Gauge Theory Of Gravity Research Articles

Defining geometric gauge theory to accommodate particles, continua, and fields

Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates quantum electrodynamics. Here we formalize and generalize the notion of a geometric gauge theory, then apply this framework to classical physical models, including an improved Lagrangian for matter field electromagnetism. We find a remarkably consistent series of actions, with straightforward limits under which each previous one may be obtained. Ancillary benefits include a gauge-independent Galilean Lagrangian, a geometric interpretation for the unusual metric dependence of four-momentum, a modern treatment of the effects of worldline variation on the four-current, a gauge theory of gravity which includes a matter field, and consistent units for matter field electromagnetism.

Nonassociative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics

We elaborate on a model of nonassociative and noncommutative gauge gravity for the de Sitter gauge group SO(4,1) embedding extensions of the affine structure group Af(4,1) and the Poincaré group ISO(3,1). Such nonassociative gauge gravity theories are determined by star product R-flux deformations in string theory and can be considered as new avenues to quantum gravity and geometric and quantum information theories. We analyse physically important and geometric thermodynamic properties of new classes of generic off-diagonal cosmological solitonic solutions encoding nonassociative effective sources. Particularly, we focus on modelling by such solutions of locally anisotropic and inhomogeneous dark matter and dark energy structures generated as nonassociative solitonic hierarchies. Such accelerating cosmological evolution scenarios cannot be described in the framework of the Bekenstein–Hawking thermodynamic formalism. This motivates a change in the gravitational thermodynamic paradigm by considering nonassociative and relativistic generalizations of the concept of W-entropy in the theory of Ricci flows. Finally, we compute the corresponding modified G. Perelman’s thermodynamic variables and analyse the temperature-like evolution of cosmological constants determined by nonassociative cosmological flows.

Manifestly covariant variational principle for gauge theories of gravity

A variational principle for gauge theories of gravity is presented, which maintains manifest covariance under the symmetries to which the action is invariant, throughout the calculation of the equations of motion and conservation laws. This is performed by deriving explicit manifestly covariant expressions for the Euler-Lagrange variational derivatives and Noether’s theorems for a generic action of the form typically assumed in gauge theories of gravity. The approach is illustrated by application to two scale-invariant gravitational gauge theories, namely Weyl gauge theory (WGT) and the recently proposed ‘extended’ Weyl gauge theory (eWGT), where the latter may be considered as a novel gauging of the conformal group; the method can also be straightforwardly applied to other theories with smaller or larger symmetry groups. In addition, the approach enables one easily to establish the relationship between manifestly covariant forms of variational derivatives obtained when one or more of the gauge field strengths is set to zero either before or after the variation is performed. This is illustrated explicitly for both WGT and eWGT in the case where the translational gauge field strength (or torsion) is set to zero before and after performing the variation, respectively. Published by the American Physical Society 2024

Energy–momentum and angular momentum densities in the Poincaré gauge theory of gravity

Abstract In the $\overline{\rm {Poincar\acute{e}}}$ gauge theory of gravity, we examine the energy–momentum and angular momentum densities of the source of the gravitational field (gauge potentials $A^{k}{}_{\mu }, \, A^{kl}{}_{\mu }$). There are two types of these quantities, the Hilbert-type densities ${\boldsymbol \Theta}_{k}{}^{\mu },\, {\boldsymbol \Phi}_{kl}{}^{\mu }$, which appear in the right-hand sides of the gravitational field equations, and $\, ^{M}{\boldsymbol T}_{k}{}^{\mu }, \, ^{M}{\boldsymbol S}_{kl}{}^{\mu }$, which are the densities (Noether currents) of the generators of $T^{4}\underline{\otimes }SL(2,C)$ transformations. We show that these are identical to each other, respectively, i.e., ${\boldsymbol \Theta}_{k}{}^{\mu }\equiv \, ^{M}{\boldsymbol T}_{k}{}^{\mu } ,\, {\boldsymbol \Phi}_{kl}{}^{\mu }\equiv \, ^{M}{\boldsymbol S}_{kl}{}^{\mu }$, in parallel with the cases of the electromagnetic and Yang–Mills fields.

Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity

In this letter, we present the first study of Hawking radiation as a tunneling process within the framework of non-commutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole (NC SBH) within the gauge theory of gravity, employing the Seiberg-Witten (SW) map and the star product. Then, we compute the emission spectrum of outgoing massless particles using the quantum tunneling mechanism. In the first scenario, we calculate the tunneling rate of massless particles crossing the event horizon of the NC SBH with lower frequencies. Our results reveal pure thermal radiation. Notably, we find that the Hawking temperature remains consistent in both the classical thermodynamics and the quantum tunneling approach, suggesting equivalence between these two approaches in NC spacetime. However, in the case of massless particle emission with higher frequencies, we account for energy conservation resulting in the tunneling rate to deviate from pure thermal radiation. This tunneling rate remains consistent with an underlying unitary quantum theory. We establish a relationship between this deviation and the change in the black hole entropy, revealing a logarithmic correction to the entropy within this geometry. Furthermore, we demonstrate that non-commutativity enhances the correlations between two successively emitted particles. Additionally, we determine the NC density number of particle emission and conclude by discussing the implications of our findings.

Symmetries in Cartan’s formalism: A review with examples

We review an algorithm, in the context of gauge and gravity theories described by differential forms, to read off the symmetries of a physical system out of its action, which was originally proposed in [C. Corral and Y. Bonder, Symmetry algebra in gauge theories of gravity, Class. Quantum Grav. 36 (2019) 045002]. In particular, we study the interplay between gauge symmetries and a gauge-covariant version of diffeomorphisms dubbed local translations. We focus on the role of boundary terms and conserved charges that were not discussed in the original proposal. We provide a review of the formalism and analyze several examples of classical theories, including gauge theories coupled to matter fields in flat space and gravitational theories in different dimensions.

Search for Manifestations of Spin–Torsion Coupling

We investigate the axial vector spin–torsion coupling effects in the framework of the Poincaré gauge theory of gravity with the general Yang–Mills type Lagrangian. The dynamical equations for the “electric” and “magnetic” components of the torsion field variable are obtained in the general form and it is shown that the helicity density and the spin density of the electromagnetic field appear as the physical sources. The modified Maxwell’s equations for the electromagnetic field are derived, and the electromagnetic wave propagation under the action of the uniform homogeneous torsion field is considered. We demonstrate the Faraday effect of rotation of the polarization for such a wave and establish the strong bound on the possible cosmic axial torsion field from the astrophysical data.

Torsion Fields Generated by the Quantum Effects of Macro-bodies

We generalize Einstein’s General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed by the Cambridge group. GTG is a “spin-torsion” theory, according to which, gravitational effects are described by a pair of gauge fields defined over a flat Minkowski background spacetime. The matter content is completely described by the Dirac spinor field, and the quantum effects of matter are identified as the spin tensor derived from the spinor field. The existence of the spin of matter results in the torsion field defined over spacetime. Torsion field plays the role of Bohmian quantum potential which turns out to be a kind of repulsive force as opposed to the gravitational potential which is attractive. The equivalence principle remains and essential in this theory so that GR is relegated to a locally approximate theory wherein the quantum effects (torsion) are negligible. As a toy model, we assume that the macro matter content can be described by the covariant Dirac equation and apply this theory to the simplest radially symmetric and static gravitational systems. Consequently, by virtue of the cosmological principle, we are led to a static universe model in which the Hubble redshifts arise from the torsion fields.

Dark matter candidate from torsion

The stable pseudo-scalar degree of freedom of the quadratic Poincaré Gauge theory of gravity is shown to be a suitable dark matter candidate. We find the parameter space of the theory which can account for all the predicted cold dark matter, and constrain such parameters with astrophysical observations.

Gravitational waves in gauge theory gravity with a negative cosmological constant

In this paper, we discuss the gravitational waves in the context of gauge theory gravity with a negative cosmological constant. The gauge theory gravity is a gravity theory under gauge formulation in the language of geometric algebra. In contrast to general relativity, the background spacetime in gauge theory gravity is flat, the gauge freedom comes from the fact that equations in terms of physical quantities should be kept in a covariant form under spacetime displacement and rotation. Similar to the electromagnetism, the gauge formulation enables us to interpret the gravitational force as a gauge force on the background flat spacetime. The dynamical fields that describe the gravitational interactions are those position and rotation gauge fields introduced as the requirement of the gauge covariance. The gravitational field equations can be derived from the least action principle with the action as a gauge invariant quantity built from the covariant field strength. We discuss the gravitational wave solutions of the field equations with a negative cosmological constant, and show that these solutions are of Petrov type-N. We also discuss the velocity memory effect by calculating the velocity change of an initially free falling massive particle due to the presence of the gravitational waves.

