Data for Kerr BHs with scalar hair

Here, the numerical data described in the paper "Construction and physical properties of Kerr black holes with scalar hair", arXiv:1501.04319 [gr-qc], is made available for public use.

This paper is an invited contribution to the Focus Issue on "Black holes and fundamental fields" to appear in Classical and Quantum Gravity, Edited by Paolo Pani and Helvi Witek.

It expands on the solutions first presented in the paper "Kerr black holes with scalar hair", Phys. Rev. Lett. 112 (2014) 221101; e-Print: arXiv:1403.2757, by C. Herdeiro and E. Radu.

The attachment "Data_files.zip", contains five data files:
- configuration-I.dat
- configuration-II.dat
- configuration-III.dat
- configuration-IV.dat
- configuration-V.dat
These files contain the data for the five reference solutions described in the paper above. These solutions are:

Configuration I   : a typical boson star (BS) belonging to the main branch of BS solutions;
                   - the input parameters are:  (r_H=0; w= 0.85; m=1)
                   - ADM mass=1.25; ADM angular momentum 1.30
                   - BH mass=0; BH angular momentum=0
                   - Scalar field mass=1.25; Scalar field angular momentum=1.30

========================================================

Configuration II  : a (vacuum) Kerr BH in the region of non-uniqueness;
                   - the input parameters are:  (r_H=0.0662902; Omega_H= 1.11118)
                   - ADM mass=0.415; ADM angular momentum 0.172
                   - BH mass=0.415; BH angular momentum=0.172
                   - Scalar field mass=0; Scalar field angular momentum=0

========================================================

Configuration III : a KBHSH in the region of non-uniqueness with the same (M, J) as the Kerr BH in Configuration II;
                   - the input parameters are:  (r_H=0.2;  Omega_H=0.975; m=1)
                   - ADM mass=0.415; ADM angular momentum 0.172
                   - BH mass=0.393; BH angular momentum=0.15
                   - Scalar field mass=0.022; Scalar field angular momentum=0.022

========================================================

Configuration IV  : a KBHSH close to the main branch of BSs (which are likely to be stable);
                   - the input parameters are:  (r_H=0.1;  Omega_H=0.82; m=1)
                   - ADM mass=0.933; ADM angular momentum 0.739
                   - BH mass=0.234; BH angular momentum=0.114
                   - Scalar field mass=0.699; Scalar field angular momentum=0.625

========================================================

Configuration V  : a KBHSH in a region which is likely to be unstable;
                   - the input parameters are:  (r_H=0.04, Omega_H=0.68; m=1)
                   - ADM mass=0.975; ADM angular momentum 0.85
                   - BH mass=0.018; BH angular momentum=0.002
                   - Scalar field mass=0.957; Scalar field angular momentum=0.848
 

========================================================

The data is presented in the following order, in the files (F_i,\phi,W are the metric and scalar functions used in the paper):

--------------------------------
X_1   theta_1 F1 F2 F0 phi W
X_2   theta_1 F1 F2 F0 phi W
...
X_251 theta_1 F1 F2 F0 phi W

X_1   theta_2 F1 F2 F0 phi W
X_2   theta_2 F1 F2 F0 phi W
...
X_251 theta_2 F1 F2 F0 phi W

X_1   theta_30 F1 F2 F0 phi W
X_2   theta_30 F1 F2 F0 phi W
...
X_251 theta_30 F1 F2 F0 phi W
--------------------------------

where the grid points are:
X_k=(k-1)/250 (k=1,..,251)
 and
theta_k=(k-1)*Pi/29/2 (k=1,..,30)

The corresponding values for \pi/2<\theta\leq\pi
result from the reflection symmetry of the solutions along the equatorial plane.

X=x/(1+x) is a compactified radial coordinate,  0\leq x\leq 1

where
x=\sqrt{r^2-r_H^2} was a new radial coordinate defined in the paper;

The coordinate transformation between r and the radial coordinate R
of the Boyer-Lindquist form of the Kerr metric is given in the Appendix A of the paper.

AttachmentSize
Data_files.zip1.84 MB
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