GitHub

Catalogue of metrics

Gradus.jl implements a library of metrics ready to use for integrations and rendering.

Note

To implement your own custom metrics, please see Implementing a new metric. If you have a complex metric, please open an issue requesting for it to be added.

Currently available metrics

Gradus.DilatonAxion — Type
struct DilatonAxion{T} <: AbstractStaticAxisSymmetric{T}

Einstein-Maxwell-Dilaton-Axion metric.

  • M = 1.0: Singularity mass.
  • a = 0.0: Singularity spin.
  • β = 0.0: Dilaton coupling strength.
  • b = 1.0: Axion coupling strength.
source
Gradus.JohannsenMetric — Type
struct JohannsenMetric{T} <: AbstractStaticAxisSymmetric{T}

The Johannsen (20xx) metric.

  • M = 1.0: Black hole mass.
  • a = 0.0: Black hole spin.
  • α13 = 0.0: $\alpha_{13}$ deviation parameter.
  • α22 = 0.0: $\alpha_{22}$ deviation parameter.
  • α52 = 0.0: $\alpha_{52}$ deviation parameter.
  • ϵ3 = 0.0: $\epsilon_{3}$ deviation parameter.
source
Gradus.JohannsenPsaltisMetric — Type
struct JohannsenPsaltisMetric{T} <: AbstractStaticAxisSymmetric{T}

Johannsen and Psaltis 2011

  • M = 1.0: Black hole mass.
  • a = 0.0: Black hole spin.
  • ϵ3 = 0.0: $\epsilon_{3}$ deviation parameter.
source
Gradus.KerrMetric — Type
struct KerrMetric{T} <: AbstractStaticAxisSymmetric{T}

The Kerr metric in Boyer-Lindquist coordinates, describing a black hole with mass $M$ and angular spin $a$:

\[\begin{align*} \text{d}s^2 = &- \left( 1 - \frac{2 M r}{\Sigma} \right)\text{d}t^2 - \frac{2M r a \sin^2(\theta)}{\Sigma} \text{d}t \text{d}\phi \\ &+ \frac{\Sigma}{\Delta} \text{d}r^2 + \Sigma \text{d}\theta^2 + \left(r^2 + a^2 + \frac{2 M r a^2 \sin^2(\theta)}{\Sigma} \right) \sin^2(\theta) \text{d}\phi^2, \end{align*}\]

where

\[\Sigma = r^2 + a^2 \cos^2 (\theta), \quad \text{and} \quad \Delta = r^2 - 2Mr + a^2.\]

Parameters

  • M = 1: black hole mass.
  • a = 0: black hole spin.
source
Gradus.KerrRefractive — Type
struct KerrRefractive{T} <: AbstractStaticAxisSymmetric{T}

Kerr metric in Boyer-Lindquist coordintes with a path-length ansatz, equivalent to a refractive index n, within the coronal radius corona_radius.

  • M = 1.0: Black hole mass.
  • a = 0.0: Black hole spin.
  • n = 1.0: Refractive index within the corona.
  • corona_radius = 20.0: Radius of the corona.
source