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Hello people. I'm trying to solve Einstein's equations in vacuo for a generic line element, I can get to the equations G _ {\ alpha \ beta}, but I can't get the values for exp (\ mu) and \ exp (nu). If anyone knows thank you.

enter code here

{r,t,\phi,\theta}::Coordinate; {\mu,\nu,\rho,\sigma,\lambda,\kappa,\chi,\gamma}::Indices(values=t,r,\phi,\theta},position=fixed);

\partial{#}::PartialDerivative; g_{\mu\nu}::Metric; g^{\mu\nu}::InverseMetric;

v::Depends(r); u::Depends(r);

ss:={g{t t} = \exp(v), g{r r} =-\exp(u), g{\theta\theta} = r**2, g{\phi\phi} = r2 \sin(\theta)2}. complete(ss,$g^{\mu\nu}$);

ch := \Gamma^{\mu}{\nu\rho} = 1/2 g^{\mu\sigma} ( \partial{\rho}{g{\nu\sigma}} +\partial{\nu}{g{\rho\sigma}} -\partial{\sigma}{g_{\nu\rho}}); evaluate(ch,ss,rhsonly=True);

rm:= R^{\rho}{\sigma\mu\nu} = \partial{\mu}{\Gamma^{\rho}{\nu\sigma}} -\partial{\nu}{\Gamma^{\rho}{\mu\sigma}} +\Gamma^{\rho}{\mu\lambda}\Gamma^{\lambda}{\nu\sigma} -\Gamma^{\rho}{\nu\lambda}\Gamma^{\lambda}_{\mu\sigma}; substitute(rm,ch); evaluate(rm,ss,rhsonly=True);

rc:= R{\sigma\nu} = R^{\rho}{\sigma\rho\nu}; substitute(rc, rm) evaluate(rc, ss, rhsonly=True);

src:= R = g^{\sigma\nu}R_{\sigma\nu}; substitute(src,rc); evaluate(src,ss,rhsonly=True);

Eins := G{\sigma\nu} = R{\sigma\nu}-1/2g_{\sigma\nu}R; substitute(Eins,rc); substitute(Eins,src); evaluate(Eins,ss,rhsonly=True);

from cdb.core.component import from cdb.core.manip import

gtt = get_component(Eins,$t,t$)[1]; grr = get_component(Eins,$r,r$)[1]; gth = get_component(Eins,$\theta,\theta$)[1]; gph = get_component(Eins,$\phi,\phi$)[1];

from cdb.sympy.solvers import *

eq1:= @(gtt)-@(grr);

from sympy import *

in General questions by (200 points)
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This is my code. I seek to find the shwarzschild line element

Hi. The file is not accessible. Could you edit your question to include the commands?

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