Constraining [formula omitted] gravity by dynamical system analysis

The Palatini formalism, which assumes the metric and the affine connection as independent variables, is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, as done in the usual teleparallel theories, but we follow a completely covariant approach by imposing the constraints with suitable Lagrange multipliers. For a general quadratic theory we show how torsion naturally propagates and we reproduce the Teleparallel Equivalent of General Relativity as a particular quadratic action that features an additional Lorentz symmetry. We then study the much less explored theories formulated in a geometry with neither curvature nor torsion, so that all the geometrical information is encoded in the non-metricity. We discuss how this geometrical framework leads to a purely inertial connection that can thus be completely removed by a coordinate gauge choice, the coincident gauge. From the quadratic theory we recover a simpler formulation of General Relativity in the form of the Einstein action, which enjoys an enhanced symmetry that reduces to a second linearised diffeomorphism at linear order. More general theories in both geometries can be formulated consistently by taking into account the inertial connection and the associated additional degrees of freedom. As immediate applications, the new cosmological equations and their Newtonian limit are considered, where the role of the lapse in the consistency of the equations is clarified, and the Schwarzschild black hole entropy is computed by evaluating the corresponding Euclidean action. We discuss how the boundary terms in the usual formulation of General Relativity are related to different choices of coordinates in its coincident version and show that in isotropic coordinates the Euclidean action is finite without the need to introduce boundary or normalisation terms. Finally, we discuss the double-copy structure of the gravity amplitudes and the bootstrapping of gravity within the framework of coincident General Relativity.

The teleparallel equivalent of general relativity (TEGR) is an alternative formulation of Einstein's equations in the framework of Riemann-Cartan spacetimes. The gravitational field can be described either by the curvature of the torsion-free connection of general relativity (GR) or by the torsion of the curvature-free connection of the TEGR. Both in GR and TEGR the freedom in the choice of coordinates gives rise to the equivalence problem of deciding whether two solutions of the field equations are the same. This problem is solved by means of a invariant description of the gravitational field. We investigate whether the equivalence between GR and TEGR also holds at the level of these invariant descriptions. We show that the GR description assures equivalence in TEGR only in very special situations. These results are illustrated on teleparallel spacetimes with torsion and Gödel metric.

A simple method is shown to demonstrate that the teleparallel equivalent of general relativity can be generalized to the Weyl-invariant models. We will also show explicitly that Weyl symmetry is preserved step by step throughout the 5D Kaluza-Klein dimensional-reduction process. As a result, the dimensional reduced model will be shown to be a theory with two scalar fields. When a symmetry-breaking potential is introduced, a strong constraint will effectively turn off one of the scalar fields. For heuristic reasons, the stability properties of the power-law solution associated with the resulting one-scalar-field model will be presented explicitly. In particular, all stable modes can be solved explicitly as functions of the free parameter associated with the symmetry-breaking potential.

Big Bang nucleosynthes describes a significant process in the early universe, responsible for the formation of light nuclei a while after the Big Bang explosion. Its sensitivity to the expansion rate makes BBN an effective probe for testing deviations from standard cosmology, particularly within the framework of modified theories of gravity. In this article, we investigate the evolution of the Universe through Big Bang nucleosynthesis within the framework of f ( T , B , T G , B G ) gravity. Here, T , B , T G and B G correspond to the torsion, boundary term, teleparallel Gauss-Bonnet term, and Gauss-Bonnet boundary term, respectively. To explore the deviation from the teleparallel equivalent of general relativity, we apply the transformation f ( T , B , T G , B G ) = − T + F ( T , B , T G , B G ) . For an in-depth analysis of the Big Bang nucleosynthesis, we choose five distinct models from gravity and compared the results with the observational limits on | Δ T f T f | to examine restrictions on the free parameters associated with these models. Our outcomes indicate that f ( T , B , T G , B G ) gravity can agree with the constraint of big bang nucleosynthesis, and hence build a valid view of the universe. Moreover, we take the limiting cases of the assumed theory, that is, f ( T , B ) and f ( T ) theories, which also ensure consistency with BBN data.

Realism about general relativity (GR) seems to imply realism about spacetime curvature. The existence of the teleparallel equivalent of general relativity (TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat spacetime, and (b) TEGR is empirically equivalent to GR. Knox (Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 42(4):264–275, 2011) claims that there is no genuine underdetermination between GR and TEGR; we call this verdict into question by isolating and addressing her individual arguments. In addition, we anticipate and evaluate two further worries for realism about the torsionful spacetimes of TEGR, which we call the ‘problem of operationalisability’ and the ‘problem of visualisability’.

The so-called Geometric Trinity of Gravity includes General Relativity (GR), based on spacetime curvature; the Teleparallel Equivalent of GR (TEGR), which relies on spacetime torsion; and the Symmetric Teleparallel Equivalent of GR (STEGR), grounded in nonmetricity. Recent studies demonstrate that GR, TEGR, and STEGR are dynamically equivalent, raising questions about the fundamental structure of spacetime, the under-determination of these theories, and whether empirical distinctions among them are possible. The aim of this work is to show that they are equivalent in many features but not exactly in everything. In particular, their relationship with the Equivalence Principle (EP) is different. The EP is a deeply theory-laden assumption, which is assumed as fundamental in constructing GR, with significant implications for our understanding of spacetime. However, it introduces unresolved conceptual issues, including its impact on the nature of the metric and connection, its meaning at the quantum level, tensions with other fundamental interactions and new physics, and its role in dark matter and dark energy problems. In contrast, TEGR and STEGR recover the EP, in particular in its strong formulation, but do not rely on it as a foundational principle. The fact that GR, TEGR, and STEGR are equivalent in non-trivial predictions, but the EP is not necessary for TEGR and STEGR, suggests that it may not be a fundamental feature but an emergent one, potentially marking differences in the empirical content of the three theories. Thus, the developments within the Geometric Trinity framework challenge traditional assumptions about spacetime and may help to better understand some of the unresolved foundational difficulties related to the EP.

