Related papers: Spectral geometry of spacetime
The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time…
What if physics is just the way we perceive geometry? That is, what if geometry and physics will one day become one and the same discipline? I believe that will mean we will at last really understand physics, without postulates other than…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
Starting with a `bare' 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density…
Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the…
Rather than an a priori arena in which events take place, space-time is a construction of our mind making possible a particular kind of ordering of events. As quantum entanglement is a property of states independent of classical distances,…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon surface in an arbitrary space-time. A photon sphere is then defined as an SO(3)xR-invariant photon surface in a static spherically symmetric…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
We introduce a new type of the spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired $Spin(3,1)$ worldsheet action. Because of its…
It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
Among the many disparate approaches towards quantum gravity, the reduction of spacetime dimension in the ultraviolet regime is expected to be a common thread. The dimensionality of spacetime can be defined in various contexts. The spectral…
We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
In this article we discuss a few aspects of the space-time description of fields and particles. In sectionn II and III we demonstrate that fields are as fundamental as particles. In section IV we discuss non-equivalence of the Schwarzschild…
Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make…
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a…
Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To…