| Download
SageMath notebooks associated to the Black Hole Lectures (https://luth.obspm.fr/~luthier/gourgoulhon/bh16)
Project: BHLectures
Views: 20113Kernel: SageMath 9.5.beta7
Curvature tensor in the Oppenheimer-Snyder interior
This Jupyter/SageMath notebook is relative to the lectures Geometry and physics of black holes.
The computations make use of tools developed through the SageManifolds project.
In [1]:
'SageMath version 9.5.beta7, Release Date: 2021-11-18'
In [2]:
Interior spacetime for Oppenheimer-Snyder collapse from rest
In [3]:
Chart of conformal coordinates:
In [4]:
In [5]:
In [6]:
Ricci tensor
In [7]:
Some trigonometric simplifications are in order:
In [8]:
In [9]:
In [10]:
In [11]:
Einstein tensor
In [12]:
Energy momentum tensor
The fluid 4-velocity:
In [13]:
Check that is a unit vector:
In [14]:
In [15]:
In [16]:
Check of Einstein equation
In [17]:
Riemann tensor
In [18]:
In [19]:
Kretschmann scalar
In [20]:
In [21]:
In [22]:
Ricci squared
In [23]:
In [24]:
In [25]: