TOV Equation in (2+1)-dimensions for Perfect Fluids

fu11meta1
Messages
30
Reaction score
0

Homework Statement


Consider a perfect fluid in a static, circularly symmetric (2+1)-dimensional spacetime.

Derive the analogue of the Tolman-Oppenheimer-Volkov (TOV) equation for (2+1)-dimensions

Homework Equations


Schwarzschild metric

The Attempt at a Solution


Okay. I'm trying to think this through. I've replaced the phi component of the schwarzchild metric with some random variable because we only need circular symmetry. but where do I go from here?
 
Nevermind. I have solved it!
 
Thread 'Need help understanding this figure on energy levels'

Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
View full post »
Thread 'Understanding how to "tack on" the time wiggle factor'

Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
View full post »

Similar threads

I Solving Geodesic Eq.: Mysterious Conservation Eq. (Sec. 5.4 Carroll)
Replies
4
Views
2K
A What Are Null Basis Vectors and Metric Signatures in Kruskal Coordinates?
Replies
8
Views
2K
  • Poll Poll
Relativity Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll
Replies
5
Views
13K
A Understanding Kerr Black Holes: Metric, Killing Vectors & Event Horizons
Replies
8
Views
3K
A Gravitational Bending of Light: Equation for Photon Trajectory in Strong Fields
Replies
9
Views
2K
Why Would the TOV Equation Be Based on the Exterior Metric?
Replies
13
Views
3K
Massive Scalar Field in 2+1 Dimensions
Replies
3
Views
2K
How to reduce Einstein's equation for perfect fluids
Replies
3
Views
2K
Gravitating Perfect Fluid Solution & Mass/Energy Total
Replies
2
Views
2K
R^(1/2) Question, half dimension space meaning?
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top