Seiberg-Witten map with Lorentz-invariance and gauge-covariant star product

We develop the Seiberg-Witten map using the gauge-covariant star product with the noncommutativity tensor θμν(x). The latter guarantees the Lorentz invariance of the theory. The usual form of this map and its other recent generalizations do not consider such a covariant star product. We construct the Seiberg-Witten map for the gauge parameter, the gauge field and the strength tensor to the first order in the noncommutativity parameter θμν(x). Prescription for the generalization of the map to higher orders is also given. Interestingly, the associativity of the covariant star product both in the first and second orders requires the same constraints, namely, on the θμν(x) and on the space-time connection. This fact suggests that the same constraints could be enough to ensure the associativity in all orders. The resulting Seiberg-Witten map applies both to the internal and space-time gauge theories. Comparisons with the Seiberg-Witten map based on other (non-covariant) star products are given and some characteristic properties are also presented. As an application, we consider the GL(2,C) noncommutative gauge theory of gravitation, in which it is shown that the connection determines a space-time with symplectic structure (as proposed by Zumino et al [33]). This example shows that the constraints required for the associativity of the gauge-covariant star product can be satisfied. The presented GL(2,C) noncommutative gauge theory of gravitation is also compared to the one (given by Chamseddine [44]) with non-covariant star product.

Conservation laws in gauge gravity theory

We analyze the conservation laws in the gauge gravity theory which are derived for the general class of gravitational models with the action invariant under the local Poincaré and the diffeomorphism group. The consistent Noether-Lagrange formalism is developed, revealing the important role of the auxiliary Goldstone and Stueckelberg fields, with the help of which we construct the composite gauge fields that have a clear geometrical and physical meaning.

Wormholes in Poincarè gauge theory of gravity

In this work, we study static spherically symmetric solutions representing wormhole configurations in Poincarè gauge theory ( PGT ). The gravitational sector of the Lagrangian is chosen as a subclass of PGT Lagrangians for which the spin-[Formula: see text] is the only propagating torsion mode. The spacetime torsion in PGT has a dynamical nature even in the absence of intrinsic angular momentum (spin) of matter, hence torsion can play a principal role in the case of usual spin-less gravitating systems. We therefore consider a spin-less matter distribution with an anisotropic energy–momentum tensor ( EMT ) as the supporting source for wormhole structure to obtain a class of zero tidal force wormhole solutions. It is seen that the matter distribution obeys the physical reasonability conditions, i.e. the weak ( WEC ) and null ( NEC ) energy conditions either at the throat and throughout the spacetime. We further consider varying equations of state in radial and tangential directions via definitions [Formula: see text] and [Formula: see text] and investigate the behavior of state parameters at the throat of wormhole. We observe that our solutions allow for wormhole configurations without the need of exotic matter. Observational features of the wormhole solutions are also discussed utilizing gravitational lensing effects. It is found that the light deflection angle diverges at the throat (which indeed, effectively acts as a photon sphere) and can get zero and negative values depending on the model parameters.

Gravitational lensing by a black hole in Poincaré gauge theory of gravity

In this paper, by using a recently found black hole solution in the framework of the Poincaré gauge theory of gravity, we study gravitational lensing for a system where the lens is a static spherically symmetric black hole. By analyzing the equations of motion for light rays in a spacetime with torsion, we derive the deflection angle as the light emitted from a source pass through near the black hole and numerically solve the resulting integral. We also study the effects of torsion on the position of images. The results show that the presence of torsion slightly alters both the deflection angle and position of images in this setup.

