| Download
SageMath notebooks associated to the Black Hole Lectures (https://luth.obspm.fr/~luthier/gourgoulhon/bh16)
Project: BHLectures
Views: 20113Kernel: SageMath 9.3.beta8
Images of an accretion disk around a Kerr black hole
This Jupyter/SageMath notebook is relative to the lectures Geometry and physics of black holes.
In [1]:
'SageMath version 9.3.beta8, Release Date: 2021-03-07'
In [2]:
In [3]:
Functions and for critical null geodesics
We use and denote simply by .
In [4]:
In [5]:
In [6]:
The radii and of the two horizons:
In [7]:
Critical radii , , , , and
In [8]:
In [9]:
In [10]:
In [11]:
We add the radius of the marginally stable orbit:
In [12]:
as well as the radius of outer and inner polar orbits:
In [13]:
In [14]:
In [15]:
Prograde timelike ISCO radius compared to various radii of spherical photon orbits
In [16]:
In [17]:
In [18]:
In [19]:
In [20]:
In [21]:
In [22]:
In [23]:
In [24]:
rmin : 1.00000001000000 rmax : 3.99999996000000
rmin_col : 1 rmax_col : 4.0
In [25]:
rmin : 1.00000001000000 rmax : 3.99999996000000
rmin_col : 1 rmax_col : 4.0
Half-width of the image in units of :
In [26]:
fsize = 10.0963959215444 m/r_obs
In [27]:
Default resolution of SageMath images:
In [28]:
Default resolution of Matplotlib images:
In [29]:
In [30]:
In [31]:
In [32]:
a95_th00 resolution: (500, 500, 3)
figsize: (5.0, 5.0)
a/m = 0.950000000000000 theta_obs = 0
extent: (-10.0963959215444, 10.0963959215444, -10.0963959215444, 10.0963959215444)
rmin : 2.49118715973461 rmax : 2.49420141399888
rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268
<IPython.core.display.Javascript object>
a95_th30 resolution: (500, 500, 3)
figsize: (5.0, 5.0)
a/m = 0.950000000000000 theta_obs = 1/6*pi
extent: (-10.0963959215444, 10.0963959215444, -10.0963959215444, 10.0963959215444)
rmin : 1.76846188276999 rmax : 3.23697774665377
rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268
<IPython.core.display.Javascript object>
a95_th60 resolution: (500, 500, 3)
figsize: (5.0, 5.0)
a/m = 0.950000000000000 theta_obs = 1/3*pi
extent: (-10.0963959215444, 10.0963959215444, -10.0963959215444, 10.0963959215444)
rmin : 1.44011965009280 rmax : 3.76536147242618
rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268
<IPython.core.display.Javascript object>
a95_th90 resolution: (500, 500, 3)
figsize: (5.0, 5.0)
a/m = 0.950000000000000 theta_obs = 1/2*pi
extent: (-10.0963959215444, 10.0963959215444, -10.0963959215444, 10.0963959215444)
rmin : 1.38628054232578 rmax : 3.95534727811920
rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268
<IPython.core.display.Javascript object>
In [ ]: