A complementary covariant approach to gravito-electromagnetism

From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor equations of motion, the gravitational continuity equation, the conservation of the energy, the energy-momentum tensor, the field tensor, and the constraints concerning these fields. The Lagrangian formulation is also exhibited as an unified and simple formulation that will be useful for future investigation.

On the calculation of covariant expressions for Dirac bilinears

In this article, various approaches to calculate covariant expressions for the bilinears of Dirac spinors are presented. For this purpose, algebraic equations defining Dirac spinors are discussed. Following that, a covariant approach for spacetime parameterization is presented and the equations defining Dirac spinors are written fully in terms of Lorentz scalars. After presenting how the tensorial bilinears can be reduced to combinations of scalar bilinears with appropriate Lorentz structures, a covariant recipe for the calculation of scalar bilinears is provided.

1 + 3 covariant perturbations in power-law f(R) gravity

We applied the 1+3 covariant approach around the Friedmann–Lemaître–Robertson–Walker (FLRW) background, together with the equivalence between f(R) gravity and scalar-tensor theory to study cosmological perturbations. We defined the gradient variables in the 1 + 3 covariant approach which we used to derive a set of evolution equations. Harmonic decomposition was applied to partial differential equations to obtain ordinary differential equations used to analyse the behavior of the perturbation quantities. We focused on dust dominated area and the perturbation equations were applied to background solution of $$\alpha R+\beta R^{n}$$ α R + β R n model, n being a positive constant. The transformation of the perturbation equations into redshift dependence was done. After numerical solutions, it was found that the evolution of energy-density perturbations in a dust-dominated universe for different values of n decays with increasing redshift.

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.

On multifluid perturbations in scalar–tensor cosmology

In this paper, the scalar–tensor theory is applied to the study of perturbations in a multifluid universe, using the [Formula: see text] covariant approach. Both scalar and harmonic decompositions are instituted on the perturbation equations. In particular, as an application, we study perturbations on a background Friedmann-Robertson-Walker (FRW) cosmology consisting of both radiation and dust in the presence of a scalar field. We consider both radiation-dominated and dust-dominated epochs, respectively, and study the results. During the analysis, quasi-static approximation is instituted. It is observed that the fluctuations of the energy density decrease with increasing redshift, for different values of [Formula: see text] of a power-law [Formula: see text] model.

Duality rules for more mixed-symmetry potentials

$T$ - and $S$-duality rules among the gauge potentials in type II supergravities are studied. In particular, by following the approach of [J. J. Fernández-Melgarejo et al., arXiv:1909.01335], we determine the $T$- and $S$-duality rules for certain mixed-symmetry potentials, which couple to supersymmetric branes with tension $T\propto g_s^{-n}$ ($n\leq 4$). Although the $T$-duality rules are rather intricate, we find a certain redefinition of potentials which considerably simplifies the duality rules. After the redefinition, potentials are identified with components of the $T$-duality-covariant potentials, which have been predicted by the $E_{11}$ conjecture. Since our approach is based on $U$-duality, we can also determine the 11D uplifts of the mixed-symmetry potential, unlike the $T$-duality-covariant approach known in the literature. We also study the field strengths of the mixed-symmetry potentials.