Related papers: Geometric formulation of generalized root-$T\bar{T…

Theory of gravity is considered in the Regge-Teitelboim approach in which the pseudo-Riemannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of…

Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…

In this paper, we present our study on the $T\bar{T}$-deformation of non-relativistic complex scalar field theory. We find the closed form of the deformed Lagrangian by using the perturbation and the method of characteristics. Furthermore…

Here (the last paper in a series of four) we end our presentation of the basics of a systematical approach to the differential geometry of a smooth manifold M (supporting a metric field g and a general connection del) which uses the…

Double field theory provides T-duality covariant generalized tensors that are natural extensions of the scalar and Ricci curvatures of Riemannian geometry. We search for a similar extension of the Riemann curvature tensor by developing a…

Perturbation of gravitational fields may be decomposed into scalar,vector and tensor components.In this paper we concern with the evolution of tensor mode perturbations in a spatially closed deSitter background of RW form. It may be thought…

We rewrite the recently derived cubic action of Double Field Theory on group manifolds [arXiv:1410.6374] in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field…

In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wide variety of astrophysical scales. Through…

Generalized Kerr-Schild nilpotent deformations of an arbitrary background spacetime $\overline{g}_{\m\n}(x)$ are considered. Those are of the form $\overline{g}_{\m\n}+l_\m l_\n$ with $l^2=0$. The relationship between the Ricci tensor of…

This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…

We study the $T\bar{T}$ deformation of the chiral bosons and show the equivalence between the chiral bosons of opposite chiralities and the scalar fields at the Hamiltonian level under the deformation. We also derive the deformed Lagrangian…

Generalized dilaton gravity in 2d is the most general consistent deformation of the Jackiw-Teitelboim model that maintains local Lorentz invariance. The action is generically not power-counting renormalizable, thus going beyond the class of…

We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a…

We extend the geometrical ideas of the spacetime deformations to study the physical foundation of the post-Riemannian geometry. To this aim, we construct the theory of 'two-step spacetime deformation' as a guiding principle. We address the…

We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that in…

We generalize previous work by considering a novel gravitational model with an action given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field and a kinetic term constructed from the gradients of the…

Integrable deformations of type IIB superstring theory on $\mathrm{AdS}_5\times S^5$ have played an important role over the last years. The Yang-Baxter deformation is a systematic way of generating such integrable deformations. Since its…

The aim of this paper is to generalize the definition of complexity for the static self-gravitating structure in $f(R,T,Q)$ gravitational theory, where $R$ is the Ricci scalar, $T$ is the trace part of energy momentum tensor and $Q\equiv…

We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, $f(T,\phi)$, thus encompassing the cases of $f(T)$ gravity and nonminimally coupled…

Using the cosmological perturbation theory in terms of the delta-N formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a…