Evaluating the Levi-Civita connection on EXCALC

[Cristobal Corral]

Dear all,

I am struggling when computing the Levi-Civita connection on EXCALC by using the command "riemannconx". I am using a frame ansatz in terms of two functions, namely f=f(r) and h=h(r), providing their explicit form beforehand. My code is the following:

---

load_package excalc;

off precise;

% Definitions %

spacedim 4;
indexrange 0,1,2,3;
pform {f,h}=0,curv(a,b)=2,eome(a)=3;

index_symmetries curv(a,b): antisymmetric;

fdomain f=f(r),h=h(r);

%%%% Solution to the field equations %%%

f:= 1 + 2m/r - (lamb/3)r**2;
h:=1/f;

% Vierbein ansatz %

coframe e(0)=sqrt(f)d t, e(1)=sqrt(h)d r, e(2)=rd x, e(3)=rsin(x)d y with metric g=-e(0)e(0) + e(1)e(1) + e(2)e(2) + e(3)*e(3);

frame ee;

factor e,^;

% Riemannian Lorentz connection %

riemannconx om;

om(a,b);

% Torsion-free condition %

d e(a) + om(a,-b)^e(b);

% 2-form curvature %

curv(a,b):= d om(a,b) + om(a,-c)^om(c,b);

% Bianchi identities %

curv(a,-b)^e(b);
d curv(a,b) + om(a,-c)^curv(c,b) + om(b,-c)^curv(a,c);

% Einstein field equations %

eome(-a):= eps(-a,-b,-c,-d)(curv(b,c) - (lamb/3)e(b)^e(c))^e(d);

end$

---

The problem is that, when computing the Levi-Civita connection om(a,b), EXCALC does not evaluate the explicit form of neither f nor h in some steps, e.g. in the computation of the components om(0,1), om(1,2), and om(1,3). Why is this?

Thank you very much in advance,

Cristóbal.

[Eberhard Schruefer]

Hi Cristóbal,
Thanks for the report. Indeed there is a necessary resimplification step missing when in a coframe statement variables are used that have an assigned value. I commited a correction to the coframe statement right now. The fix will be included in next snapshot.
Eberhard

[Cristobal Corral]

Dear Eberhard,

Thank you very much for your reply and support. I am looking forward to the next snapshot.

All the best,

Cristóbal.