Kerr metric derivation (Adler, Bazin & Schiffer)

seanjadson
Messages
2
Reaction score
0
I have a problem understanding part of Adler, Bazin and Schiffer's (Introduction to General Relativity 2nd Edition) derivation of the Kerr metric. I would be grateful if someone could explain where I am going wrong. My problem concerns the transition from the O(m2) equation (7.15b) to (7.24). For the first term of (7.15b) I get:

m2.lm.ln[4(A.la)|a-8A2]

while for the second term (INCLUDING the minus sign preceding the 2 Minkowski metrics):

m2.lm.ln[-6A2-2.la|b.lb|a+2.la|b.la|b]

Adding these 2 expressions does not produce a factor of the LHS of (7.24), although subtracting them does.
 
Physics news on Phys.org
Found my mistake; the first term should be the negative of that shown.
 

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

A Kerr Metric Time Dilation Formula: Deriving Absolute Form
Replies
19
Views
3K
A Understanding Kerr Black Holes: Metric, Killing Vectors & Event Horizons
Replies
8
Views
4K
Validity of Schwarzschild Metric in Real BHs
Replies
5
Views
2K
A Derive Radial Momentum Eq. in Kerr Geometry
Replies
1
Views
2K
I Minkowski Spacetime KVF Symmetries
Replies
32
Views
2K
How to Derive Radial Geodesics in Kerr Metric?
Replies
11
Views
4K
I Calculating Perturbative Expansion of Metric Inverse in Cosmology
Replies
1
Views
2K
Deriving L-T Metric: Understanding Schwarzschild & Einstein's GR
Replies
4
Views
4K
How did Einstein derive the meaning of Schwarzchild's metric
Replies
10
Views
2K
Deriving Einstein Tensor & Inverse for Gϴdel Metric in Cartesian Coordinates
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top