Perspectives of perihelion precession in torsion modified gravity

Killing symmetries are revisited in [Formula: see text] bulk geometric torsion (GT) perturbation theory to investigate the perihelion precession. Computation reveals a nonperturbative (NP) modification to the precession known in General Relativity (GR). Remarkably the analysis reassures our proposed holographic correspondence between a perturbative GT in bulk and a boundary GR coupled to [Formula: see text]. In fact, the topological correction is sourced by a non-Newtonian potential in GR and we identify it with an “electro-gravito” (EG) dipole. Interestingly, the dipole correction is shown to possess its origin in a [Formula: see text]-form underlying a propagating GT and leads to a NP gravity in [Formula: see text].

Aspects of gravitational wave/particle duality: Bulk torsion ↔boundary gravity correspondence

A geometric torsion (GT) underlying a [Formula: see text]-form in a [Formula: see text]-dimensional [Formula: see text] gauge theory is revisited with a renewed perspective for a nonperturbation (NP) gravity in [Formula: see text]. In this context, we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a [Formula: see text] coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is identified as a mass dipole and is shown to be sourced by a propagating GT. A detailed analysis is performed in a bulk GT to show a modification to the precession of perihelion in a boundary NP gravity. The perspective of an electromagnetic (EM) wave in the bulk is investigated to reveal a spin [Formula: see text] (mass-less) quantum sourced by an apparent 2-form. A Goldstone scalar is absorbed by the apparent 2-form to describe a massive [Formula: see text]-form in the coulomb gauge. Alternately a Goldstone scalar together with a local degree of GT and 2-form is argued to govern a composite (mass-less) spin [Formula: see text] particle in Lorentz gauge. Both the scenarios, further ensure a graviton in a boundary NP gravity. A qualitative analysis reveals a (noninteracting) graviton underlying a plausible gravitational wave/particle duality in NP gravity.

Nonholonomic jet deformations, exact solutions for modified Ricci soliton and Einstein equations

Let [Formula: see text] be a pseudo-Riemannian metric of arbitrary signature on a manifold [Formula: see text] with conventional [Formula: see text]-dimensional splitting, [Formula: see text] determined by a nonholonomic (nonintegrable) distribution [Formula: see text] defining a generalized (nonlinear) connection and associated nonholonomic frame structures. We work with an adapted linear metric compatible connection [Formula: see text] and its nonzero torsion [Formula: see text], both completely determined by [Formula: see text]. Our first goal is to prove that there are certain generalized frame and/or jet transforms and prolongations with [Formula: see text] into explicit classes of solutions of some generalized Einstein equations [Formula: see text], [Formula: see text], encoding various types of (nonholonomic) Ricci soliton configurations and/or jet variables and symmetries. The second goal is to solve additional constraint equations for zero torsion, [Formula: see text], on generalized solutions constructed in explicit forms with jet variables and extract Levi-Civita configurations. This allows us to find generic off-diagonal exact solutions depending on all space time coordinates on [Formula: see text] via generating and integration functions and various classes of constant jet parameters and associated symmetries. Our third goal is to study how such generalized metrics and connections can be related by the so-called “half-conformal” and/or jet deformations of certain subclasses of solutions with one, or two, Killing symmetries. Finally, we present some examples of exact solutions constructed as nonholonomic jet prolongations of the Kerr metrics, with possible Ricci soliton deformations, and characterized by nonholonomic jet structures and generalized connections.

Killing symmetries as Hamiltonian constraints

The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time, while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.

Locally rotationally symmetric Bianchi type I cosmology in f(R) gravity

This manuscript is devoted to investigating a Bianchi type I universe in the context of f(R) gravity. For this purpose, we explore the exact solutions of locally rotationally symmetric Bianchi type I space–time in the metric version of f(R) gravity. The modified field equations are solved by assuming the expansion scalar θ to be proportional to the shear scalar σ, which gives A = Bn, where A and B are the metric coefficients, and n is an arbitrary constant. In particular, three solutions have been found and corresponding Killing symmetries are calculated in each case.

A geometric method of constructing exact solutions in modified f(R, T)-gravity with Yang–Mills and Higgs interactions

We show that geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in f(R, T)-modified gravity for systems of gravitational-Yang–Mills–Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein–Yang–Mills–Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. Some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed.