Dark Matter: From Dark Quarks to Dark Black Holes

1. Introduction

Through the complex conceptual jungle, from the perspective of the combined relationship between electric charge and color charge, the existence of basic fermions and basic bosons that have no charge but only color charge has never been theoretically prohibited. Dark quarks, dark gluons, and neutrinos may be the leading candidates for the elementary particles that make up dark matter. Three-color dark quarks can form dark neutrons and other dark baryons. Dark quarks and dark antiquarks can form dark mesons and then dark hadron clusters until they form dark neutron stars and dark black holes. They can also participate in forming bright and dark composite hadrons, and then form bright and dark composite atomic nuclei until they form bright and dark composite neutron stars and bright and dark composite black holes.

2. A more concise relationship between hadron charge number and quark number

In 1932, to explain the symmetry of protons and neutrons, Heisenberg introduced the concepts of isospin and the third component of isospin, which provided a new perspective for understanding the strong interaction. Later, the Gell-Mann-Nishishima relation revealed the relationship between hadron charge and its isospin third component and supercharge¹:

Here, $Q$ is the hadron charge number, $I_3$ is the third component of isospin, $Y$ is the hypercharge, $B$ is the baryon number, and $s,c,b,t$ are the strange, charm, bottom, and top quark numbers, respectively.

However, in this formula, due to the introduction of isospin and hypercharge, up quarks and down quarks are not treated equivalently to strange, charm, bottom, and top quarks. Furthermore, because too many concepts are introduced, the transparency of the theory is obscured. If, according to Occam’s razor principle, it is agreed that the quark number of each quark is +1, the quark number of each antiquark is -1, the baryon number of baryons is +1, the baryon number of antibaryons is -1, and the baryon number of mesons is 0, then a more concise relationship can be obtained:

In this way, the concepts of isospin and hypercharge can be eliminated, and charge multiplets can replace the concept of isospin multiplets. Suppose the first-generation quarks and leptons are regarded as ground-state quarks and ground-state leptons, and the second- and third-generation quarks and leptons are regarded as excited states of ground-state quarks and leptons. In that case, the elementary particle table will be more concise.

3. From dark quarks, dark hadrons to dark neutron stars and dark black holes

From the perspective of the combination of charge and color charge, the basic fermion with neither charge nor color charge is the neutrino, the basic fermion with only charge but no color charge is the charged lepton, the basic fermion with both charge and color charge is the quark, and the last possibility is the basic fermion with no charge but only color charge, which we call the dark quark. Theoretically, the existence of basic fermions with no charge but only color charge has never been prohibited. The corresponding intermediate boson that transmits color charge interactions between dark quarks is the dark gluon.

The up quark, down quark, and ground state dark quark constitute the charge triplet of the ground state quark, and the electron and ground state neutrino constitute the charge doublet of the lepton. The first generation of dark quarks is the ground state dark quark, and the second and third generations of dark quarks are the excited states of the ground state dark quark. Three dark quarks can carry three kinds of color charges, respectively, to form dark baryons; among these, three ground-state dark quarks form ground-state dark baryons, namely dark neutrons. Since they cannot continue to decay into brighter dark baryons, dark neutrons can exist as stably as protons. Dark quarks and dark antiquarks can form dark mesons. Dark baryons and dark mesons are collectively called dark hadrons.

Relatively speaking, quarks with electric charge can be called bright quarks. Similarly, neutrinos with no electric charge can be called dark leptons, and leptons with an electric charge can be called bright leptons. Bright quarks, gluons, and bright leptons are basic bright particles. Dark quarks, dark gluons, and dark leptons may be the basic dark particles that make up dark matter. The relationship between their electric charges is

When $n=1$ , we get the charge number of the down-type quark; when $n=2$ , we get the charge number of the up-type quark; when $n=3$ , we get the charge number of the charged lepton; when $n=0$ , we get the charge number of the dark quark and dark lepton (i.e., the neutrino). The charge relationship between their antiparticles is

Dark neutrons can form dark neutron pairs, dark neutron clusters, and even dark neutron stars, while dark quarks can form dark quark stars and even dark black holes. In theory, dark quarks can also form bright-dark composite hadrons with bright quarks. And dark neutrons can also form bright-dark composite atomic nuclei with protons and neutrons, and then form bright-dark composite atoms with electrons, and even bright-dark composite planets and stars.

4. Dark black hole and bright black hole

Schwarzschild black holes are spherically symmetric, non-rotating, and uncharged black holes, while Kerr black holes are spherically symmetric, uncharged, and rotating.^2–4 In fact, black holes that strictly meet the conditions of ideal Schwarzschild and Kerr are dark black holes composed of dark matter.^3,4 The event horizon radius of a Schwarzschild black hole (the Schwarzschild radius) is:

The event horizon radius of a Kerr black hole (the Kerr radius) is⁴:

From a classical mechanics perspective, $r_{m1}=\frac{\mathit{GM}}{c^2}$ represents the minimum orbital radius for photons around a Schwarzschild black hole, also known as the first gravitational radius. The Schwarzschild radius $r_s=\frac{2\mathit{GM}}{c^2}$ is the escape radius for photons around a Schwarzschild black hole, also known as the second gravitational radius.³ Thus, we can preliminarily investigate the internal structure and properties of dark black holes.

By contrast, black holes that are charged or neutral but have a magnetic moment are considered bright black holes. Kerr–Newman black holes are rotating, charged black holes, and the Kerr–Newman radius is⁵:

Reissner–Nordström black holes are non-rotating, charged black holes, and their radius is^6,7:

For charged black holes, $r_{Q1}=\frac{{\mathit{kQ}}^2}{{\mathit{Mc}}^2}$ represents the first radius caused by the interaction of electric charge, and $r_{Q2}=\frac{2{\mathit{kQ}}^2}{{\mathit{Mc}}^2}$ the second radius. $r_{\mathit{MQ}}=\sqrt{\frac{{\mathit{GkQ}}^2}{c^4}}$ is the fusion radius caused by the combined effects of gravity and charge interaction. Due to different physical meanings, just as the charge radius, magnetic moment radius, and mass-radius of an electron are not necessarily suitable to merge into a unified radius, the radii of charged black holes that originate from gravity, charge interaction, and magnetic moment interaction are not necessarily suitable to merge into a single radius. We can test these conjectures through astronomical observations and high-energy experiments, exploring the structure and properties of bright black holes, dark black holes, and bright–dark composite black holes.

5. Conclusion

In this paper, we proposed a new theoretical framework for understanding dark quarks, dark hadrons, and their role in forming dark astrophysical structures such as dark neutron stars and dark black holes. By reformulating the hadron charge-quark number relationship, we demonstrated a more concise and symmetric charge classification, eliminating unnecessary conceptual complexities.

Additionally, we examined the nature of black holes formed from dark matter and compared them with bright black holes, including Kerr and Reissner-Nordström black holes. Our analysis suggests that gravitational and charge interactions should be considered separately when determining black hole radii, offering new perspectives on their internal structure.

The implications of this study extend to both particle physics and astrophysics, particularly in the search for dark matter candidates and their astrophysical manifestations. Future high-energy experiments and astronomical observations will be crucial in testing these theoretical predictions and further understanding the composition of the universe.