Related papers: Spectral geometry of spacetime
It is suggested, that a curved 4-dimensional space-time manifold is a strained elastic plate in multidimensional embedding space-time. Its thicknesses along extradimensions are much less than 4-dimensional sizes. Reduced 4-dimensional free…
Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working…
We present the notion of temporal Lorentzian spectral triple which is an extension of the notion of pseudo-Riemannian spectral triple with a way to ensure that the signature of the metric is Lorentzian. A temporal Lorentzian spectral triple…
One of the deepest insights from the general theory of relativity is the relational nature of spacetime. While it is a generally agreed on that the nature of spacetime must be drastically different at the Planck scale, it has been a common…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
We propose a formulation of the holographic principle, suitable for a background independent quantum theory of cosmology. It is stated as a relationship between the flow of quantum information and the causal structure of a quantum…
In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum…
Sufficient conditions for the well-posedness of the initial value problem for the scalar wave equation are obtained in space-times with hypersurface singularities
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously…
The nature of the change in perspective that accompanies the proposal of a unified physical theory deriving from the single dimension of time is elaborated. On expressing a temporal interval in a multi-dimensional form, via a direct…
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…
A surface theoretic view of non-perturbative quantum gravity as "spin-foams" was proposed by Baez. A possibility of constructing such a model was studied some time ago based on (2+1) dimensional general relativity as a reformulation of the…
We show the geometric consequences that the holographic principle has on the spacetime. Namely, we prove that complete spacelike hypersurfaces in a spacetime that satisfies the holographic principle are non-parabolic. This has important…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
We present a cyclic symmetric space-time, admitting closed time-like curves (CTCs) which appear after a certain instant of time, i. e., a time-machine space-time. These closed time-like curves evolve from an initial spacelike hypersurface…
We derive the gravitational Hamiltonian starting from the Gauss-Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the…
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background…