Scalar-tensor-vector gravity theory is tested by black hole photon rings

TL;DR

This study analyzes the photon ring and shadow of Reissner-Nordström black holes within scalar-tensor-vector gravity, deriving bounds on model parameters using EHT data and highlighting the potential for observational tests of quantum gravity models.

Contribution

It provides the first detailed analysis of black hole photon rings in scalar-tensor-vector gravity, establishing observational criteria to distinguish modified gravity effects from general relativity.

Findings

Photon ring size increases with the MOG parameter ()

Impact parameter interval widens with increasing charge (Q)

Bounds on () and (Q) derived from EHT data

Abstract

This paper investigates the photon ring and shadow structure of the Reissner-Nordstr\"om black hole in the scalar-tensor-vector gravitational framework. The black hole is characterized by the ( MOG) parameter (\alpha) and the charge (Q). The study finds that as (\alpha) increases, the event horizon radius (r_h), photon sphere radius (r_{ph}), and critical impact parameter (b_{ph}) all increase, while these decrease as (Q) increases. The innermost stable circular orbit radius (r_{isco}) exhibits similar monotonic behavior. Ray-tracing shows that as (Q) increases, the impact parameter (b) interval between the lensing ring and photon ring widens; (b_{\text{ph}}) is non-degenerate, and the photon ring radius is uniquely determined by (\alpha) and (Q). Using $EHT$ constraints on (SgrA^*) and (M87^*), the bounds on (\alpha) and (Q) are derived. For (Q = 0), (0.5), and (1), the allowed ranges are (\alpha \in [0, 0.06]), ([0, 0.11]), and ([0.19, 0.36]), respectively. Radiative simulations show that for fixed (Q), larger (\alpha) leads to a larger, non-degenerate photon ring. The Schwarzschild case is approached only when both (\alpha) and (Q) are small. This provides a computational basis for testing modified black holes and offers a non-degenerate observational criterion for distinguishing quantum gravity models, consistent with current $EHT$ data. Future observations with $ngEHT$ and multi-band polarization can further test this. The results suggest that studying the photon ring structure of a Reissner-Nordstr\"om black hole in scalar-tensor-vector gravity provides a unique optical diagnostic for potential quantum-gravity tests and black hole properties.