Related papers: Minimal Length and Small Scale Structure of Spacet…

Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a…

It has recently been argued that if spacetime $\mathcal M$ possesses non-trivial structure at small scales, an appropriate semi-classical description of it should be based on non-local bi-tensors instead of local tensors such as the metric…

A recently developed tool allows for a description of spacetime as a manifold with a Lorentz-invariant (lower) limit length built-in. This is accomplished in terms of geometric quantities depending on two spacetime events (bitensors) and…

We consider spacetime endowed with a zero-point length, i.e. with an effective metric structure which allows for a (quantum-mechanically arising) finite distance $L_0$ between events in the limit of their coincidence. Restricting attention…

All our observations that characterise space and time are expressed in terms of non-local, bi-tensorial objects such as geodesic intervals between events and two-point (Green) functions. In this contribution, I highlight the importance of…

The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by…

The physical origin of spacetime discreteness remains a central open problem in quantum gravity, with most existing approaches relying on specific microscopic structures or model-dependent assumptions. In this letter, spacetime discreteness…

The minimal requirement for cosmography - a nondynamical description of the universe - is a prescription for calculating null geodesics, and timelike geodesics as a function of their proper time. In this paper, we consider the most general…

In this paper, we consider a specific model, implementing the existence of a fundamental limit distance $L_0$ between (space or time separated) points in spacetime, which in the recent past has exhibited the intriguing feature of having a…

We question the emergence of a minimal length in quantum spacetime, comparing two notions that appeared at various points in the literature: on the one side, the quantum length as the spectrum of an operator L in the Doplicher Fredenhagen…

We study the recently reported qmetric (or zero-point-length) expressions of the Ricci (bi)scalar $R_{(q)}$ (namely, expressions of the Ricci scalar in a spacetime with a limit length $L_0$ built in), focusing specifically on the case of…

It is generally believed that any quantum theory of gravity should have a generic feature --- a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such…

We investigate the quantum structure of spacetime at fundamental scales via a novel, Lorentz-invariant noncommutative coordinate framework. Building on insights from noncommutative geometry, spectral theory, and algebraic quantum field…

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…

Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…

For a mapping $f\colon X\to Y$ between metric spaces the function $\text{lip} f\colon X\to[0,\infty]$ defined by $\text{lip} f(x)=\liminf_{r\to0}\frac{\text{diam} f(B(x,r))}{r}$ is termed the lower scaled oscillation or little lip function.…

Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, function of the point $P$ and the vector…

In this article, we prove that for a definable set in an o-minimal structure with connected link (at 0 or infinity), the inner distance of the link is equivalent to the inner distance of the set restricted to the link. With this result, we…

Local conformal symmetry is usually considered to be an approximate symmetry of nature, which is explicitly and badly broken. Arguments are brought forward here why it has to be turned into an exact symmetry that is spontaneously broken. As…

We argue that the minimal length discretization generalizing the Heisenberg uncertainty principle, in which the gravitational impacts on the non--commutation relations are thoughtfully taken into account, radically modifies the spacetime…