Related papers: Continuity equations for general matter: applicati…
We complete the program of spectral geometry, in the sense that we show that a manifold's shape, i.e., its metric, can be reconstructed from its resonant sound when tapped lightly, i.e., from its spectrum, -- if in addition we also record…
Within the cosmic screening approach, we obtain the exact formulas for the velocity-independent gravitational potentials produced by matter in the form of discrete sources distributed in the open and closed Universes. These formulas…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
It is pointed out that quantum vacuum fluctuations may give rise to a curvature of space-time equivalent to the curvature currently attributed to dark energy. A simple calculation is made, which suggests that the value of the dark energy…
This report offers a modern perspective on the problem of negative energy, based on a re-examination of the concept of time direction as it arises in a classical and quantum-mechanical context. From this analysis emerges an improved…
Theories with a curved momentum space, which became recently of interest in the quantum-gravity literature, can in general violate many apparently robust aspects of our current description of the laws of physics, including relativistic…
We explore the well know mass deficit/surplus phenomenon in General Relativity to suggest that it could play a part in the dark matter conundrum. Specifically in collapses and condensations of matter associated with negative intrinsic…
In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite…
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without…
A long-standing topic of interest in the general theory of relativity is the embedding of curved spacetimes in higher-dimensional flat spacetimes. The main purpose this paper is to show that the embedding theory can account for the…
Astrophysical observations are pointing out huge amounts of dark matter and dark energy needed to explain the observed large scale structures and cosmic accelerating expansion. Up to now, no experimental evidence has been found, at…
The new uncertainty relation is derived in the context of the canonical quantum theory with gravity for the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities which determine…
Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its…
General relativity is incomplete because it cannot describe quantum effects of space-time. The complete theory of quantum gravity is not yet known and to date no observational evidence exists that space-time is quantized. However, in most…
We construct a theory of particles moving in curved both momentum space and spacetime, being a generalization of Relative Locality. We find that in order to construct such theory, with desired symmetries, including the general coordinate…
We consider General Relativity with matter and radiation, one of these fluids being coupled to vacuum. We find that Universe dynamics starts by an inflation phase if the coupled fluid has a negative energy density at early time. Then, there…
The fact that the energy densities of dark energy and matter are similar currently, known as the coincidence problem, is one of the main unsolved problems of cosmology. We present here a model in which a spatial curvature of the universe…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying $p=\gamma \rho$ ($0\leq \gamma \leq 1$), where $\gamma=1$ represents a stiff or Zeldovich fluid. Using…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…