Isentropic processes for axisymmetric Black Holes

TL;DR

This work analyzes whether a charged test particle can be absorbed by a stationary axisymmetric black hole without increasing the black hole entropy. Using a theory-agnostic near-horizon thermodynamic framework, it shows that isentropic absorption is classically forbidden for any non-extremal 3+1 dimensional black hole, encoded in the behavior of the effective potential $V_{eff}$ near the horizon. Focusing on Kerr–Newman black holes in GR, the authors then treat the process quantum mechanically via tunneling, with a dominant contribution governed by the Euclidean action $S_E$ and tunneling probability $\Gamma \propto e^{-2 S_E}$ where $S_E = \int_{r_+}^{r_2} \frac{dr}{\sqrt{V_{eff}(r)}}$. The results reveal a parameter dependence: smaller $M$ and smaller horizon radius, larger charge $Q$, and smaller particle angular momentum $L$ all enhance tunneling, especially near the equator, suggesting non-perturbative channels for entropy growth and raising questions about entropy bounds and information dynamics in black hole spacetimes.

Abstract

We demonstrate that the isentropic absorption of a classical charged test particle is classically forbidden for all 3+1 dimensional stationary, non-extremal, axisymmetric black holes in any diffeomorphism invariant theory of gravity. This result is derived purely from the near-horizon geometry and thermodynamic properties of the black hole spacetime, independent of the specific gravitational theory. We further consider the Kerr-Newman black hole in general relativity and analyse, using the quantum tunnelling approach, the conditions under which isentropic absorption may become allowed. Broader implications for the second law and extremality bounds are discussed.

Figures (3)

• Figure 1: The above plots show the effective potential experienced by a charged particle for isentropic absorption by a Kerr-Newman black hole in general relativity. The expression for the effective potential is given in Eq.\ref{['eq:9']}, with $E'(r) \equiv E - qA_t(r)= qA_t(r_+) + \Omega(L - qA_\phi(r_+)) -qA_t(r)$ for the isentropic absorption. The unit of $\theta$ is taken to be radians, so the plots are near the equator.
• Figure 2: The above plots show the Euclidean action experienced by a charged particle for isentropic absorption by a Kerr-Newman black hole in general relativity. The turning points exist only for certain values of parameters. The plots used the parameter values for which the turning point exists.
• Figure 3: The above plots show the Euclidean action experienced by a charged particle for isentropic absorption vs the radius of the outer horizon of a Kerr-Newman black hole in general relativity. The turning points exist only for certain values of parameters. The plots used the parameter values for which the turning points exist.