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:
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.
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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
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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.
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
Dear Eberhard,
Thank you very much for your reply and support. I am looking forward to the next snapshot.
All the best,
Cristóbal.
Last edit: Cristobal Corral 2020-02-19