At Ultra High Densities, Which Kind Of Wormholes You May Find? (Quantum / Physics)

The quark structure of baryonic matter is the central paradigm of the present-day elementary particle physics. At very high densities, which can be achieved in the interior of neutron stars, a deconfinement transition can break the baryons into their constitutive components, the quarks, thus leading to the formation of the quark-gluon plasma. Moreover, the strange quark matter, consisting of a mixture of u, d and s quarks, may be the most energetically favorable state of matter.

The existence of a large variety of color superconducting states of quark matter at ultra-high densities has also been suggested and intensively investigated. At very high densities, matter is expected to form a degenerate Fermi gas of quarks in which the quark Cooper pairs with very high binding energy condense near the Fermi surface. This phase of the quark matter is called a color superconductor. Such a state is significantly more bound than ordinary quark matter. This implies that at extremely high density the ground state of quark matter is the superconducting Color-Flavor-Locked (CFL) phase, and that this phase of matter rather than nuclear matter may be the ground state of hadronic matter.

The thermodynamic properties of the quark matter are well-known from a theoretical point of view, and several equations of state of the dense quark-gluon plasma have been proposed in the framework of a Quantum Chromodynamical approach, such as the MIT bag model equation of state and the equations of state of the superconducting Color-Flavor-Locked phase.

Motivated by these theoretical models, Harko and colleagues now explored the conditions under which wormhole geometries may be supported by the equations of state considered in the theoretical investigations of quark-gluon interactions. Since quark-gluon plasma can exist only at very high densities, the existence of the quark-gluon wormholes requires quark matter at extremely high densities. In these systems the basic physical parameters describing the properties of the QCD quark-gluon plasma (bag constant, gap energy, quark masses) become effective, density and interaction dependent quantities. It is this specific property of the strong interactions they have used to generate specific mathematical functional forms of the bag function and of the gap function that could make possible the existence of a wormhole geometry supported by a strongly gravitationally confined normal or superconducting quark-gluon plasma.

In our paper, we investigated the possibility that wormhole geometries can be realized by using quark matter, in both normal and superconducting phases. To describe quark matter we adopt the Massachusetts Institute of Technology (MIT) bag model equation of state, while for the investigation of the superconducting quark matter we consider the equation of state obtained in a first order expansion of the free energy of the system.

— told Harko, lead author of the study.

In the case of the normal quark-gluon plasma, wormhole solutions can be obtained by assuming either a specific dependence of vaccum pressure (B) on the shape function b, or some simple functional representations of B. In both cases in the limit of large r the bag function tends to zero lim_(r→∞) B = 0, and in this limit the equation of state of the quark matter becomes the radiation type equation of the normal baryonic matter, p = ε/3. Therefore, once the density of the quark matter increases after a deconfinement transition, a density (radial coordinate) dependent bag function could lead to the violation of the null energy condition, with the subsequent generation of a wormhole supported by the quark-gluon plasma. A high intensity electric field with a shape function dependent charge distribution could also play a significant role in the formation of the wormhole.

“By appropriately choosing the forms of the bag and gap functions several wormhole type solutions of the gravitational field equations are obtained, with the matter source represented by normal and superconducting quark matter, respectively.”

— told Mak, author of the study.

While, in the case of the superconducting quark matter the gravitational field equations can be solved by assuming that both the bag function and the gap function are shape function and s quark mass dependent quantities. However, in the large r limit, in order to reobtain the standard baryonic matter equation of state, the condition of the vanishing of the mass of the s quark is also required, lim_(r→∞) m_s = 0. The assumption of a zero asymptotic u, d and s quark mass is also frequently used in the study
of quark star models.

Reference: Tiberiu Harko, Francisco S. N. Lobo and M. K. Mak, “Wormhole geometries supported by quark matter at ultra-high densities”, International Journal of Modern Physics D, Vol. 24, No. 01, 1550006 (2015).

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