Related papers: Embedding Versus Immersion in General Relativity
Humans are able to conceive physical reality by jointly learning different facets thereof. To every pair of notions related to a perceived reality may correspond a mutual relation, which is a notion on its own, but one-level higher. Thus,…
In this paper we give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We give many examples of how to formulate…
Strategies intended to resolve the problem of time in quantum gravity by means of emergent or hidden timefunctions are considered in the arena of relational particle toy models. In situations with `heavy' and `light' degrees of freedom, two…
We investigate the viability of a recently proposed generalization of the Ashtekar-Olmedo-Singh spacetime for the effective description of the interior region of a Schwarzschild black hole within the framework of loop quantum cosmology. The…
Einstein's dream of describing elementary particles as solutions of a classical field theory is severely limited by our current understanding of Nature. Quantum theory is inconsistent with any local realistic theory such as evolving…
We propose a global minimal embedding of the Schwarzschild theory in a five-dimensional flat space by using two surfaces. Covariant field equations are deduced for the gravitational forces.
We show how to embed spacelike slices of the Schwarzschild wormhole (or Einstein-Rosen bridge) in R3. Graphical images of embeddings are given, including depictions of the dynamics of this nontraversable wormhole at constant Kruskal times…
A procedure is described to construct generalised Scherk-Schwarz uplifts of gauged supergravities. The internal manifold, fluxes, and consistent truncation Ansatz are all derived from the embedding tensor of the lower-dimensional theory. We…
We explore further the proposal that general relativity is the hydrodynamic limit of some fundamental theories of the microscopic structure of spacetime and matter, i.e., spacetime described by a differentiable manifold is an emergent…
Traditionally, the embedding procedure for spherically symmetric spacetimes has been restricted to the equatorial plane $\theta = \pi/2$. This conventional approach, however, encounters a fundamental limitation: not every spherically…
The essay is devoted to the problem of time in the context of quantum cosmology, which acquires a philosophical level to date. At an example of the minisuperspace model, we show that this problem is illusive in the sense that it does not…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
We consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and then go on to discuss a sense in which…
We show that it is possible to embed the 1+1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2+1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and…
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…
In contrast to Einstein's theory, the first order formulation of gravity turns out to be a natural habitat for double-sheeted spacetime solutions which satisfy the vacuum field equations everywhere. These bridge-like geometries exhibit…
Compared with word embedding based on point representation, distribution-based word embedding shows more flexibility in expressing uncertainty and therefore embeds richer semantic information when representing words. The Wasserstein…
In this note the Schwarzschild and Kerr solutions are constructed for 3 space and $N$ time dimensions. Solutions, by construction, possesses symmetry with respect to rotations in time volume.
The notion of singular generalized Finsler spacetime and singular generalized Berwald spacetime are introduced and their relevance for the description of classical gravity discussed. A method to construct examples of such generalized…
We discuss how to embed quantum nonlocality in an approximately classical spacetime background, a question which must be answered irrespective of any underlying microscopic theory of spacetime. We argue that, in deterministic…