- #1
Huashan
- 7
- 0
I've read a few papers about derivation of the Schwarzschild metric by using the equivalence principle ( http://cdsweb.cern.ch/record/1000100/files/0611104.pdf" )... but I couldn't understand them completely
they assume , According to Einstein’s equivalence principle, that the influence of gravitation on phenomena in a local reference frame that is at rest in the field is equivalent to the influence of the accelerated motion of a local reference frame in which phenomena are described in the absence of gravitation . ( till now there is no problem ).
and then for such an accelerated frame they write the metric in the form :
(no problem yet ).
then... they relate the local coordinates x’, t’ in the accelerated frame to the corresponding coordinates in the stationary frame by the usual differential form of the Lorentz transformation for the value of the velocity that has been reached , by the formulae :
here is the problem ... can these frames be related to each other by the above expressions ?? According to the fact that one of them is non-inertial frame? ... the derivation of the above expressions are based on the fact that the frames are inertial and moving with respect to each other with a constant velocity v .
Can anybody help me?? ...
they assume , According to Einstein’s equivalence principle, that the influence of gravitation on phenomena in a local reference frame that is at rest in the field is equivalent to the influence of the accelerated motion of a local reference frame in which phenomena are described in the absence of gravitation . ( till now there is no problem ).
and then for such an accelerated frame they write the metric in the form :
(no problem yet ).
then... they relate the local coordinates x’, t’ in the accelerated frame to the corresponding coordinates in the stationary frame by the usual differential form of the Lorentz transformation for the value of the velocity that has been reached , by the formulae :
here is the problem ... can these frames be related to each other by the above expressions ?? According to the fact that one of them is non-inertial frame? ... the derivation of the above expressions are based on the fact that the frames are inertial and moving with respect to each other with a constant velocity v .
Can anybody help me?? ...
Last edited by a moderator: