Black hole shadow and acceleration bounds for spherically symmetric spacetimes

TL;DR

This paper investigates the relationship between black hole shadow parameters and acceleration bounds for radial uniformly accelerated trajectories in various static spherically symmetric black hole spacetimes, revealing universal relations.

Contribution

It establishes explicit connections between black hole shadow features and acceleration bounds, valid across multiple gravity theories and spacetime geometries.

Findings

Photon sphere radius equals the bound on closest approach distance.

Shadow radius equals the inverse of the acceleration bound.

Relations hold universally in different gravity theories for Schwarzschild-type black holes.

Abstract

We explore an interesting connection between black hole shadow parameters and the acceleration bounds for radial linear uniformly accelerated (LUA) trajectories in static spherically symmetric black hole spacetime geometries of the Schwarzschild type. For an incoming radial LUA trajectory to escape back to infinity, there exists a bound on its magnitude of acceleration and the distance of closest approach from the event horizon of the black hole. We calculate these bounds and the shadow parameters, namely the photon sphere radius and the shadow radius, explicitly for specific black hole solutions in $d$-dimensional Einstein's theory of gravity, in pure Lovelock theory of gravity and in the $\mathcal{F}(R)$ theory of gravity. We find that for a particular boundary data, the photon sphere radius $r_{ph}$ is equal to the bound on radius of closest approach $r_b$ of the incoming radial LUA trajectory while the shadow radius $r_{sh}$ is equal to the inverse magnitude of the acceleration bound $|a|_b$ for the LUA trajectory to turn back to infinity. Using the effective potential technique, we further show that the same relations are valid in any theory of gravity for static spherically symmetric black hole geometries of the Schwarzschild type. Investigating the trajectories in a more general class of static spherically symmetric black hole spacetimes, we find that the two relations are valid separately for two different choices of boundary data.