1. 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 Classication (2010) 83C57
1 Introduction
The physical universe began with exponentially increasing size from a tiny cosmic egg
of energy density dened by the Planck energy. This idea may have begun with the
D. Leadenham
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E-mail: douglasleadenham@gmail.com

2. 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 dened. Temperature is a property
of matter in our de Sitter space, and temperature measurements are dened 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.
Denition 1 Planck energy EP :
EP =
c5
G
Equivalence of energy and mass is known to all.
Denition 2 Einstein's formula:
E = mc2
In general relativity mass and length are also equivalent.
Denition 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 × 10−57
m
and
rgp = 2.48 × 10−54
m
Compare these to their respective interaction radii, the Compton radius and proton
radius.
rC = 3.86 × 10−13
m
rp = 8.77 × 10−16
m
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

3. 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 denition of mass, its energy equivalent, and the energy in the eld around the
mass are not well dened. Use Earth as an example.
Denition 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⊗c2
2G
Modeling the eld with all the mass inside the gravitational radius, we get
ug =
R2
g⊗c4
32πG
1
r4
which is the energy density as a function of distance from the gravitational radius,
an inverse 4
th
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 =
∞ˆ
Rgm
um (r) dV =
∞ˆ
Rgm
R2
gmc4
32πG
1
r4
4πr2
dr =
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
1
4 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. 4 D. Leadenham
Table 1 Fundamental Particle Energies
Fundamental particles Energy, E, MeV Energy, E, MeV Particle Data Group
model, E2 = exp(aE1) coupling, a = 0.9801, MeV−1 as observed current mass measurement
electron, e− 0.511 0.511 baseline particle
up-quark, u 1.65 2.3 stable nuclear component
down-quark, d 5.04 4.8 stable nuclear component
charged 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 coecient
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)))

5. First matter 5
Table 2 Higher Energies
Higher energy particles Energy, E, GeV Energy, E, GeV Particle Data Group
model, E2 = exp(bE1) coupling, b = 0.8335, GeV−1 as observed measurement
proton, p 0.938272 0.938272 stable baseline particle
D∗
s0(2317)± 2.19 2.318 charmed, strange meson
B±
c 6.18 6.276 bottom, charmed meson
top quark, t 173.21 173.21 best current mass estimate
Table 3 Possible Dark Matter
Hypothetical particles Energy, E, TeV Model mirror
model, E2 = exp(qE1) coupling, q = 1.5028, TeV−1 particle energy, TeV
lightest mirror particle observed 0.375 1.4×109 model stable energy
possible heavier mirror particle 1.76 1.22 × 1016 Planck energy, EP l
even heavier mirror particle 14.02 1.152×10−7dimensionless (model stable energy)/EP l
energy 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
conrmed 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. 6 D. Leadenham
In Table 3 the coupling is
0.8335GeV −1
1.5028T eV −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 conrmation, 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 conrmed 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

7. 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. 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 condence. 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 - even
you, Journal Volume(number), page numbers (2016)
[2] D. Leadenham, Topics in 21st Century PhysicsThe 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 Letters
116(150001), (2016)