3
votes
2answers
128 views

In what way are the Mathematical universe hypothesis and A New Kind of Science connected

The Mathematical universe hypothesis, mainly by Max Tegmark and A new Kind of Science, mainly by Stephen Wolfram both claim (as least as I understand it) that at its innermost core reality is ...
-1
votes
1answer
115 views

The Emperor's New Mind or Shadows of the mind? [closed]

OK - I have never posted on this site before, and I hope this question isn't closed as "request for reference" but here goes: I'm a software guy who likes to dabble in math, physics and cosmology. ...
2
votes
0answers
42 views

Regular initial data

I have a very basic question. What exactly is meant by "regular" initial data in general relativity? Does it mean smooth? at least $C^{2}$? All literature on the subject just uses this term without ...
1
vote
0answers
39 views

Maximal development/Development of a solution

I'm having troubles to rigorously understand what a development (or maximal development) of a solution is in General Relativity. I was reading a paper by Burnett and Rendall and they write "By maximal ...
3
votes
2answers
328 views

(Co)homology of the universe

In this post let $U$ be the universe considered as a manifold. From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
2
votes
0answers
176 views

How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?

Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
2
votes
1answer
245 views

Vanishing Ricci flow on a curved manifold

If I understand this right the Ricci flow on a compact manifold given by $\partial g_{\mu \nu} = - 2R_{\mu \nu} + \frac{2}{n}\!R_{\alpha}^{\alpha} \,g_{\mu \nu}$ tends to expand negatively curved ...
9
votes
8answers
684 views

Mathematical Universe Hypothesis

What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc. I ...
2
votes
0answers
217 views

Singularities in Bianchi models in general relativity ( physical science)

what are the conditions to check point type singularity in a bianchi type model ? bianchi type model are of Type I,II,III,IX,IV or u can say we use different Bianchi type models having some specific ...
3
votes
1answer
502 views

What is a maximal analytic extension?

Can someone explain (as rigorously as possible) what is involved in analytically continuing, say, the Schwarzschild solution to the Kruskal manifold? I understand the two metrics separately but I'm ...