Good question. Well, the general approach is based on a covariant formalism, providing one with global conservation laws in asymptotically flat spacetimes. For example, it can be used to give the mass of an isolated black-hole (which is asymptotically flat). A more recent and general approach...
No it does not fall from sky. It is basically a tensor quantity that has conserved components following the fact that almost every physical theory must be invariant under a global set of transformations assigned to the Poincare group (translations in space and time and rotations and boosts). The...
Hello
Including charge in the equations of motion opens the door to Lorentz force to be applied on the test particles. This happens to be the case if an electromagnetic stress tensor is added to the gravitational one since the Lorentz force is related with electromagnetic strength tensor...
There is one big hole in our comments here: the lack of scientific percision. If you really think that we can talk about, in relation to the topic here, a new spacetime with CTCs whatever it is, please provide us with the mathematical construction. From the beginning you've just insisted on...
Well, I guess you have no idea what a Deutsch-Politzer spacetime is! You should take a look at this paper http://ls.poly.edu/~jbain/philrel/philrellectures/15.TimeMachines.pdf
In the case of a DP spacetime, time axis is bent over in such a way that the neighbourhood of +infinity meets that...
Topology is irrelevant that allows you to have Deutsch-Politzer spacetime in GR with CTCs. The fact is that here the choice of coordinates is messy! By "messy" I mean if det g = 0 at some point(s) in spacetime, then either you have chosen a bad coordinate system, or you have to bond coordinates...
In fact I don't think GR accepts such a nonsense! Because if time here is not bounded, you can stand at someplace say (x_0,y_2,z_0) to only observe you getting accelerated to the speed of light as your hand-watch shows t=k\pi.
AB
This is a very poor metric. It certainly has uncountably many coordinate singularities and so it is not a suitable case for Minkowski spacetime! Taking T=\cos(t), we have -dT^2=-sin^2(t)dt^2 . But this only works if 0=<t<\pi/2 which means time is bounded from above!
Very bizarre!
You seem to have gotten it all confused!
They use an standard metric for a space associated with spherical coordinates-based metric. For example, to compute
A_{r;r}
one must know that if there are one-forms and basis vectors involved in the equation, then it is also mandatory to know...
This only holds when one knows that
\frac{\delta g_{\lambda a} }{\delta g_{\mu \nu}} =\delta ^{\mu}_{\lambda}}\delta ^{\nu}_{a}}
and thus
\frac{\delta \partial_{\kappa}g_{\lambda \alpha } }{\delta g_{\mu \nu}} =\partial_{\kappa}(\delta ^{\mu}_{\lambda}}\delta ^{\nu}_{\alpha}})=0...
You better take h to be \tilde{h} because I guess it is a tensor not weighted tensor (in agreement with your notation). Of course the result will still be a tensor density because the weight factor would by no means disappear in the end. In fact one can show that the best stance for the...
Oh if you have noticed I've made a mistake in my penult post here. In fact you can read the right term left from integration by parts in my first post:
-\int_{\Omega} [\int \frac{\partial}{\partial u^{\kappa}} (\frac{dz^{\mu}}{ds}\frac{\partial u^\kappa }{\partial x^{\mu}}) \delta^{...