Related Experiment Video
Updated: Oct 4, 2025
05:39
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
5.3K
Identifying Riemannian Singularities with Regular Non-Riemannian Geometry.
Kevin Morand1, Jeong-Hyuck Park1, Miok Park2
1Department of Physics, Sogang University, 35 Baekbeom-ro, Mapo-gu, Seoul 04107, Korea.
Physical Review Letters
|February 11, 2022
Summary
Double field theory reveals that singular spacetimes in general relativity are regular non-Riemannian geometries. These "singularities" are coordinate singularities, with particles freezing and strings becoming chiral near them.
Area of Science:
- Theoretical physics
- String theory
- General relativity
Background:
- General relativity describes spacetime using Riemannian geometry.
- Singularities in general relativity pose theoretical challenges.
- Double field theory offers a broader framework for spacetime.
Purpose of the Study:
- To investigate the nature of singular spacetimes within double field theory.
- To re-interpret singularities in general relativity as regular geometries.
- To analyze the behavior of particles and strings near these identified geometries.
Main Methods:
- Utilizing the framework of double field theory.
- Analyzing generalized metrics and coordinate transformations.
- Computing geodesic completeness and string frame behavior.
Main Results:
- Singular spacetimes of general relativity correspond to regular non-Riemannian geometries in double field theory.
- Divergences are identified as coordinate singularities of the generalized metric.
- An impenetrable non-Riemannian sphere is found, outside which geodesics are complete.
Conclusions:
- The concept of spacetime singularities in general relativity can be resolved within double field theory.
- Non-Riemannian geometries provide a more complete description of spacetime.
- Physical phenomena near these points include particle freezing and chiral string behavior.
Related Concept Videos
01:19Degree of Curvature and Radius of Curvature
200
The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of...
200
01:19Routh-Hurwitz Criterion II
454
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
454
01:15Routh-Hurwitz Criterion I
354
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
354
01:27Gauss's Law: Planar Symmetry
8.5K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
8.5K
01:18Deformations in a Symmetric Member in Bending
289
When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
289
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
346
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
346