Related papers: Light cones in relativity: Real, complex and virtu…
The motion of particles on spherical $1 + 3$ dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this…
In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
Some well-known Lorentzian concepts are transferred into the more general setting of cone structures, which provide both the causality of the spacetime and the notion of cone geodesics without making use of any metric. Lightlike…
Spin networks, the quantum states of discrete geometry in loop quantum gravity, are directed graphs whose links are labeled by irreducible representations of SU(2), or spins. Cosmic strings are 1-dimensional topological defects carrying…
The $f(R)$ gravity models formulated in Einstein conformal frame are equivalent to Einstein gravity together with a minimally coupled scalar field. The scalar field couples with the matter sector and the coupling term is given by the…
In order to extend our approach based on SU$*$(4), we were led to (real) projective and (line) Complex geometry. So here we start from quadratic Complexe which yield naturally the 'light cone' $x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{0}^{2}=0$…
We present a new gauge for asymptotically flat spacetime that can treat future and past null infinities ($\mathscr{I}^{+}$ or $\mathscr{I}^{-}$) democratically. Our gauge is complementary to Bondi and Ashtekar-Hansen gauges, and is adapted…
We construct gravitational backgrounds dual to a family of field theories parameterized by a relevant coupling. They combine a non-trivial scalar field profile with a naked singularity. The naked singularity is necessary to preserve Lorentz…
We present a turnkey solution, ready for implementation in numerical codes, for the study of linear structure formation in general scalar-tensor models involving a single universally coupled scalar field. We show that the totality of…
A theory is developed to describe the nonlocal effect of spacetime quantization on position measurements transverse to macroscopic separations. Spacetime quantum states close to a classical null trajectory are approximated by plane…
Support material for lectures at the May '25 Galileo Galilei Institute school on asymptotic sym- metries and flat holography. Contains an introduction to Noether theorem for gauge theories and gravity, covariant phase space formalism,…
In this lecture I summarize recent developments on strings propagating in curved spacetime. Exact conformal field theories that describe gravitational backgrounds such as black holes and more intricate gravitational singularities have been…
The null-surface formulation of general relativity -- recently introduced -- provides novel tools for describing the gravitational field, as well as a fresh physical way of viewing it. The new formulation provides ``local'' observables…
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…
In this work, we study linearised gravitational fields on the entire Minkowski space-time including space-like infinity. The generalised conformal field equations linearised about a Minkowski background are utilised for this purpose. In…
This article gives a review of a recent construction, the ambient cosmological metric, and its implications for the global geometry of the universe. According to this proposal, the universe is a bounding hypersurface carrying a conformal…
We consider convex spacelike polyhedra oriented in Minkowski space. These are the classical analogues of spinfoam intertwiners. We point out a parametrization of these shapes using null face normals, with no constraints or redundancies. Our…
We present a twistor description for null two-surfaces (null strings) in 4D Minkowski space-time. The Lagrangian density for a variational principle is taken as a surface-forming null bivector. The proposed formulation is reparametrization…
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of…