A Singularity Formation and Breakdown Ricci Tensor

  • A
  • Thread starter Thread starter Alien101
  • Start date Start date
Alien101
Messages
13
Reaction score
2
TL;DR Summary
Ricci flow equation
The Ricci tensor fails systematically in the Ricci flow equation: "due to the highly non-linear nature of the Ricci flow equation, singularities form in finite time. These singularities are curvature singularities, which means that as one approaches the singular time the norm of the curvature tensor blows up to infinity".

Case Study: Type I and Type II Singularities:

Citing a research that identified two types of singular breakdowns: "Type I and Type II singular points" where "the Riemannian curvature tensor has to blow up at least at a Type I rate" and "the Ricci curvature must blow up near every singular point of a Ricci flow".

Is this "blow-up" a physical necessity or a limitation of our tensor calculus approach?
 
Physics news on Phys.org
Why did you post this in the relativity subforum?
 
Reply
  • Like
Likes physics2222 and Alien101
Alien101 said:
TL;DR Summary: Ricci flow equation
Your post includes several direct quotes. What is the source of these quotations?
 
Alien101 said:
Citing a research
What research? Please give a reference. Otherwise we don't have a valid basis for discussion.
 
Thread 'Can this experiment break Lorentz symmetry?'

Thread 'Can this experiment break Lorentz symmetry?'

1. The Big Idea: According to Einstein’s relativity, all motion is relative. You can’t tell if you’re moving at a constant velocity without looking outside. But what if there is a universal “rest frame” (like the old idea of the “ether”)? This experiment tries to find out by looking for tiny, directional differences in how objects move inside a sealed box. 2. How It Works: The Two-Stage Process Imagine a perfectly isolated spacecraft (our lab) moving through space at some unknown speed V...
View full post »

Thread '1-Way Speed of Light'

Does the speed of light change in a gravitational field depending on whether the direction of travel is parallel to the field, or perpendicular to the field? And is it the same in both directions at each orientation? This question could be answered experimentally to some degree of accuracy. Experiment design: Place two identical clocks A and B on the circumference of a wheel at opposite ends of the diameter of length L. The wheel is positioned upright, i.e., perpendicular to the ground...
View full post »

Thread 'How can a black hole absorb matter?'

According to the General Theory of Relativity, time does not pass on a black hole, which means that processes they don't work either. As the object becomes heavier, the speed of matter falling on it for an observer on Earth will first increase, and then slow down, due to the effect of time dilation. And then it will stop altogether. As a result, we will not get a black hole, since the critical mass will not be reached. Although the object will continue to attract matter, it will not be a...
View full post »

Similar threads

A Ricci tensor for Fermi normal coordinates
Replies
1
Views
729
I Computing Ricci Tensor Coefficients w/ Tetrad Formalism
Replies
8
Views
2K
Fun with Carminati-McLenaghan invariants
Replies
2
Views
2K
I Non-zero components of Riemann curvature tensor with Schwarzschild metric
Replies
14
Views
7K
A Weyl tensor and coordinate acceleration
Replies
12
Views
2K
On the order of indices of the Christoffel symbol of the 1st kind
Replies
19
Views
2K
Understanding the Ricci Curvature Tensor in Einstein's Field Equations
Replies
7
Views
4K
Studying Special Features in Metrics: Tensors & Differential Geom.
Replies
3
Views
2K
Information content of the metric, Riemannian and Ricci tensors
Replies
6
Views
4K
Can a Vanishing Ricci Tensor Prove Flat Space in Dimensions Higher than Three?
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top