# [LORENE] grv2 Newtonian

Eric Gourgoulhon Eric.Gourgoulhon at obspm.fr
Mon Nov 3 18:00:47 CET 2003

Dear Reinhard,

Thanks to your message, I've just realized there was an error
in Etoile_rot::grv2() in the Newtonian case, the result of
which was an (apparent) low precision as estimated from grv2()
in Newtonian computations. I've corrected this error and
committed a new version of et_rot_global.C in Lorene.
So please perform a cvs update to get a correct computation
of GRV2 for Newtonian configurations.

Actually the GRV2 error indicator is meaningfull in the
Newtonian case, because the Newtonian limit of the GRV2 identity
\int_0^\pi \int_0^\infty [ p + \rho v^2 - {1\over 8\pi G} (\nabla
\Phi)^2 ] r dr d\theta = 0

where p, \rho, v and \Phi are respectively the fluid pressure, mass density,
velocity and the gravitational potential (see Eq. (31) of Bonazzola &
Gourgoulhon,
Class. Quantum Grav. 11, 1775 (1994)).

You are right when you say that the corresponding relativistic
2D-Poisson equation
is actually not solved in the Newtonian case. However the above integral
identity is still non trivial and must be satisified by the solution.
Therefore Etoile_rot::grv2() evaluates the relative error in the above
integral.

Best wishes,

Eric.

Reinhard Prix wrote:

>Hi,
>
>if I understand this correctly, the '2D-viriel'-error grv2() is
>meaningless in the Newtonian case (I suppose the corresponding
>2D-Poisson equation is not actually solved in that case?).
>
>If this is so, would it not be better (for clarity) to set
>grv2 -> 0  in the non-relativistic case?
>
>Best,
>Reinhard
>
>
>

--
Eric Gourgoulhon
Laboratoire de l'Univers et de ses THeories (LUTH)
UMR 8102 du CNRS / Observatoire de Paris, F-92195 Meudon Cedex, France
tel: +33 1.45.07.74.33 (secretariat : +33 1.45.07.75.10)
e-mail: Eric.Gourgoulhon at obspm.fr    WWW: http://www.luth.obspm.fr/