[Paper Review] Theory-agnostic tests of gravity with black hole shadows

Sourabh Nampalliwar, Saurabh Kumar|arXiv (Cornell University)|Aug 2, 2021

Astrophysical Phenomena and Observations6 citations

TL;DR

This paper investigates the robustness of theory-agnostic gravity tests using black hole shadows observed by the Event Horizon Telescope and future instruments. It finds that while many deviation parameters suffer from degeneracy and washout effects, the lowest-order deviation parameter $ w_{01} $ in the $ W $-function parametrization can be robustly constrained with future high-precision measurements, offering a reliable path for strong-field gravity tests.

ABSTRACT

Observations of black hole shadows with the Event Horizon Telescope have paved way for a novel approach to testing Einstein's theory of general relativity. Early analyses of the measured shadow put constraints on theory-agnostic parameters typically used to study deviations from Einstein's theory, but the robustness of these constraints was called into question. In this letter, we use a generic theory-agnostic metric to study the robustness of parameter estimation with BH shadows, taking into consideration current measurements made with the Event Horizon Telescope and future measurements expected with the Event Horizon Imager. We find that the robustness issue is highly nuanced, and parameter constraints can be highly misleading if parameter degeneracy is not handled carefully. We find that a certain kind of deviation is particularly well suited for the shadow based analysis, and can be recovered robustly with shadow measurements in the future.

Motivation & Objective

• To assess the robustness of theory-agnostic gravity tests using black hole shadow observations from the Event Horizon Telescope and the future Event Horizon Imager.
• To investigate how higher-order deviation parameters affect the estimation of leading-order non-GR parameters in parametrized metrics.
• To determine whether certain deviation parameters can be reliably constrained despite parameter degeneracies and measurement uncertainties.
• To evaluate the synergy potential between black hole shadow measurements and other strong-field gravity tests.
• To identify specific parametric deviations that are uniquely and robustly measurable via shadow-based analyses.

Proposed method

• The study employs a generic, theory-agnostic metric parametrization to model deviations from general relativity in the spacetime of spinning black holes.
• It uses numerical ray-tracing techniques based on the formalism of Nampalliwar et al. (2020b) and Bambi et al. (2017) to compute the apparent boundary (shadow) of black holes.
• The shadow size and shape are derived from the photon orbit radius $ r_{\text{ph}} $ and the metric component $ g_{tt} $, using equations (1) and (2) for spherically symmetric cases.
• Bayesian inference is applied to estimate parameters, with priors on deviation parameters and spin, using both current EHT measurements and future projected measurements.
• The analysis compares constraints across multiple cases: fixing higher-order parameters, allowing degeneracies, and testing the independence of $ w_{01} $ from $ w_{02} $ and spin.
• The study evaluates the impact of observational uncertainties and the assumption of an equatorial observer on parameter estimation robustness.

Experimental results

Research questions

• RQ1 Can theory-agnostic parameters in parametrized black hole metrics be robustly estimated from black hole shadow observations, despite degeneracies with higher-order parameters?
• RQ2 Which specific deviation parameters are resilient to washout effects from higher-order terms in the parametrization?
• RQ3 How do current and future shadow measurements compare in constraining non-GR parameters, particularly in the presence of spin and higher-order deviations?
• RQ4 To what extent can shadow-based constraints be combined with other observational techniques to break degeneracies and improve gravity tests?
• RQ5 Is there a subset of deviation parameters that can be reliably measured via shadows, even when others are degenerate or unconstrained?

Key findings

• The parameter $ w_{01} $, representing the lowest-order deviation in the $ W $-function parametrization, is robustly constrained by future shadow measurements, even in the presence of spin and higher-order parameters.
• In contrast, the $ a_{01} $ parameter suffers from severe washout effects due to degeneracy with $ a_{02} $, rendering current constraints non-robust and unreliable.
• Constraints on black hole spin are also non-robust when higher-order parameters are ignored, as both current and future measurements yield unbounded estimates.
• The degeneracy between $ w_{01} $ and $ w_{02} $ is minimal, as $ w_{02} $ has a negligible effect on the shadow, allowing $ w_{01} $ to be independently constrained.
• Future high-precision measurements are essential for robustly constraining $ w_{01} $, as current EHT data alone do not provide tight bounds due to degeneracy.
• The results suggest that shadow-based tests can provide unique, independent constraints on gravity, especially when combined with other techniques like gravitational waves or X-ray spectroscopy.