Dirac particle in Newman-Unti-Tamburino spacetime

TL;DR

The study derives the Dirac equation for a spin-1/2 particle in the original NUT spacetime using the tetrad formalism and achieves complete variable separation into angular and radial parts. Angular solutions are expressed in hypergeometric functions, yielding a NUT-dependent quantization Λ^2 = N(N ± 4 a ε); the radial problem is analyzed for massive and massless fermions, with massive cases showing a horizon-based Hawking temperature T = 1/[2π(r_g + √(r_g^2 + 4 a^2))] and emission suppression as the NUT charge grows, while massless cases lead to confluent Heun function solutions and purely imaginary resonances ε_I = −i(3+2n)/(4 r_2). In the small-NUT-charge and extremal limits, the analysis reveals perturbative corrections to Schwarzschild, a degenerate horizon with entropy vanishing, and nontrivial wave characteristics tied to the NUT parameter. Overall, the work demonstrates that the NUT charge systematically alters angular quantization, horizon scattering, and resonance structures, providing potential observational discriminants from Kerr or Schwarzschild spacetimes.

Abstract

We derive the Dirac equation for a particle in the background of the Newman-Unti-Tamburino (NUT) spacetime by applying the tetrad formalism, and separate the angular and radial parts. We get the system of two differential equations for angular functions and the system of four differential equations for radial functions. We solve the angular equations in terms of hypergeometric functions and find the NUT-charge dependent quantization rule for the angular separation constant. As a result of studying the radial equations, we demonstrate that the probability of particle-antiparticle production on the outer event horizon decreases with the increase of the NUT charge. For the massless fermion, we construct the solution of the radial system of Dirac equation in terms of the confluent Heun functions that allows to get the NUT-charge dependent scattering resonances with imaginary energies. Under the assumption of small NUT charge, we study the extremal NUT black hole with a single horizon, when the Bekenstein-Hawking entropy vanishes identically, and reveal the non-zero NUT charge effects in wave characteristics.

Figures (5)

• Figure 1: The dependencies of real parts and absolute values of the functions $T_1$ (solid lines) and $T_2$ (dashed lines) on the variable $\theta$. Parameters: $m=3/2$; $n=4$; $a=0$ (black), $a=1$ (pink).
• Figure 2: The real (solid lines) and imaginary (dashed lines) parts of the functions $R_{11}$, $R_{12}$ of the wave function (\ref{['tofig2']}) for the case of massless fermion. Parameters: $r_g=1$; $\epsilon=1$;$N=3$; $a=0$ (black), $a=0.1$ (pink).
• Figure 3: The real (a) and imaginary (b) parts and absolute values (c) of the potential $P(x)$ in dependence on the NUT parameter $a$. Values of $a$ decreased sequentially ($1$, $0.9$, $0.7$, $0.5$, $0.3$, $0.1$, $0$) from solid to pointed lines.
• Figure 4: The real (solid lines) and imaginary (dashed lines) parts of the components $R_{11}$, $R_{12}$ of the wave function (\ref{['radNUTextremal']}) at the NUT parameter $a=0.05$ (black) and $a=0.1$ (pink); $N=1, \, \, \epsilon=10.$
• Figure 5: The Hawking temperature for Kerr (left) and NUT (right) black holes in dependence on the angular momentum $J$ and NUT-parameter $a$, respectively.