Related papers: Metric-Affine Manifold
A relativistic theory constructed on Riemann-Cartan manifold with a derived totally antisymmetric torsion is proposed. It follows the coincidence of the autoparallel curve and metric geodesic. The totally antisymmetric torsion naturally…
We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on…
This is a significantly improved version with new applications. We show that there are many cohomogeneity one manifolds which do not admit an analytic invariant metric with non-negative sectional curvature, although they do have a smooth…
Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor…
Here we treat the problem: given a torsion-free connection do its geodesics, as unparametrised curves, coincide with the geodesics of an Einstein metric? We find projective invariants such that the vanishing of these is necessary for the…
We review the notion of shape tensor of an embedded manifold, which efficiently combines intrinsic and extrinsic geometry, and allows for intuitive understanding of some basic concepts of classical differential geometry, such as parallel…
We consider a class of models in the framework of metric-affine gravity and establish their correspondence to the bosonic sector of a class of no-scale supergravity models. The excellent inflationary behavior of the gravitational models…
We reformulate Einstein's theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first…
We give a new characterisation of the unparametrised geodesics, or distinguished curves, for affine, pseudo-Riemannian, conformal, and projective geometry. This is a type of moving incidence relation. The characterisation is used to provide…
We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding…
We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in…
Neutral particles can be guided and focussed using electric field gradients that focus in one transverse direction and defocus in the other, alternating between the two directions. Such a guide is suitable for transporting particles that…
We study the number of propagating degrees of freedom, at non-linear order, in torsion gravity theories, a class of modified theories of gravity that include a propagating torsion in addition to the metric. We focus on a three-parameter…
We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different Riemann-Cartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant…
For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas…
Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only…
Effects manifesting quantum geometry have been a focus of physics research. Here, we reveal that quantum metric plays a crucial role in nonlinear electric spin response, leading to a quantum metric spin-orbit torque. We argue that enhanced…
The purely affine, metric-affine and purely metric formulation of general relativity are dynamically equivalent and the relation between them is analogous to the Legendre relation between the Lagrangian and Hamiltonian dynamics. We show…
The polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the…
This article starts with the mathematical definition, concrete description, and physical meaning of Cartan's torsion. I proceed with the argumentation that torsion is required for the description of intrinsic spin. Moreover I argue that the…