Related papers: Visualizing curved spacetime
For over a century Minkowskian spacetime has dominated discussions of space contraction and time dilation within special relativity. Brown and Pooley have called into question both the assumptions of Minkowski and the effects his presumed…
Simultaneity is a well-defined notion in special relativity once a Minkowski metric structure is fixed on the spacetime continuum (manifold) of events. In quantum gravity, however, the metric is not expected to be a fixed, classical…
It is proposed that spacetime should be regarded as an evolving block universe, bounded to the future by the present time, which continually extends to the future. This future boundary is defined at each time by measuring proper time along…
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…
We study the reparametrization invariant system of a classical relativistic particle moving in (5+1) dimensions, of which two internal ones are compactified to form a torus. A discrete physical time is constructed based on a quasi-local…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly…
We show that the 1+1 dimensional reduction (i.e., the radial plane) of the Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how features of this spacetime can be seen from the embedding diagram. The purpose of this…
Deformed relativistic kinematics have been considered as a way to capture residual effects of quantum gravity. It has been shown that they can be understood geometrically in terms of a curved momentum space on a flat spacetime. In this…
We generalize the notion of a dielectric analog Schwarzschild black hole model to analog models of arbitrary space-times; in particular, the approach is not restricted to static space-times. This is done by establishing a correspondence…
A classical dynamical system in a four-dimensional Euclidean space with universal time is considered. The space is hypothesized to be originally occupied by a uniform substance, pictured as a liquid, which at some time became supercooled.…
In this note, we use isothermic coordinate systems to explore global properties of space-like surfaces with constant mean curvature in the Lorentz-Minkowski three-space.
The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
A generalization of the notion of ellipsoids to curved Riemannian spaces is given and the possibility to use it in describing the shapes of rotating bodies in general relativity is examined. As an illustrative example, stationary,…
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry,…
Analogue spacetimes, (and more boldly, analogue models both of and for gravity), have attracted significant and increasing attention over the last decade and a half. Perhaps the most straightforward physical example, which serves as a…
I provide a prescription to define space, at a given moment, for an arbitrary observer in an arbitrary (sufficiently regular) curved space-time. This prescription, based on synchronicity (simultaneity) arguments, defines a foliation of…
Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the…
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic…
Gravity simulators are laboratory systems where small excitations like sound or surface waves behave as fields propagating on a curved spacetime geometry. The analogy between gravity and fluids requires vanishing viscosity, a feature…