energy of particles remaining stable, or more

precisely, metastable, decreased in proportion also. This modeling exercise runs the

scenario backwards from electrons and protons to their next higher energy counterparts.

This works exponentially from the electron to up- and down-quarks, then to the pion

�eld of the nucleus. Table 1 illustrates the model. Note that the working independent

variable is energy, but energy, mass and length are equivalent in relativity theory, as

explained in the introduction.

This model is a simple exponential function of energy with a coupling coe�cient

to the anthropic MeV scale for nuclear interactions. It is always possible to �t an

exponential function between two points, in this case the electron and pion energies.

What is interesting is that points in between are close to the quark energies in every

nucleus of matter. This could be a coincidence, but it makes the model quite appealing.

The exponential model even looks impressive.

Eup ≈ exp (aEe)

Edn ≈ exp (aEup) ≈ exp (a exp (aEe))

Eπ ≈ exp (aEdn) ≈ exp (a exp (a exp (aEe)))

Table 2 shows how the same model progresses from the proton energy to higher

energy meson states that are unstable at present ambient energy density. Apply another

coupling b in the exponential model beginning with the proton and ending with the top

quark. Here the intermediate energies lie close to mesons that can decay into proton-

antiproton pairs besides many lower energy particles. It has always been a source of

amazement that there are so many intermediate particles. There is reason to think that

all of them are highly composite, and the more energy they have, the more components

they have to decay into. The composite particle model has neutrinos composed of two

dyons of opposite electric charge, the electron and every up- and down-quark composed

of six dyons, so that every proton and neutron will have a total of 18. One sees in Table

2 that the coupling times energy is 0.9801MeV −1

0.8335GeV −1 × 1000MeV/GeV , so the expansion

is driven 1176 times more strongly than at the more recent, later time in the universe's

expansion.

This is the exponential energy expression for Table 2.

Et ≈ exp (bEB) ≈ exp (b exp (b exp (bEp)))

First matter 5

Table 2 Higher Energies

Higher energy particles Energy, E, GeV Energy, E, GeV Particle Data Groupmodel, E2 = exp(bE1) coupling, b = 0.8335, GeV−1 as observed measurementproton, p 0.938272 0.938272 stable baseline particleD∗s0(2317)

± 2.19 2.318 charmed, strange mesonB±c 6.18 6.276 bottom, charmed mesontop quark, t 173.21 173.21 best current mass estimate

Table 3 Possible Dark Matter

Hypothetical particles Energy, E, TeV Model mirrormodel, E2 = exp(qE1) coupling, q = 1.5028, TeV−1 particle energy, TeVlightest mirror particle observed 0.375 1.4×109 model stable energypossible heavier mirror particle 1.76 1.22× 1016 Planck energy, EPleven heavier mirror particle 14.02 1.152×10−7dimensionless (model stable energy)/EPlenergy at �rst appearance of stable particles 1.4×109 0.999998 dimensionless Expected value = 1

Table 3 shows what may be the origin of dark matter. This is a speculative ex-

trapolation of the model results of Tables 1 and 2, given a third coupling q to the

TeV energy scale. All that is known is that the 750 GeV event observed at the LHC

is almost certainly an annihilation of a particle and its antiparticle.[3] Figure 1 is a

diagram of such a diphoton event in the ATLAS detector. The key assumption is that

all known particles, even neutrinos, are composite, although this has not yet been

con�rmed experimentally.

Figure 1: The photons are indicated by the clusters of energy shown in green.

(Courtesy: CERN)

This is the exponential energy expression for Table 3.

Estable ≈ exp (qEheavier) ≈ exp (q exp (q exp (qEmirror)))

6 D. Leadenham

In Table 3 the coupling is 0.8335GeV −1

1.5028TeV −1 × 1000GeV/TeV , or 555 times stronger

expansion than in the later epoch of Table 2.

4 Dark matter model

The composite nature of matter is described in detail in 21st Century Physics, Chap-

ter 5.[2] The nature of mirror matter is not known, but its existence is corollary to

composite matter as the book describes. Even without experimental con�rmation, the

composite model has been theorized for decades ever since Paul Dirac �rst proposed the

so-called magnetic monopole. Composite matter, including the mirror matter category,

is composed of paired-up Dirac monopoles or dyons.[1]

The 750 GeV event appears to be an immediate annihilation of the lowest energy

pair of mirror particles. The LHC can produce collisions of 13 TeV, so a 0.750 TeV event

should be observed often enough for con�rmed detection. What happens with dyons is

that pairs are produced copiously in the nascent universe. The pair has a Dirac string

connecting them that at low energy pulls them back together. In the nascent universe

the energy density is so high that the pair can separate. The particle poles have an

enormous magnetic �eld that stretches through the string. The poles move in opposite

directions in the energetic universe until they land on an opposite magnetic charge and

stick there, but the string remains. These strings, called black strings by mathematical

theorists, comprise the extended dark matter �eld that remains today. The object that

one of the pair sticks to is a collection of dyons that has not yet dissociated, remaining

as a lump of magnetic dipoles. After the ambient energy has decreased enough, the

lumps and trailing strings become enclosed by an event horizon from which no energy

can escape. This makes black holes and black strings attached to them. (Science toy

and gift shops sell permanent dipole magnets in a lump or chain for the money in your

wallet. The model is realistic.)

