Related papers: Constructing Spacetime from the String Worldsheet
In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to…
It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
We give a brief overview of the nature of spacetime emerging from string theory. This is radically different from the familiar spacetime of Einstein's relativity. At a perturbative level, the spacetime metric appears as ``coupling…
Admitting non-Riemannian geometries, Double Field Theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in General Relativity with regular non-Riemannian geometries. The…
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…
The notion of a "point" is essential to describe the topology of spacetime. Despite this, a point probably does not play a particularly distinguished role in any intrinsic formulation of string theory. We discuss one way to try to determine…
This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
We introduce a definition of symmetry generating vector fields on manifolds which are equipped with a first-order reductive Cartan geometry. We apply this definition to a number of physically motivated examples and show that our newly…
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 show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein-like equation.…
General Relativity offers the possibility to model attributes of matter, like mass, momentum, angular momentum, spin, chirality etc. from pure space, endowed only with a single field that represents its Riemannian geometry. I review this…
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding…
Recently, a link between Lorentzian and Finslerian Geometries has been carried out, leading to the notion of wind Riemannian structure (WRS), a generalization of Finslerian Randers metrics. Here, we further develop this notion and its…
The concept of deformation of Riemannian geometry is reviewed, with applications to gravitation and cosmology. Starting with an analysis of the cosmological constant problem, it is shown that space-times are deformable in the sense of local…
Ooguri, Vafa, and Verlinde have outlined an approach to two-dimensional accelerating string cosmology which is based on topological string theory, the ultimate objective being to develop a string-theoretic understanding of "creating the…
Jacobson theorem (Ref. \cite{jacobson}) shows that Einstein gravity may be understood as a thermodynamical equation of state; a microscopic realization of this result is however lacking. In this paper, we propose that this may be achieved…