Shadows of parametrized axially symmetric black holes allowing for separation of variables

TL;DR

This paper investigates axially symmetric black hole metrics that permit variable separation, demonstrating that near the black hole, shadows depend on few parameters, and approximations are valid in specific theories like Einstein-dilaton-Gauss-Bonnet.

Contribution

It constrains general axially symmetric black hole metrics by symmetry requirements, linking metric properties to observable shadow features and providing approximations in certain theories.

Findings

Black-hole shadow depends on few deformation parameters near the black hole.

Separation of variables constrains metric functions and influences shadow shape.

Approximate shadow modeling is effective in Einstein-dilaton-Gauss-Bonnet theory.

Abstract

Metric of axially symmetric asymptotically flat black holes in an arbitrary metric theory of gravity can be represented in the general form which depends on infinite number of parameters. We constrain this general class of metrics by requiring the existence of additional symmetries, which lead to the separation of variables in the Hamilton-Jacobi and Klein-Gordon equations, and show that once the metric functions change sufficiently moderately in some region near the black hole, the black-hole shadow depends on a few deformation parameters only. We analyze the influence of these parameters on the black-hole shadow. We also show that the shadow of the rotating black hole in the Einstein-dilaton-Gauss-Bonnet theory is well approximated if the terms violating the separation of variables are neglected in the metric.