Large Scale Structure of Spacetime Study Group

clejan
Messages
2
Reaction score
0
Is anyone interested in going through Hawking and Ellis' book by the title above and posting questions and insights? My interest is in singularities in higher dimensional spacetime, and whether there are other ways to achieve singularities (and their zoology) besides large enough mass. I am interested in 4 dimensional hypersurfaces of signature change in 5 or higher dimensional spacetime, where the normal to the surface is not timelike.
Thanks,
-Iuval
 
Physics news on Phys.org
clejan said:
Is anyone interested in going through Hawking and Ellis' book by the title above and posting questions and insights? My interest is in singularities in higher dimensional spacetime, and whether there are other ways to achieve singularities (and their zoology) besides large enough mass. I am interested in 4 dimensional hypersurfaces of signature change in 5 or higher dimensional spacetime, where the normal to the surface is not timelike.
Thanks,
-Iuval

Ask again in Quantum Physics, you'll get a better response to Hawking there.
 
ryuunoseika said:
Ask again in Quantum Physics, you'll get a better response to Hawking there.

No, clejan should not ask again in Quantum Physics. As clejan knows, this book is about classical general relativity, and has nothing to do with quantum theory or Hawking radiation.
 
George is correct.
-IC
 
If I had the time, I would be willing to participate.
I think such a focused study group on an online forum would be interesting.

Here was one on Differential Forms https://www.physicsforums.com/showthread.php?t=67268 a while back.
(I was too busy back then to participate... but I would read some entries every now and then.)
 

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'Hawking After 54 Years Confirmed: BH surfaces don't shrink'

Abstract The gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-filter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal masses ## m_1=33.6_{-0.8}^{+1.2} M_{⊙} ## and ## m_2=32.2_{-1. 3}^{+0.8} M_{⊙}##, and small spins ##\chi_{1,2}\leq 0.26 ## (90% credibility) and negligible eccentricity ##e⁢\leq 0.03.## Postmerger data excluding the peak region are consistent with the dominant quadrupolar...
View full post »

Similar threads

Insights The Einstein Field Equation in a Static, Spherically Symmetric Spacetime
Replies
23
Views
4K
A "Monstrous Higgs and Leech Spacetime"
Replies
0
Views
3K
Conditions for spacetime to have flat spatial slices
4
Replies
158
Views
22K
A Equations for computing null geodesics in Schwarzschild spacetime
Replies
8
Views
3K
I Why is the observed local region of space flat?
Replies
25
Views
3K
Conservation laws in GR: a messy picture?
Replies
9
Views
4K
I Trying To Conceptualize Two Dimensions Of Time
Replies
2
Views
4K
I Is there a fine structure constant running anomaly?
Replies
2
Views
3K
How could spacetime become discretised at the Planck scale?
Replies
27
Views
8K
The modern Large-Scale Structure of Spacetime book
Replies
15
Views
13K

Hot Threads

Recent Insights

Back
Top