5 Black hole model

When stable particles formed, the universe had two sectors: Planck space where the

energy came from and what we now call anti-de Sitter space where particle interactions

occur, the interior of nucleons, for example. The sectors had become separated by an

event horizon. Lumps of dyons, with a very large energy density, were enclosed by the

horizon so no more dyons could escape. The ones that had escaped were pinned to

the lumps that captured them, and the trailing magnetic �elds became enclosed by

the horizon to form black strings. As the original cosmic egg of particles dissociated,

particles and their antiparticle partners could annihilate producing copious showers

of lower energy particles and photons. The stages of this evolutionary universe are

outlined in Tables 1-3. The lumps of dyons that got enclosed by the horizon became

black holes, and the enclosed magnetic �elds became black strings.

Black holes are persistent and will remain for the duration of the universe. Large

ones are cold and get larger and colder with time, as they acquire mass. Only the tiniest

ones radiate energy faster than they acquire it by capturing matter. The �energy at

formation of stable particles� in the last row of Table 3 is that associated with the �rst

appearance of electrons and up- and down-quarks, that remain stable for the rest of

time. The dimensionless fraction was obtained from an analysis of galaxy rotation at

First matter 7

the birth of the galaxy. This analysis is described in 21st Century Physics, Chapter

3, with the motivation given by the need for dark matter to account for the speed of

disk stars in orbit around the centers of galaxies. Black holes at the centers of galaxies

account for Keplerian orbital motion; dark matter in galaxy halos is needed to account

for the non-Keplerian orbital motion.[2]

6 How it could work

Observation suggests that all galaxies have super massive black holes at their centers.

Without these black holes it is hard to understand how matter could be collected

together in a billion years or so to make bright galaxies with bright, massive stars.

The Jeans instability would not work in the homogenous hydrogen-helium gas that

we see as the source of the cosmic microwave background. Quasars and active galactic

nuclei seen at large distances are simply explained as these large black holes acquire

mass, as normal matter circulating around them loses energy and angular momentum

by collisional and tidal friction, radiating intensely.

The primordial dyon lumps are not of a uniform size; they follow a power law by

which the largest ones are the least frequent, and the smallest are the most frequent.

The small ones are the primordial black holes that have been sought by observation for

decades, and never found. So, where are they? Inside stars. The two recent gravitational

wave events resulted from the merger of a pair of closely orbiting stellar black holes. It

is reasonable that these stellar black holes would draw normal matter inward the same

as galaxies do. Is this how early stars form? It seems so.

In 21st Century Physics, Chapter 4, is a description of how our Sun can have a

pair of tiny black holes at its center.[2] Primordial black holes are everywhere in the

universe, hidden in stars.

7 Disappearing 750 GeV event

The recent announcement by Bruno Lenzi of CERN for the ATLAS team, and Chiara

Rovelli for C.M.S. [www.ichep2016.org] that the diphoton events reported at the LHC

are not seen any longer, after much more data had been collected, does not exclude the

possibility that such events did happen. Figure 1 is a picture of one. Almost a decade

ago this writer suggested that dark matter would interact weakly with the beams of the

LHC. The researcher immediately responded that such a dark matter particle would

be �boosted far down the line� out of the detector and so not detected. That would be

true of particles, but the model this author proposes is that dark matter is black strings

connected to black holes. Black strings would behave more like taut guitar strings.

Black strings that orbit the Sun at a large distance from Earth are not the likely

participants. Black strings orbiting the Milky Way, connected to the super-massive

black hole at the galactic center, would pass through Earth like neutrinos do, except

sporadically, not in a more or less steady current. These are the strings that would

interact with the LHC beams. Black strings comprising dark matter are clumpy, just

as the simulations of the developing universe show them to be. Normal matter collects

around the clumps of strings to make galaxy clusters. Clumpy strings would pass Earth

sporadically, and it is believed that there is a giant �gure-eight clump centered on the

Milky Way's black hole that orbits every 66 million years. There are also likely to be

8 D. Leadenham

smaller clumps spaced out randomly in their orbits, and possibly one of these small

clumps produced the observed 750 GeV events.

The LHC beams collide at predetermined locations in the detectors. Strings passing

through the collision regions would add a lot of energy there, because the string is part

of an event horizon connected to a black hole. This would add enough energy to push

the interaction over the threshold energy to produce the smallest mirror matter particle

pair that then annihilate as a diphoton event. Look closely at Figure 1 and see that

the two 375 GeV photons are not quite collinear. That suggests that another object,

whether string or particle, intersected the collision point, adding energy and momentum

at an angle to the beams.

Let us not lose con�dence. The 750 GeV diphoton events will reappear, but it would

be nice to see them before another 33 million years have passed.

8 Conclusion

This is a brief description of the universe's beginning, stopping at the place where the

hydrogen-helium gas and preceding black holes and black strings began to organize

normal matter and energy into the stars and galaxies that are observed today. It

is speculative and conjectural because we cannot observe times earlier than the 13.8

billion year old cosmic microwave background, or past the horizon of black holes. Based

on known particle and relativity models, we can, however, eliminate all but the logically

consistent models that theorists like to promote. So we will promote them.

References

[1] D. Leadenham, Antimatter Missing? Not Really: Half of everything is antimatter - evenyou, Journal Volume(number), page numbers (2016)

[2] D. Leadenham, Topics in 21st Century Physics�The Universe As Presently Understood�,page numbers. (DJLeBooks, Menlo Park, California 94025, 2016)

[3] R. Garisto, Theorists React to the CERN 750 GeV Diphoton Data, Physical Review Letters116(150001), (2016)