Related papers: Potentials for transverse trace-free tensors
It is well known that Einstein General Relativity can be expressed covariantly in bi-metric spacetime, without the uncertainties which arise from the effects of gravitational energy-momentum pseudo-tensors. However the effect that the…
The correspondence between stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples…
The correspondence of stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in…
The transverse traceless spin-two tensor harmonics on $S^3$ and $H^3$ may be denoted by $T^{(kl)}{}_{ab}$. The index $k$ labels the (degenerate) eigenvalues of the Laplacian $\square$ and $l$ the other indices. We compute the bitensor…
Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators and apply it to problems closely related to classifying…
We obtain a local two weight $Tb$ theorem with an energy side condition for higher dimensional fractional Calder\'{o}n-Zygmund operators. The proof follows the general outline of the proof for the corresponding one-dimensional $Tb$ theorem…
We consider a scalar-tensor theory of gravitation with the scalar source being the trace of the stress-energy tensor of the scalar field itself and matter. We obtain an example of a numerical solution of the cosmological equations which…
We study the dynamical description of scalar-tensor gravity by performing the best-fit analysis for two cases of exponential and power-law form of the potential and scalar field function coupled to the curvature. The models are then tested…
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…
We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini…
A scalar--tensor theory of gravity, containing an arbitrary coupling function $F(\phi)$ and a general potential $V(\phi)$, is considered in the context of a spatially flat FLRW model. The use of reparametrization invariance enables a…
We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat…
We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers,…
In the present work we study a concrete model of Scalar--Tensor theory of gravity characterized by two free parameters, and compare its predictions against observational data and constraints coming from supernovae, solar system tests as…
We present the coupling of the torsion scalar $T$ and the trace of energy-momentum tensor $\mathcal{T}$, which produces new modified $f(T,\mathcal{T})$ gravity. Moreover, we consider the functional form $f(T,\mathcal{T}) =\alpha…
We report a significant finding in Quintessence theory that the the scalar fields with tracker potentials have a model-independent scaling behaviour in the expanding universe. So far widely discussed exponential,power law or hyperbolic…
Determining the most general, consistent scalar tensor theory of gravity is important for building models of inflation and dark energy. In this work we investigate the number of degrees of freedom present in the theory of beyond Horndeski.…
We study a modification of the Plebanski action, which generically corresponds to a bi-metric theory of gravity, and identify a subclass which is equivalent to the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories. In this manner,…