Finite-Distance Imaging of Relativistic Equilibrium Tori around Genuine Kerr--Bertotti--Robinson Black Holes

Abstract

We calculate finite-distance images of stationary, pressure-supported tori around genuine, electrically neutral Kerr--Bertotti--Robinson black holes using general relativistic ray tracing with gray emission and absorption. The emitting volume is bounded by a constant-specific-angular-momentum equilibrium free surface, and the observer is placed at a radius of $50M$. Along the investigated external-field sequence, integrated brightness and apparent size both increase strongly as the field modifies the equilibrium source and photon propagation. Higher torus filling has a different effect: in a representative sequence, brightness grows by a factor of $5.9$ while the intensity-weighted image size increases by only $10\%$. Increasing viewing inclination enhances lateral brightness contrast. Stronger self-absorption can coexist with higher absolute brightness because emission and absorption scale together in the adopted gray prescription. At common pressure center and filling, increasing the dimensionless spin from $0.5$ to $0.95$ dims the retrograde sequence by a factor of about $7$ as its equilibrium contracts, whereas prograde brightness changes by only $2\%$. These contrasting responses show how the equilibrium boundary, fluid motion, and optical depth jointly shape the brightness, scale, and asymmetry of finite-distance torus images.