latentcorpse
Nov14-10, 04:14 PM
Physically reasonable matter with energy-momentum tensor T^{ab} is expected to satisfy the weak energy condition, i.e. T_{ab}u^au^b \geq 0 for all timelike u^a. Give a physical interpretation for this condition. You measure the
components of T^a{}_b in some basis and determine its eigenvalues \lambda and eigenvectors v^a satisfying
T^a{}_bv^b = \lamda v^a
You find that it has precisely one timelike eigenvector with eigenvalue \rho and three spacelike eigenvectors with eigenvalues p_{(\alpha )}. Under which necessary and sufficient condition on these eigenvalues is the weak energy condition satis ed?
According to Wald, T_{ab}u^au^b physically represents the energy density of matter as measured by an observer whose 4-velocity is u^a. It is generally believed that for all physically reasonable classical matter this energy density is nonnegative - hence the weak energy condition. Is this a suitable physical interpretation or have I missed anything crucial out?
And I couldn't get anywhere with the eigenstuff part of the question. Any ideas for this bit?
Thanks a lot.
components of T^a{}_b in some basis and determine its eigenvalues \lambda and eigenvectors v^a satisfying
T^a{}_bv^b = \lamda v^a
You find that it has precisely one timelike eigenvector with eigenvalue \rho and three spacelike eigenvectors with eigenvalues p_{(\alpha )}. Under which necessary and sufficient condition on these eigenvalues is the weak energy condition satis ed?
According to Wald, T_{ab}u^au^b physically represents the energy density of matter as measured by an observer whose 4-velocity is u^a. It is generally believed that for all physically reasonable classical matter this energy density is nonnegative - hence the weak energy condition. Is this a suitable physical interpretation or have I missed anything crucial out?
And I couldn't get anywhere with the eigenstuff part of the question. Any ideas for this bit?
Thanks a lot.