Bound orbits around charged black holes with exponential and logarithmic electrodynamics

TL;DR

This paper derives exact solutions for charged black holes in nonlinear electrodynamics, analyzes photon orbits, and explores their thermodynamic stability and phase transitions, revealing unique bound orbit structures and stability properties.

Contribution

It introduces new black hole solutions with magnetic charge from exponential and logarithmic NLED and studies their geodesics and thermodynamics.

Findings

Photon can have stable bound orbits, including non-circular ones.

Black hole stability is enhanced in nonlinear regimes with smaller radii.

Thermodynamic behavior approaches Schwarzschild-like in strong nonlinear regimes.

Abstract

We present exact black hole solutions endowed with magnetic charge coming from exponential and logarithmic nonlinear electrodynamics (NLED). Classically, we analyze the null and timelike geodesics, all of which contain both the bound and the scattering orbits. Using the effective geometry formalism, we found that photon can have nontrivial stable (both circular and non-circular) bound orbits. The noncircular bound orbits for the one-horizon case mostly take the form of precessed ellipse. For the extremal and three-horizon cases we find many-world orbits where photon crosses the outer horizon but bounces back without hitting the true (or second, respectively) horizon, producing the epicycloid and epitrochoid paths. Semiclassically, we investigate their Hawking temperature, stability, and phase transition. The nonlinearity enables black hole stability with smaller radius than its RN counterpart. However, for very-strong nonlinear regime, the thermodynamic behavior tends to be Schwarzschild-like.