Gravitating Meron-like topological solitons in massive Yang–Mills theory and the Einstein–Skyrme model

We show that Merons in D-dimensional Einstein–Massive–Yang–Mills theory can be mapped to solutions of the Einstein–Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connection $$A=\lambda U^{-1}dU$$ A = λ U - 1 d U , the massive Yang–Mills equations reduce to the Skyrme equations for the corresponding group element U. In the same way, the energy–momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the SU(2) case and show that introducing a mass for the Yang–Mills field restricts Merons to live on geometries given by the direct product of $$S^3$$ S 3 (or $$S^2$$ S 2 ) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for $$D=4$$ D = 4 and $$D=5$$ D = 5 . Finally, we comment on possible generalisations.

The Structured Wall-Turbulence, a Galilean Relativistic Phenomenon

The relationship between heavenly bodies and earthly behavior along with its importance took many centuries before the rigor scientific understanding enabled the true influences on Earth, such as its complicated motion and perceived other regularities in the behavior of earthly objects. One of these was the tendency for all things in one vicinity to move in the same downward direction according to the influence that is known as gravity property. Moreover, matter was observed to transform, sometimes, from one form into another, such as with melting of ice or vaporizing/cavitation of water, but the total quantity of that matter never seemed to change, which reflects the law at which we now refer to as the conservation/ integrity of mass, including its latent energy. Much latter it is noticed that planet Earth forms a self-regulating complex system, i.e. the Earth’s surface is alive, that is known as the Gaia hypothesis, reflected in the Newton-Galilei dynamics through the law of equal action and reaction for stress vector and tensor, respectively. In addition, at was noticed that there are many material bodies with the important property that they retain their shapes, excepting the flowing fluids, whence the idea of rigid spatial motion arose, and it becomes possible to understood spatial relationships in terms a precise, well-defined geometry, the Euclidian three-dimensional geometry. Though the heavenly bodies are permanently moving in a self-built on universe like a timeless perpetuum mobile, the time remains an important property for the behaviors/motions of an Earth-bound object due to their relativity as against the diurnal rotation depending on the velocities of the impacted object. In contrast to the constant inertia condition where for small starting velocities and accelerations the Newton’s determinist principle is applied, the onset of a motion of the Earth-bound material bodies, at higher velocities and accelerations (O(g)), involves changes of moving matter/inertia under influence of gravitational field via some intrinsic latent motions/processes. They achieve the kinetic-gravitational mutual energy transfer obeying the Galilei’s law of inertia for self-equilibrating impact forces. The intrinsic motions, at the cellular scale (10-6 m), are responsible for the kinetic trinity of the momentum, kinetic energy and power, and they represent what it is called structured turbulence, i.e. a Galilean space-time structure according to the mathematical idea of a bundle (or fibre bundle) and its gauge connection. The bundle and gauge connection are a kind of Galilean transformation to a system moving with constant velocity carrying its relativistic non-inertial fraction as a blend of structure less turbulence and non-rigorously defined intermittency of a non-inertial motion.

Best Matching: Technical Details

The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

Shape dynamical loop gravity from a conformal Immirzi parameter

The Immirzi parameter of loop quantum gravity is a one-parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of geometric operators, despite being irrelevant at the classical level. The parameter’s appearance in the area and volume spectra to the same power as the Planck area suggest that it plays a role in determining the fundamental length scale of space. In fact, a consistent interpretation is that it represents a constant rescaling of the kinematical spatial geometry. An interesting realization is that promoting the Immirzi parameter to be a general conformal transformation leads to a system which can be identified as analogous to the linking theory of shape dynamics. A three-dimensional gravitational gauge connection is then constructed within the linking theory in a manner analogous to loop quantum gravity, thereby facilitating the application of the established procedure of loop quantization.

Superconducting and Antiferromagnetic Phases of Space-Time

A correspondence between the SO5 theory of high-TC superconductivity and antiferromagnetism, put forward by Zhang and collaborators, and a theory of gravity arising from symmetry breaking of a SO5 gauge field is presented. A physical correspondence between the order parameters of the unified SC/AF theory and the generators of the gravitational gauge connection is conjectured. A preliminary identification of regions of geometry, in solutions of Einstein’s equations describing charged-rotating black holes embedded in de Sitter space-time, with SC and AF phases is carried out.

Physical Quantities of Reissner-Nordström Spacetime with Arbitrary Function and Regularized Procedure

We use the covariant teleparallel approach to compute the total energy ofa spherically symmetric frame with an arbitrary function, that is,ℑ(r). We show how the total energy is always effected by the inertia. When use is made of the pure gauge connection, teleparallel gravity always yields the physically relevant result. We also calculate the total conserved charge and show how inertia spoils the physics in the time coordinate direction. Therefore, a regularized expression is employed to get a plausible value of energy. Finally, we use the Euclidean continuation method, in the context of TEGR, to calculate the energy, Hawking temperature, entropy, and first law of thermodynamics.