Area51

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Hi.

Im working with GRtensor iii package for Maple.

The goal is to obtain values of specific product of the Ricci tensor and scalar function in FRW spacetime together with second order covariant derivative acting on this product. .

grdef(

After i defined general 2 covariant derivatives acting on that product

 grdef( 

I have errors when i want to define contracted forms of this expression/tensor:

grdef(

which should be scalar quantity (fY*Rab );ab

grdef(

and this should have only 2 lower indices ac

Hovewer i obtain errors for both cases
Error, (in grtensor:-grdef) lhs/rhs index conflict.

grtensor_v2.mw

Hi

I have trouble with solving this ODE system using dsolve command:

and 

 

This system have following solutions:

where

and

C's and A are constants of integration.

 

They're equations from this paper https://arxiv.org/abs/1710.01910 (45 and 47). 
               

However, my solution differs from correct one - in output there are hypergeometric functions everywhere.

Is there any way to fix/convert this solution? Or to get rid of these functions (my f1 solution looks very close to original one but with coupled hypergeometric function). 
 

`` ``

``

``

 

``

sysode := 2*q*(3*q-1)*f1(tau)/tau^2+2*q*(diff(f1(tau), tau))/tau+diff(f1(tau), tau, tau)+(kappa^2+f2(tau))*(1+omega)*(tau/t0)^(-(3*(3+omega))*q) = 0, (54*q^3-30*q^2+4*q)*f1(tau)/tau^3+(24*q^2-4*q)*(diff(f1(tau), tau))/tau^2+11*q*(diff(f1(tau), tau, tau))/tau+diff(f1(tau), tau, tau, tau)-3*omega*(1+omega)*(kappa^2+f2(tau))*q*(tau/t0)^(-(3*(1+omega))*q)/tau = 0;

2*q*(3*q-1)*f1(tau)/tau^2+2*q*(diff(f1(tau), tau))/tau+diff(diff(f1(tau), tau), tau)+(kappa^2+f2(tau))*(1+omega)*(tau/t0)^(-3*(3+omega)*q) = 0, (54*q^3-30*q^2+4*q)*f1(tau)/tau^3+(24*q^2-4*q)*(diff(f1(tau), tau))/tau^2+11*q*(diff(diff(f1(tau), tau), tau))/tau+diff(diff(diff(f1(tau), tau), tau), tau)-3*omega*(1+omega)*(kappa^2+f2(tau))*q*(tau/t0)^(-3*(1+omega)*q)/tau = 0

(1)

``

``

simplify(dsolve([sysode], build));

{f1(tau) = _C1*tau^(-q+1/2-(1/2)*(-20*q^2+4*q+1)^(1/2))+_C2*tau^(-q+1/2+(1/2)*(-20*q^2+4*q+1)^(1/2))+_C3*tau^(-9*q+2)*hypergeom([-(1/12)*(16*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-16*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(4*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-4*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega), f2(tau) = (-695520*(q^2+(11/21)*q+2/21)*(tau/t0)^(3*q*(omega+5))*_C3*(q-3/10)*omega*q*(q^2-(25/69)*q+2/69)*tau^(-9*q)*hypergeom([-(1/12)*(4*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-4*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(-8*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(8*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega)-89424*(q^2*(tau/t0)^(3*q*(omega+7))*omega^2*tau^(-9*q)*_C3*(q^2-(25/69)*q+2/69)*hypergeom([-(1/12)*(-8*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(8*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(-20*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(20*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega)+(7/3)*(q^2+(11/21)*q+2/21)*(hypergeom([-(1/12)*(16*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-16*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(4*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-4*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega)*_C3*(tau/t0)^(3*(3+omega)*q)*(q^2-(25/69)*q+2/69)*tau^(-9*q)+(1/69)*kappa^2*(1+omega)))*(q^2-(7/9)*q+2/9))/((1+omega)*(4*q-(-20*q^2+4*q+1)^(1/2)-3)*(8*q-(-20*q^2+4*q+1)^(1/2)+3)*(8*q+(-20*q^2+4*q+1)^(1/2)+3)*(4*q+(-20*q^2+4*q+1)^(1/2)-3))}

(2)

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