Related papers: Conformal Symmetry, Accelerated Observers and Nonl…
A correlation between accelerated motion and a noncompact 5th dimension is proposed. The curvature invariants and the stress energy tensor in the bulk depend only on the 5th dimension $w$ and vanish asymptotically while the proper…
This work is devoted to the relativistic generalization of Chasles' theorem, namely to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the…
We describe the conformal symmetries of asymptotically flat spacetime. These represent an extension of the BMS group that we call the conformal BMS group. Its general features are discussed.
Using spacetime algebra, the geometric algebra of spacetime, the general problem of relativistic addition of velocities is addressed. The successive application of non-collinear Lorentz boosts is then studied in Minkowski spacetime. Even…
We use Generalized Fermi-Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We…
General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…
We discuss conformal issues of pure and extended teleparallel gravity. In particular, we present formulations of conformal transformation in teleparallel gravity. Furthermore, we propose conformal scalar and gauge field theories in…
This is the second of three papers on Conformal General Relativity (CGR). The conformal group is introduced here as the invariance group of the partial order of causal events in $n$D spacetime. Its general structure, discrete symmetries and…
When introducing special relativity, an elegant connection to familiar rules governing Galilean constant acceleration can be made, by describing first the discovery at high speeds that the clocks (as well as odometers) of different…
The measurement of an electromagnetic radiation field by a linearly accelerated observer is discussed. The nonlocality of this process is emphasized. The nonlocal theory of accelerated observers is briefly described and the consequences of…
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead…
We show that conformal transformations on the generalized Minkowski space $\mathbb{R}^{p,q}$ map hyperboloids and affine hyperplanes into hyperboloids and affine hyperplanes. We also show that this action on hyperboloids and affine…
We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as…
We prove that for a certain class of Lorentzian manifolds, namely causal spacetimes without observer horizons, conformal transformations can be classified into two types: escaping and non-escaping. This means that successive powers of a…
Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new…
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…
We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1+1 and 1+3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up…
We introduce an approach to compute the renormalisation group flow of relational observables in quantum gravity which evolve from their microscopic expressions towards the full quantum expectation value. This is achieved by using the…
A geometric framework for metrics of maximal acceleration which is applicable to large proper accelerations is discussed, including a theory of connections associated with the geometry of maximal acceleration. In such a framework it is…
Conformal transformations of the following kinds are compared: (1) conformal coordinate transformations, (2) conformal transformations of Lagrangian models for a D-dimensional geometry, given by a Riemannian manifold M with metric g of…