"isotropic coordinates" for the Schwarzschild metric : ds2 = F2 dt2 - G4

Pulsar = ParametricPlot3D[. {. Sin[t] Cos[p],. Sin[t] Sin[p],. Cos[t]. },. {t, 0, Pi}, {p, 0, 2 Pi}, PlotPoints Ø {20, 60}],. ViewPoint Ø {0, 0, 1}, PlotRange Ø {{-5, 5}, {-5, 5}, ...
Télécharger le PDF
404KB taille 2 téléchargements 216 vues
commentaire
Report
Test1.nb

1

‡ We are using cartesian "isotropic coordinates" for the Schwarzschild metric : ds2 = F2 dt2 - G4 Hdx2 + dy2 + dz2 L, where the functions F[r] and G[r] are defined below. By definition, alpha = GM / 2Rc 2 , where M is the star's mass (a pulsar) and R its radius. All coordinates ( x, y z ) are measured in R units. Below, we solve the geodesic equation for a photon moving around the star.

In[72]:=

alpha := H6.672 * 10-11 L H1.4 * 1.99 * 1030 L ê H2 H10000L H299792458L^ 2L r@s_D := Sqrt@x@sD ^ 2 + y@sD ^ 2 + z@sD^ 2D F@s_D := H1 - alpha ê r@sDL ê H1 + alpha ê r@sDL G@s_D := H1 + alpha ê r@sDL

X@s_D := 8x@sD, y@sD, z@sD< K@s_D := D@X@sD, sD A@s_D := D@F@sD, sD ê F@sD - 2 D@G@sD, sD ê G@sD B@s_D := D@G@sD, sD ê G@sD 8

In[246]:= LightPath1 = NDSolve@

x£ £ @sD ã - Simplify@A@sD H [email protected]@sD ê [email protected]@sD LD x@sD - 4 B@sD x£ @sD, y£ £ @sD ã - Simplify@A@sD H [email protected]@sD ê [email protected]@sD LD y@sD - 4 B@sD y£ @sD, z£ £ @sD ã - Simplify@A@sD H [email protected]@sD ê [email protected]@sD LD z@sD - 4 B@sD z£ @sD, x@0D ã -1.5, y@0D ã 0, z@0D ã 0, x£ @0D ã 0, y£ @0D ã 1, z£ @0D ã 0