THE LAWS OF MOTION IN GAUGE THEORIES OF GRAVITY

The general theory of relativity (GR) states that the matter that generates the gravitational field cannot move arbitrarily, it must obey certain equations that follow from the equations of the gravitational field as conditions for their compatibility. In this article we analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Object: to consider the laws of motion in gauge theories of gravitation. Task to analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Conclusions: it is proved that the equation of an arbitrary gauge field of internal symmetry regardless of the specific type of its Lagrangian can be written both in the form of Einstein's equation and in superpotential form, i.e. as an expression of the total current of gauge charges through the superpotential determined by a specific type of Lagrangian that is, in the form of the Young-Mills equations. So this is a consequence of purely-symmetry theory. Also, a statement is proved in which the constraints on the equations of some fields, which follow from the assumption of the equations of motion for other fields. Research perspectives: nowadays, scientists register gravitational waves and analyze the conditions for their emission, and interest in the problem of motion has been renewed. Note that theories of gravity with higher derivatives of field variables in the Lagrangian of the gravitational field (for example, f(R)-theories) have become very popular in the present. Note that on the basis of the laws of motion of charged matter considered in the article in the gauge theory of gravity, it is possible to successfully further investigate the laws of motion in other theories of gravity, which can be useful in various areas of theoretical and experimental physics.

A black hole solution of higher-dimensional Weyl–Yang–Kaluza–Klein theory

We consider the Weyl–Yang gauge theory of gravitation in a (4 + 3)-dimensional curved space-time within the scenario of the non-Abelian Kaluza–Klein theory for the source and torsion-free limits. The explicit forms of the field equations containing a new spin current term and the energy–momentum tensors in the usual four dimensions are obtained through the well-known dimensional reduction procedure. In this limit, these field equations admit (anti-)dyon and magnetic (anti-)monopole solutions as well as non-Einsteinian solutions in the presence of a generalized Wu–Yang ansatz and some specific warping functions when the extra dimensions associated with the round and squashed three-sphere S 3 are, respectively, included. The (anti-)dyonic solution has similar properties to those of the Reissner–Nordström–de Sitter black holes of the Einstein–Yang–Mills system. However, the cosmological constant naturally appears in this approach, and it associates with the constant warping function as well as the three-sphere radius. It is demonstrated that not only the squashing parameter ℓ behaves as the constant charge but also its sign can determine whether the solution is a dyon/monopole or an antidyon/antimonopole. It is also shown by using the power series method that the existence of nonconstant warping function is essential for finding new exact Schwarzschild-like solutions in the considered model.

Observational constraints in metric-affine gravity

We derive the main classical gravitational tests for a recently found vacuum solution with spin and dilation charges in the framework of Metric-Affine gauge theory of gravity. Using the results of the perihelion precession of the star S2 by the GRAVITY collaboration and the gravitational redshift of Sirius B white dwarf we constrain the corrections provided by the torsion and nonmetricity fields for these effects.

The problem of motion in gauge theories of gravity

In this article we consider the problem to what extent the motion of gauge-charged matter that generates the gravitational field can be arbitrary, as well as what equations are superimposed on the gauge field due to conditions of compatibility of gravitational field equations. Considered problem is analyzed from the point of view symmetry of the theory with respect to the generalized gauge deformed groups without specification of Lagrangians. In particular it is shown, that the motion of uncharged particles along geodesics of Riemannian space is inherent in an extremely wide range of theories of gravity and is a consequence of the gauge translational invariance of these theories under the condition of fulfilling equations of gravitational field. In the cause of gauge-charged particles, the Lorentz force, generalized for gauge-charged matter, appears in equations of motion as a consequence of the gauge symmetry of the theory under the condition of fulfilling equations of gravitational and gauge fields. In addition, we found relationships of equations for some fields that follow from the assumption about fulfilling of equations for other fields. At the end of the article there is an Appendix, which briefly describes the main provisions and facts from the theory of generalized gauge deformed groups and presents the main ideas of a single group-theoretical interpretation of gauge fields of both external (space-time) and internal symmetry, which is an alternative to their geometric interpretation.

Overview and perspectives on metric-affine gravity

The main purpose of this work is to give an overview of a generalization of the theory of general relativity, namely metric-affine gravity. We rederive an expression for the Lie derivative of the metric in the case of metric-affine theory and discuss some consequences of such an expression. As a gauge theory of gravitation it may be considered as an upshot of a gauging procedure of the general affine group, or its double covering. A historical approach of such a theory is also contained including the key results. One concludes with some perspectives on the calculation of topological observables in that theory viewed as topological gravity theory.

Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories

Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity.