
doi: 10.1007/bf00653596
For the static line element in spherical symmetry \(ds^ 2=e^{\nu}dt^ 2-e^{\lambda}dr^ 2-r^ 2(d\theta^ 2+\sin^ 2 \theta d\phi^ 2)\) Einstein-Maxwell field equations for charged perfect fluid are: \(r^{- 2}-e^{-\lambda}(r^{-2}-\lambda '/r)=8\pi \delta +q^ 2/r^ 4\), (*) \(d((e^{-\lambda}-1)/r^ 2)/dr+d((e^{-\lambda}\nu '/2r))/dr+e^{- \lambda -\nu}d((e^{\nu}\nu '/2r))/dr=4q^ 2/r^ 5\), \(q=4\pi \int^{r}_{0}\rho e^{\lambda /2}r^ 2dr\), \(\mu =4\pi \int^{r}_{0}\delta r^ 2dr\); here \(\nu\), \(\lambda\), \(\delta\), \(\rho\), q, \(\mu\) are all functions of r; q and \(\mu\) are ''charge'' and ''mass'' inside the sphere of radius r. Introducing (**) \(X=\nu '/2r\), from (*) one gets the linear differential equation for \(e^{-\lambda}\) with known general solution. Moreover, introducing \(\phi\) (r) as follows: (***) \(r^ 2(X^ 1+X^ 2r-r^{-3})=(X\phi -r^{-1})(1+Xr^ 2)\), one gets from (*), (**), (***) the equation for X(r) of Bernoulli type, again with known general solution. Using the obtained solutions, the authors show that some previously known results are particular cases of the general solutions.
Quantum hydrodynamics and relativistic hydrodynamics, Classical field theories, Einstein-Maxwell field equations, charged perfect fluid, general solution, Electromagnetic fields in general relativity and gravitational theory, static line element in spherical symmetry, Exact solutions to problems in general relativity and gravitational theory
Quantum hydrodynamics and relativistic hydrodynamics, Classical field theories, Einstein-Maxwell field equations, charged perfect fluid, general solution, Electromagnetic fields in general relativity and gravitational theory, static line element in spherical symmetry, Exact solutions to problems in general relativity and gravitational theory
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 1 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
