# SSBH

**Repository Path**: hustsl/ssbh

## Basic Information

- **Project Name**: SSBH
- **Description**: Single Spinning Black Hole Simulation
- **Primary Language**: C
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2021-09-02
- **Last Updated**: 2023-05-20

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# CTT Initial Data

Following CTT, the initial data for a single spinning blackhole can be obtained by solving

```math
\Delta \psi+{1\over8}\psi^5K_{ij}K^{ij}=0
```
The punctured version is
```math
\psi=1+{\mathcal{M}\over r}+u \\

\Delta u+{9J^2r\sin^2\theta\over4[(u+1)r+\mathcal{M}]^7}=0
```
Solve it by
```math
u^{(k+1)}(r)=\int {9J^2r'\sin^2\theta\over16\pi[(u^{(k)}+1)r'+\mathcal{M}]^7|r-r'|}\mathrm{d}^3r'
```
In spherical coordinate,
```math
u^{(k+1)}(r,\theta)=\int\limits_0^\pi\mathrm{d}\theta'\int\limits_0^{r_0}\mathrm{d}r'
{9J^2r^3\sin^3\theta 
f\left(
{2r'r\sin\theta\sin\theta'\over r^2+r'^2-2r'r\cos\theta\cos\theta' }
\right)
\over 4[(u^{(k)}+1)r'+\mathcal{M}]^7
\sqrt{r^2+r'^2-2r'r\cos\theta'\cos\theta}}
```
where 
```math
f(x)=\int\limits_0^{2\pi}{\mathrm{d}\psi\over\sqrt{1-x\cos\psi}}
```

# TODOs
- [ ] recover $\gamma_{ij}$ and $K_{ij}$. 
- [ ] calculate the ADM mass
- [ ] implement parallelization
- [ ] evolve use ADM/BSSN/z4c scheme