Here, the numerical data described in the paper "Kerr black holes with Proca hair", arXiv:1603.02687 [gr-qc] [1], is made available for public use.
The data is presented in the same form as the data we have previously made available here for Kerr black holes with scalar hair, described in the paper "Construction and physical properties of Kerr black holes with scalar hair", Class. Quant. Grav. 32 (2016) 144001; arXiv:1501.04319 [gr-qc] [2], which 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.
The data for the Proca star was obtained in the paper "Proca Stars: gravitating Bose-Einstein condensates of massive spin 1 particles", Richard Brito, Vitor Cardoso, Carlos A. R. Herdeiro, Eugen Radu, Phys. Lett. B752 (2016) 291-295; arXiv:1508.05395 [gr-qc].
The data for Kerr black holes with Proca hair can be found in the attachment "Data_files_KBHsPH.zip", which 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 [1] above. These solutions are:
========================================================
Configuration I : a typical Proca star (PS) belonging to the main branch of PS solutions;
- the input parameters are: (r_H=0; w=0.9 ; m=1)
- ADM mass=1.456; ADM angular momentum=1.500
- BH mass=0; BH angular momentum=0
- Proca field mass=1.456; Proca field angular momentum=1.500
========================================================
Configuration II : a (vacuum) Kerr BH in the region of non-uniqueness;
- the input parameters are: (r_H=0.1945 ; Omega_H=1.0432)
- ADM mass=0.365 ; ADM angular momentum= 0.128
- BH mass =0.365 ; BH angular momentum= 0.128
- Proca field mass=0; Proca field angular momentum=0
========================================================
Configuration III : a KBHPH in the region of non-uniqueness with the same (M, J) as the Kerr BH in Configuration II;
- the input parameters are: (r_H=0.2475; Omega_H=0.9775; m=1)
- ADM mass=0.365 ; ADM angular momentum=0.128
- BH mass =0.354 ; BH angular momentum=0.117
- Proca field mass=0.011; Proca field angular momentum=0.011
========================================================
Configuration IV : a KBHPH close to the first branch of PSs;
- the input parameters are: (r_H=0.09; Omega_H=0.863; m=1)
- ADM mass=0.915; ADM angular momentum=0.732
- BH mass=0.164; BH angular momentum=0.070
- Proca field mass=0.751; Proca field angular momentum=0.662
========================================================
Configuration V : a KBHPH well inside the domain of existence;
- the input parameters are: (r_H=0.06, Omega_H=0.79; m=1)
- ADM mass=1.173; ADM angular momentum=1.079
- BH mass=0.035; BH angular momentum=0.006
- Proca field mass=1.138; Proca field angular momentum=1.073
========================================================
The data is presented in the following order, in the files (F_i, W are the metric functions and H_i, V are the Proca functions used in the paper [1] above):
--------------------------------
X_1 theta_1 F1 F2 F0 W H1 H2 H3 V
X_2 theta_1 F1 F2 F0 W H1 H2 H3 V
...
X_251 theta_1 F1 F2 F0 W H1 H2 H3 V
X_1 theta_2 F1 F2 F0 W H1 H2 H3 V
X_2 theta_2 F1 F2 F0 W H1 H2 H3 V
...
X_251 theta_2 F1 F2 F0 W H1 H2 H3 V
X_1 theta_35 F1 F2 F0 W H1 H2 H3 V
X_2 theta_35 F1 F2 F0 W H1 H2 H3 V
...
X_261 theta_35 F1 F2 F0 W H1 H2 H3 V
--------------------------------
where the grid points are:
X_k=(k-1)/260 (k=1,..,261)
and
theta_k=(k-1)*Pi/34/2 (k=1,..,35)
The corresponding values for pi/2< hetaleqpi
result from the reflection symmetry of the solutions along the equatorial plane.
X=x/(1+x) is a compactified radial coordinate, 0leq xleq 1
where
x=sqrt{r^2-r_H^2} was a new radial coordinate defined in the paper [1] above;
The coordinate transformation between r and the radial coordinate R
of the Boyer-Lindquist form of the Kerr metric is given in Section 4 of paper [1] above or the Appendix A of the paper [2] above.