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Solution to Einstein's Field Equations where T^uv not= 0?Many of the widely-studied solutions to Einstein's field equations are taken in vacuo, that is, at events where the energy momentum tensor T^uv=0. This includes Schwarzchild and Kerr geometries, for example. Have there been many exact solutions found where T^uv not= 0? I am speaking of analytical solutions where the differential equations are solved exactly, *not* numerical approximations. I am especially interested in any exact solutions based on the usual Maxwell energy tensor of electrodynamics T^u_v = (1/4pi) [F^ut F_vt - (1/4) lambda^u_v F^st F_st]. I am interested in solutions both where F^uv_u=0 (free space) and also where F^uv_u=J^v (space with current sources). Conditions of interest include static spherical symmetry in the nature of Schwarzchild, and rotation with spherical symmetry about the z-axis in the nature of Kerr. To be clear, I am *not* looking for solutions where the metric is assumed to be a Minkowski metric. Lots of analyses assume a flat-space background for electrodynamics. Rather, I am looking for *exact* solutions, to the extent that such solutions are known, which derive a curved spacetime metric from the electromagnetic field strength tensor, that is, which derive g_uv = g_uv(F^uv) via the Maxwell tensor T^u_v, whereby T^u_v(g_uv, F_uv) simply becomes T^u_v(F_uv) once the g_uv(F^uv) are found. Thanks. Jay R. Yablon Email: [Only registered and activated users can see links. Click Here To Register...] |

Solution to Einstein's Field Equations where T^uv not= 0?"Jay R. Yablon" < [Only registered and activated users can see links. Click Here To Register...].com> wrote in message news:G_iSf.18215$[Only registered and activated users can see links. Click Here To Register...].com...You might try posting this on sci.physics.research. Martin Hogbin |

Solution to Einstein's Field Equations where T^uv not= 0?> You might try posting this on sci.physics.research. I sent it there three days ago, but nobody is minding the store right now. Nothing new has posted there since Monday. I expect it will post there soon. Jay R. Yablon |

Solution to Einstein's Field Equations where T^uv not= 0?Wikipedia seems to have a pretty good section on this: [Only registered and activated users can see links. Click Here To Register...]-- Ben |

Solution to Einstein's Field Equations where T^uv not= 0?Thank you, that is helpful. Jay. -- _____________________________ Jay R. Yablon Email: [Only registered and activated users can see links. Click Here To Register...]"Ben Rudiak-Gould" < [Only registered and activated users can see links. Click Here To Register...].uk> wrote in messagenews:dvcn9f$jom$ [Only registered and activated users can see links. Click Here To Register...].cam.ac.uk... |

Solution to Einstein's Field Equations where T^uv not= 0?In sci.physics Ben Rudiak-Gould < [Only registered and activated users can see links. Click Here To Register...].uk> wrote:This looks pretty good. If you want more, the standard source is the "exact solutions" book -- Stephani, Kramer, MacCallum, Hoenselaers, and Herlt, _ Exact Solutions of Einstein's Field Equations_ (second edition, 2003), Cambridge University Press. There's also an online searchable database at [Only registered and activated users can see links. Click Here To Register...]but this requires that you know a bit about what you're looking for. Steve Carlip |

Solution to Einstein's Field Equations where T^uv not= 0?Ben Rudiak-Gould wrote: Yes, that wiki on GR is quite good, given the difficulty of the subject. One can go to the Electrovacuum solution and encounter the Rainich *issues*, but that doesn't satisfy Jay's g_uv = g_uv(F_uv) question regarding an exact solution. There's more at, [Only registered and activated users can see links. Click Here To Register...]which focuses on antisymmetrization to relate 4 and 5D. In Tolman's "Relativity" book, pg.265 is the classical treatment but that approach, as far as I know, has been largely discredited because it depends on the self energizing of a the fundamental charge, and that effect is theoretically weak and not substantiated by by any experiment, that I can find. Hopefully someone else can provide an answer to Jay's question, apart from, [Only registered and activated users can see links. Click Here To Register...]which provides a sort of bench-mark to attack the problem. Regards Ken S. Tucker |

Solution to Einstein's Field Equations where T^uv not= 0?Thank you for the suggestion re the "exact solutions" book. I browsed it on Amazon, and it is just what I am looking for, so I placed an order for it. Jay R. Yablon -- _____________________________ Jay R. Yablon Email: [Only registered and activated users can see links. Click Here To Register...]< [Only registered and activated users can see links. Click Here To Register...]> wrote in messagenews:dvcqqr$98b$ [Only registered and activated users can see links. Click Here To Register...]... |

Solution to Einstein's Field Equations where T^uv not= 0?Jay R. Yablon wrote: > $$ No. $$ YABsolutely no. --Jay R Yablon. $$ Maxwell used REAL "flat" plates in air to derive his equations. $$ This is why GR is only "approximately" flat, at-great-distance. $$ Even a dot has extreme "curvature", so you can imagine a point. $$ GR is a "point-SURFACE manifold" at the end of it's WORLD-line. $$ This is why GR is NOT a "local" theory (where it's all Newton). $$ This is why GR is a "far-field" theory (where it's all Newton). $$ [ The "SURFACE" of a GR-"POiNT" is "FLAT-at-a-GREAT-distance ]. $$ $$ Tom R ought derive a set from lab work ..using "CURVED" plates. $$ [Just let the PLATEs be M1 and m1 and the air as the "AEther"]. $$ $$ Hope this helps, ```Brian A M Stuckless, Ph.T (Tivity). GR CUT OFF it's own WORLD-line, having DECLARED no PRiOR geometry. p.s. A GR-"geodesic" is *NOT* Uncle Al's "OTHER LONGER way round". Re: Solution to Einstein's Field Equations where T^uv not= 0?. |

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