Function Repository Resource:

BlackHoleModelData

Source Notebook

Get data about various black hole models

Contributed by: Jason Martinez

ResourceFunction["BlackHoleModelData"][solution]

returns the metric for the specified solution of the Einstein field equations.

ResourceFunction["BlackHoleModelData"][solution,property]

returns the symbolic expression for the specified property in the given metric.

ResourceFunction["BlackHoleModelData"][solution,property,{var1quantity1,var2quantity2, }]

inserts the specified values quantityi for the variables vari into expressions.

ResourceFunction["BlackHoleModelData"][solution,property,attribute]

gives the value of the specified attribute.

Details and Options

ResourceFunction["BlackHoleModelData"][] returns a list of all available solutions.
ResourceFunction["BlackHoleModelData"]["Properties"] returns all available properties for the solutions.
Properties include:
"Coordinates"the coordinate system of the solution
"Entropy"entropy
"HorizonArea"area of the event horizon
"HorizonRadius"radius of the event horizon
"Metric"Association of nonzero metric components for the solution
"PenroseDiagram"Penrose diagram
"SurfaceGravity"gravity at the event horizon boundary
"Temperature"temperature
The variables returned by ResourceFunction["BlackHoleModelData"] are expressed with the QuantityVariable wrapper.
"Metric" is returned as an Association with the Keys corresponding to the component labels for each component.
When specifying a list of values to insert into an expression, an input variable value can be specified with varvalue; var can be a string or QuantityVariable, and value can be a number, symbol or Quantity.
ResourceFunction["BlackHoleModelData"][solution,property,attributes] can be used to get more information about the QuantityVariable objects within the symbolic expression.
Allowed attributes include:
"QuantityVariableDimensions"list of base dimensions for all variables
"QuantityVariableNames"English names for all variables
"QuantityVariablePhysicalQuantities"physical quantities for all variables
"QuantityVariables"list of all variables in the formula
"QuantityVariableTable"details on all variables for the formula

Examples

Basic Examples (3) 

Obtain the metric for a particular solution to the Einstein field equations:

In[1]:=
ResourceFunction["BlackHoleModelData"]["Schwarzschild"]
Out[1]=

Learn the expression for the entropy of a black hole in the Reissner–Nordstrom solution:

In[2]:=
ResourceFunction["BlackHoleModelData"]["ReissnerNordstrom", "Entropy"]
Out[2]=

Determine the temperature of a rotating charged black hole with the mass of a million suns:

In[3]:=
ResourceFunction[
 "BlackHoleModelData"]["KerrNewman", "Temperature", {"M" -> 10^6 StarData["Sun", "Mass"], "J" -> Quantity[10^9, "Joules" "Seconds"], "Q" -> Quantity[10^6, "Coulombs"]}]
Out[3]=

Scope (8) 

List all supported solutions:

In[4]:=
ResourceFunction["BlackHoleModelData"][]
Out[4]=

List the available properties:

In[5]:=
ResourceFunction["BlackHoleModelData"]["Properties"]
Out[5]=

Look up the metric to a particular solution:

In[6]:=
ResourceFunction["BlackHoleModelData"]["KerrNewman"]
Out[6]=

Obtain the expressions for various black hole properties:

In[7]:=
ResourceFunction["BlackHoleModelData"]["Kerr", "HorizonArea"]
Out[7]=

Extract information on the physical quantities used to calculate the properties of black holes:

In[8]:=
ResourceFunction[
 "BlackHoleModelData"]["Kerr", "HorizonRadius", "QuantityVariables"]
Out[8]=
In[9]:=
ResourceFunction[
 "BlackHoleModelData"]["ReissnerNordstrom", "Coordinates", "QuantityVariableNames"]
Out[9]=
In[10]:=
ResourceFunction[
 "BlackHoleModelData"]["Schwarzschild", "Metric", "QuantityVariableDimensions"]
Out[10]=
In[11]:=
ResourceFunction[
 "BlackHoleModelData"]["KerrNewman", "Entropy", "QuantityVariablePhysicalQuantities"]
Out[11]=

Explore Penrose diagrams for different black hole geometries:

In[12]:=
ResourceFunction[
 "BlackHoleModelData"]["Schwarzschild", "PenroseDiagram"]
Out[12]=
In[13]:=
ResourceFunction[
 "BlackHoleModelData"]["ReissnerNordstrom", "PenroseDiagram"]
Out[13]=

Insert values for the important physical quantities of a black hole to learn the surface gravity on the event horizon:

In[14]:=
ResourceFunction[
 "BlackHoleModelData"]["ReissnerNordstrom", "SurfaceGravity", {"M" -> 10 StarData["Sun", "Mass"], "Q" -> Quantity[10^13, "Coulombs"]}]
Out[14]=

Convert that to units of standard gravity:

In[15]:=
UnitConvert[%, "StandardAccelerationOfGravity"]
Out[15]=

Physical quantities can be specified as Quantity objects or numbers:

In[16]:=
ResourceFunction[
 "BlackHoleModelData"]["Schwarzschild", "Entropy", {"M" -> 1}]
Out[16]=

Possible Issues (3) 

Quantity input is checked for the correct units:

In[17]:=
ResourceFunction[
 "BlackHoleModelData"]["Schwarzschild", "Entropy", {"M" -> Quantity[1, "Meters"]}]
Out[17]=

Only valid physical quantities are used:

In[18]:=
ResourceFunction[
 "BlackHoleModelData"]["Schwarzschild", "Entropy", {"O" -> Quantity[1, "Meters"]}]
Out[18]=

Some values are not physically realizable:

In[19]:=
ResourceFunction[
 "BlackHoleModelData"]["KerrNewman", "Temperature", {"M" -> StarData["Sun", "Mass"], "J" -> Quantity[10^10, "Joules" "Seconds"], "Q" -> Quantity[10^30, "Coulombs"]}]
Out[19]=

Version History

  • 1.1.0 – 28 September 2022
  • 1.0.0 – 08 September 2020

License Information