Related papers: Virial identities across the spacetime
Using a purely kinematical argument, the Borde-Guth-Vilenkin (BGV) theorem states that any maximal space-time with average positive expansion is geodesically incomplete, hence past eternal inflation would be necessarily singular. Recently,…
There are various types of global and local spacetime invariant in general relativity. Here I focus on the local invariants obtainable from the curvature tensor and its derivatives. The number of such invariants at each order of…
"The last remnant of physical objectivity of space-time" is disclosed in the case of a continuous family of spatially non-compact models of general relativity (GR). The {\it physical individuation} of point-events is furnished by the…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
We propose a simple, nonlocal modification to general relativity (GR) on large scales, which provides a model of late-time cosmic acceleration in the absence of the cosmological constant and with the same number of free parameters as in…
To capture important physical properties of a spacetime we construct a new diagram, the card diagram, which accurately draws generalized Weyl spacetimes in arbitrary dimensions by encoding their global spacetime structure, singularities,…
Braneworld cosmology supported by a bulk scalar field with an exponential potential is developed. A general class of separable backgrounds for both single and two-brane systems is derived, where the bulk metric components are given by…
We study past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant. These exact radiative solutions of Einstein's equations exist in the future of any sufficiently smooth initial data, and they…
The identities satisfied by two-dimensional chiral quantum fields are studied from the point of view of vertex algebras. The Cauchy-Jacobi identity (or the Borcherds identity) for three mutually local fields is proved and consequently a…
We show that (3+1) vacuum spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike…
Assuming Temporal and Configurational Relationalism, GR as Geometrodynamic's DeWitt supermetric alongside local Lorentzian Relativity with its universal finite maximum propagation speed arises as one of very few options from Feeding…
The well-known identity involving the expression presented in the above title is considered in Riemannian and in Euclidean space without restriction on the coordinate system adopted therein. The Riemann and Ricci tensors intrinsically…
Cosmic voids are becoming key players in testing the physics of our Universe. Here we concentrate on the abundances and the dynamics of voids as these are among the best candidates to provide information on cosmological parameters. Cai,…
We quantify the degree of nonlinearity and stochasticity of the clustering of biased objects, using cosmological N-body simulations. Adopting the peaks and the halos as representative biasing models, we focus on the two-point correlation of…
Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini. The theory predicts the existence of a…
In cognitive science and AI, a longstanding question is whether machines learn representations that align with those of the human mind. While current models show promise, it remains an open question whether this alignment is superficial or…
Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and…
Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplify solving the problem. We consider the Nonlinear…
Generative models of human identity and appearance have broad applicability to behavioral science and technology, but the exquisite sensitivity of human face perception means that their utility hinges on the alignment of the model's…
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…