Kerr-Newman black hole in the formalism of isolated horizons

The near horizon geometry of general black holes in equilibrium can be conveniently characterized in the formalism of weakly isolated horizons in the form of the Bondi-like expansions (Krishnan B, Classical Quantum Gravity 29, 205006, 2012). While the intrinsic geometry of the Kerr-Newman black hole has been extensively investigated in the weakly isolated horizon framework, the off-horizon description in the Bondi-like system employed by Krishnan has not been studied. We extend Krishnan’s work by explicit, nonperturbative construction of the Bondi-like tetrad in the full Kerr-Newman spacetime. Namely, we construct the Bondi-like tetrad which is parallelly propagated along a nontwisting null geodesic congruence transversal to the horizon and provide all Newman-Penrose scalars associated with this tetrad. This work completes the description of the Kerr-Newman spacetime in the formalism of weakly isolated horizons and is a starting point for the investigation of deformed black holes.

Figure 1

Characteristic initial value problem for WIH.

Figure 2

Nontwisting, nonexpanding and shear-free congruence ${\ell }_K^a$ with the initial position ${\mathsf{r}}_0=0$, ${\vartheta }_0=\pi /4$.

Figure 3

Twisting, expanding and shear-free congruence ${\ell }_K^a$ with the initial position ${\mathsf{r}}_0=0.5$, ${\vartheta }_0=\pi /4$.

Figure 4

Twisting, converging and shear-free congruence $n_K^a$ for the initial position ${\mathsf{r}}_0=3$, ${\vartheta }_0=\pi /4$.

Figure 5

Nontwisting, converging and shearing congruence $n_B^a$ for the initial position ${\mathsf{r}}_0=5$, ${\vartheta }_0=\pi /4$.

Figure 6

Twisting, expanding and shearing congruence ${\ell }_K^a$ for the initial position ${\mathsf{r}}_0=2$, ${\vartheta }_0=\pi /4$.