Using Einstein field equation

kashiark
Messages
210
Reaction score
0
Gµv + Λgµv = (8πG/c4)Tµv
I have several questions. what is the µv? when we use it today do we use the cosmological constant even though the universe isn't static or does it mean something different than einstein orignally thought? what are we measuring when we use this if theyre all constants?
 
Last edited:
Physics news on Phys.org
I don't know the alt code either, but here's a copy-paster: Λ (from Wikipedia :))

The mu and nu are tensor indices, indicating that G, g and T are two-tensors. If you don't know what they are you should first of all learn about them, because they are very important constituents of the language in which GR is formulated (I recommend Carroll's book), but for now you can consider G, g and T as 4 x 4 matrices and mu, nu as simply indices, for example G00 is the top left component, etc.

The cosmological constant was written off a long time ago, but recently interest in it has arisen again. It can quite nicely explain some of the "odd" observed properties, such as the acceleration of the expansion rate of the universe and the fact that there seems to be more energy content than we'd expect. This might get you started, more advanced questions I will leave to the cosmologists out here :)
 

Thread 'I don't see how a black hole's event horizon can be crossed'

OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
View full post »

Thread 'Synchronizing clocks in an inertial frame if light is anisotropic'

ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
View full post »

Thread 'Is the variation of the metric ##\delta g_{\mu\nu}## a tensor?'

From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
View full post »

Similar threads

I Numerical Relativity -- Software to solve the Einstein field equations?
Replies
2
Views
1K
I Piecewise Functions in the Einstein Field Equations
2
Replies
57
Views
3K
Insights The Einstein Field Equation in a Static, Spherically Symmetric Spacetime
Replies
23
Views
4K
A Boundary conditions in ##\delta I=0## to derive Einstein's equations
Replies
8
Views
1K
I What's the underlying frame of the Einstein's Field Equation?
4
Replies
186
Views
11K
I Equation of state for Einstein field equations
Replies
4
Views
1K
I Einstein Field Eqns: East/West Coast Metrics
Replies
6
Views
2K
Derivations of Einstein field equations
Replies
3
Views
2K
I Einstein's Derivation of Elapsed Time for Remote Comoving Object
Replies
1
Views
2K
A Non static and isotropic solution for Einstein Field Eq
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top