Does the black hole shadow probe the event horizon geometry?

Pedro V P Cunha,Carlos A R Herdeiro,Maria J Rodriguez

doi:10.1103/physrevd.97.084020

Pedro V P Cunha, Carlos A R Herdeiro + Show 1 more

Open Access

https://doi.org/10.1103/physrevd.97.084020

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Abstract

There is an exciting prospect of obtaining the shadow of astrophysical black holes (BHs) in the near future with the Event Horizon Telescope. As a matter of principle, this justifies asking how much one can learn about the BH horizon itself from such a measurement. Since the shadow is determined by a set of special photon orbits, rather than horizon properties, it is possible that different horizon geometries yield similar shadows. One may then ask how sensitive is the shadow to details of the horizon geometry? As a case study, we consider the double Schwarzschild BH and analyse the impact on the lensing and shadows of the conical singularity that holds the two BHs in equilibrium -- herein taken to be a strut along the symmetry axis in between the two BHs. Whereas the conical singularity induces a discontinuity of the scattering angle of photons, clearly visible in the lensing patterns along the direction of the strut's location, it produces no observable effect on the shadows, whose edges remain everywhere smooth. The latter feature is illustrated by examples including both equal and unequal mass BHs. This smoothness contrasts with the intrinsic geometry of the (spatial sections of the) horizon of these BHs, which is not smooth, and provides a sharp example on how BH shadows are insensitive to some horizon geometry details. This observation, moreover, suggests that for the study of their shadows, this static double BH system may be an informative proxy for a dynamical binary.

Highlights

In relativistic gravity, the propagation of light on curved spacetimes provides a basic probe of the background’s properties
Rather than a dynamical binary, whose spacetime geometry is time dependent and known only numerically, we study a toy model known as the double Schwarzschild solution, a particular example of a Weyl solution [25]
The double Schwarzschild black holes (BHs) is a static Weyl solution with axial-symmetry, featuring two nonrotating, neutral BHs supported in equilibrium by a conical singularity which can be chosen to take the form of either two strings or one strut

Summary

Introduction

The propagation of light on curved spacetimes provides a basic probe of the background’s properties. In the particular case of BHs, a set of unstable LRs (and other FPOs) determine the edge of the BH shadow [15,16,17], the absorption cross section at high frequencies under given observation conditions. The (main) shadow presents similar features to that obtained in a dynamical binary [29] wherein the individual BHs will certainly not present similar deformations of their horizon geometry. In particular we compare the shadows obtained with those of a dynamical binary system and the horizon geometry of the BHs in the double Schwarzschild solution, presented in terms of embedding diagrams.

Shadows in the double Schwarzschild BH solution

Double Schwarzschild solution review

Shadows in double BH solution

Insensitivity to the conical singularity

Emitting star surface in static and spinning BHs

Closing remarks