Related papers: Non-Inertial Frames in Special and General Relativ…
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
We examine some common features of minimal surfaces, nonzero constant mean curvature surfaces and marginally outer trapped surfaces, concerning their stability and rigidity, and consider some applications to Riemannian geometry and general…
A review of selected topics in mathematical general relativity
General relativity provides an appropriate framework for addressing the issue of sub- or superluminality as an apparent effect. Even though a massless particle travels on the light cone, its average velocity over a finite path measured by…
Admitting non-Riemannian geometries, Double Field Theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in General Relativity with regular non-Riemannian geometries. The…
It is often assumed that the most general transformation between two inertial reference frames is affine linear in their Cartesian coordinates, an assumption which is however not true. We provide a complete derivation of the most general…
I review the conceptual, algebraical, and geometrical structure of Doubly Special Relativity. I also speculate about the possible relevance of DSR for quantum gravity phenomenology.
A critical discussion of our knowledge about extragalactic cosmic rays and magnetic fields is attempted. What do we know for sure? What are our prejudices? How do we confront our models with the observations? How can we assess the…
In this paper we scrutinize the concept of locally inertial reference frames (LIRF) in Lorentzian and Riemann-Cartan spacetime structures. We present rigorous mathematical definitions for those objects, something that needs preliminary a…
We describe a theory of gravitation on canonical noncommutative spacetimes. The construction is based on theta-twisted General Coordinate Transformations and Local Lorentz Invariance.
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
We will briefly review the definition and classification of classical and quantum singularities in general relativity. Examples of classically singular spacetimes that do not have quantum singularities will be given. We will present results…
We shortly review the state of art and perspectives of Extended Theories of Gravity.
This paper is a brief overview of a more extensive article recently published in Found. Phys. Lett. [2]. Apparent disagreement with experiment as well as internal inconsistencies found in the traditional analysis of relativistically…
Traditionally, the discussion about the geometrical interpretation of inertial forces is reserved for General Relativity handbooks. In these notes an analysis of the effect of such forces in a classical (newtonian) context is made, as well…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
The formalism of nonrelativistic quantum physics was originally considered in the context of inertial frames. Here, we report on a more general framework that includes noninertial frames and arbitrarily strong gravitational fields. We…