I Is this just a typo in Schutz' book on General Relativity?

Ahmed1029
Messages
109
Reaction score
40
I'm wondering is I'm missing something, or this should be " a non-zero component"?
Screenshot_2022-12-06-19-25-32-84_e2d5b3f32b79de1d45acd1fad96fbb0f.jpg
 
Physics news on Phys.org
The book is correct. In the momentarily comoving inertial frame the time component of the four-acceleration is indeed 0.
 
  • Like
Likes malawi_glenn and Ahmed1029
No, it means that in the MCRF the only non-zero component of ##\tilde{U}## is the zeroth one (because the three velocity is zero by definition in that frame). Hence the four acceleration (which he's just proved is orthogonal to ##\tilde{U}##) must take the form given.

I agree it's not particularly clearly written - it would be better if he'd said "##\tilde{U}## has only a ##{\tilde{U}}^0## component".
 
Last edited:
  • Like
Likes SiennaTheGr8, vanhees71, Dale and 1 other person
Ah yes, it's clear now. I thought he meant that it had only one component taking the value zero, which didn't make sense.
 
  • Like
Likes vanhees71 and Ibix
I must say this isn't the only thing I've found confusing in Schutz. The physics is sound enough, but I do feel like he really needed a better editor.
 
Last edited:
  • Like
Likes vanhees71 and Ahmed1029
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...
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...
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...
Back
Top