In this paper, we find new scalarized black holes by coupling a scalar field with the Gauss-Bonnet invariant in teleparallel gravity. The teleparallel formulation of this theory uses torsion instead of curvature to describe the gravitational interaction, and it turns out that, in this language, the usual Gauss-Bonnet term in four dimensions decays in two distinct boundary terms, the teleparallel Gauss-Bonnet invariants. Both can be coupled individually or in any combination to a scalar field, to obtain a teleparallel Gauss-Bonnet extension of the teleparallel equivalent of general relativity. The theory we study contains the familiar Riemannian Einstein-Gauss-Bonnet gravity theory as a particular limit and offers a natural extension, in which scalarization is triggered by torsion and with new interesting phenomenology. We demonstrate numerically the existence of asymptotically flat scalarized black hole solutions and show that, depending on the choice of coupling of the boundary terms, they can have a distinct behavior compared to the ones known from the usual Einstein-Gauss-Bonnet case. More specifically, nonmonotonicity of the metric functions and the scalar field can be present, a feature that was not observed until now for static scalarized black hole solutions.

In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying both torsion and non-metricity. We provide a detailed discussion on the teleparallel equivalents of General Relativity and how the two known equivalents, formulated on Weitzenböck and symmetric teleparallel geometries respectively, can be interpreted as two gauge-fixed versions of the general teleparallel equivalent. We then explore the viability of the general quadratic theory by studying the spectrum around Minkowski. The linear theory generally contains two symmetric rank-2 fields plus a 2-form and, consequently, extra gauge symmetries are required to obtain potentially viable theories.

A theory of (N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity (TEGR). The fundamental gravitational field variables are the (N+1)-dimensional vector fields, defined globally on a manifold M, and the gravitational field is attributed to the torsion. The form of Lagrangian density is quadratic in torsion tensor. We then give an exact five-dimensional spherically symmetric solution (Schwarzschild (4+1)-dimensions). Finally, we calculate energy and spatial momentum using gravitational energy—momentum tensor and superpotential 2-form.

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity (TEGR). A spacetime which is not asymptotically flat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.

The assumption that matter charges and currents could generate fields, which are called, in analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dating from the origins of General Relativity (GR). On the other hand, the Teleparallel Equivalent of GR (TEGR), as a gauge theory, seems to be the ideal scenario to define these fields, based on the gauge field strength components. The purpose of the present work is to investigate the nature of the gravitational electric and magnetic fields in the context of the TEGR, where the tetrad formalism on which it is based seems more suited to deal with phenomena related to observers. As its applications, we have studied the gravito-electromagnetic fields for the Schwarzschild solution and for the geometry produced by a spherical rotating shell in slow motion and weak field regime. The expressions obtained, at the linear regime, are very similar to those of electromagnetism.

A space of kinematic quantum states for the Teleparallel Equivalent of General Relativity is constructed by means of projective techniques. The states are kinematic in this sense that their construction bases merely on the structure of the phase space of the theory and does not take into account constraints on it. The space of quantum states is meant to serve as an element of a canonical background independent quantization of the theory.

We analyze the cosmological solutions of f(T, B) gravity using dynamical system analysis where T is the torsion scalar and B be the boundary term scalar. In our work, we assume three specific cosmological models. For first model, we consider f(T,B)=f_{0}(B^{k}+T^{m}), where k and m are constants. For second model, we consider f(T,B)=f_{0}T B, for third model, we consider f(T,B)=alpha T^{2}. We generate an autonomous system of differential equations for each models by introducing new dimensionless variables. To solve this system of equations, we use dynamical system analysis. We also investigate the critical points and their natures, stability conditions and their behaviors of Universe expansion. For first and second models, we get two stable critical points, while for third model we get one stable critical point. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. For these three models, we evaluated density parameters such as Omega _{r}, Omega _{m}, Omega _{Lambda } and omega _{eff} and deceleration parameter (q) and find their suitable range of the parameter lambda for stability. For first model, we get omega _{eff}=-0.833,-0.166 and for second model, we get omega _{eff}=-frac{1}{3}. This shows that both the models are in quintessence phase. For third model we get accelerated expansion of the Universe. Further, we compare the values of EoS parameter and deceleration parameter with the observational values.

Interval dynamic response analysis of vehicle-bridge interaction system with uncertainty

This paper provides a comprehensive analysis of the impact of wind farm integration on the stability of an electrical power system, with a particular focus on the dynamic effects induced by wind power during severe system disturbances. The primary objective is to evaluate how wind power integration influences system behavior, particularly under fault conditions. The research utilized the IEEE 9-bus test system, which consists of three generators and nine buses, as a reference benchmark for the stability analysis. Simulations and modeling were performed using PSAT (Power System Analysis Toolbox), a robust tool for static, dynamic, and control analysis of power systems, integrated with Matlab. The study specifically investigated the effects of a three-phase short circuit, representing a significant system disturbance. The dynamic analysis was structured into three phases: pre-fault, fault, and post-fault, to capture the complete impact on system behavior. The results provided valuable insights into critical electrical and electromechanical variables, shedding light on the role of wind farms in maintaining the stability of the power grid, with particular emphasis on the transmission network's resilience and response to disturbances. This work offers a deeper understanding of the integration of renewable energy sources in enhancing grid stability during extreme events.