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.

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enter code here
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{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}.

g_{\phi\phi} = r

complete(ss,$g^{\mu\nu}$);

ch := \Gamma^{\mu}*{\nu\rho} = 1/2 g^{\mu\sigma} (
\partial*{\rho}{g

*{\nu\sigma}}*

+\partial{\nu}{g

+\partial

*{\rho\sigma}}*

-\partial{\sigma}{g_{\nu\rho}});

-\partial

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}

+\Gamma^{\rho}

*{\nu\sigma}*

-\Gamma^{\rho}{\nu\lambda}\Gamma^{\lambda}_{\mu\sigma};

-\Gamma^{\rho}

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 = getcomponent(Eins,$\phi,\phi$)[1];

gph = get

from cdb.sympy.solvers import *

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

from sympy import *