[Paper Review] Quasar continuum spectrum disfavors black holes with a magnetic monopole charge

Indrani Banerjee, Vijay Shersingh Chawan+3 more|arXiv (Cornell University)|Dec 10, 2021

Astrophysical Phenomena and Observations85 references4 citations

TL;DR

This study investigates whether quasars hosting Bardeen black holes—regular black holes with a magnetic monopole charge—can be observationally distinguished from standard Kerr black holes. Using the thin-disk accretion model, the authors compute theoretical continuum spectra for Bardeen black holes and compare them with optical data from 80 Palomar Green quasars. The analysis, based on chi-square, Nash-Sutcliffe efficiency, and index of agreement, finds that black holes with a magnetic monopole charge g ≥ 0.03 are excluded at the 99% confidence level, favoring the standard Kerr solution in general relativity.

ABSTRACT

Black holes carrying a magnetic monopole charge are a subject of interest for a long time. In this work we explore the possibility of an observational evidence of such black holes carrying a magnetic monopole, namely the Bardeen rotating black holes. We derive the theoretical spectrum from the accretion disk surrounding a Bardeen black hole using the thin-disk approximation. We compare the theoretically derived spectrum in comparison to the optical data of eighty Palomar Green quasars to constrain the monopole charge parameter $g$ and the spin parameter $a$ of the quasars. From our analysis we note that the Kerr-scenario in \gr\ is observationally more favored than black holes with a monopole charge. We arrive at such a conclusion using error estimators like $\chi^2$, the Nash-Sutcliffe efficiency, the index of agreement and their modified forms. In particular, black holes with $g \geq 0.03$ are outside $99\%$ confidence interval. The implications are discussed.

Motivation & Objective

• To test whether black holes with a magnetic monopole charge (Bardeen black holes) can be observationally distinguished from standard Kerr black holes.
• To assess the viability of non-linear electrodynamics-inspired regular black holes using astrophysical data from quasars.
• To constrain the monopole charge parameter g and spin parameter a using observed continuum spectra of quasars.
• To evaluate the observational preference for the Kerr metric over monopole-charged black holes using multiple error estimators.

Proposed method

• Derive the theoretical continuum spectrum from thin accretion disks around Bardeen black holes using the Novikov-Thorne model.
• Model the accretion disk in the Bardeen metric, which incorporates a magnetic monopole charge parameter g and spin parameter a.
• Compare the theoretically computed spectra with observed optical magnitudes of 80 Palomar Green quasars.
• Apply statistical error estimators including chi-square (χ²), Nash-Sutcliffe efficiency, index of agreement, and their modified forms to quantify model fit.
• Use the χ² test to determine confidence intervals for the monopole charge g, identifying values excluded at 99% confidence.
• Fix the spin parameter a as a free parameter per quasar and derive best-fit values for g = 0 (Kerr case), then extend to non-zero g.

Experimental results

Research questions

• RQ1 Can the continuum spectrum of quasars distinguish Bardeen black holes with a magnetic monopole charge from standard Kerr black holes?
• RQ2 What is the observational upper limit on the magnetic monopole charge g for quasars based on optical data?
• RQ3 How does the fit of the Bardeen model compare to the Kerr model using multiple statistical error metrics?
• RQ4 Are there specific quasars for which the monopole charge g is constrained to zero within 99% confidence?
• RQ5 To what extent do alternative accretion disk models or additional components (e.g., corona, jet) affect the constraints on g and a?

Key findings

• Black holes with a magnetic monopole charge g ≥ 0.03 are excluded at the 99% confidence level based on χ² analysis of quasar continuum spectra.
• The Kerr solution in general relativity is observationally favored over Bardeen black holes with non-zero monopole charge, as indicated by all error estimators including χ², Nash-Sutcliffe efficiency, and index of agreement.
• For g = 0 (Kerr case), the study derives spin parameters for individual quasars, such as PG 0003+199 with a ≈ 0.89 ± 0.05, consistent with prior independent measurements.
• The monopole charge g ≳ 0.13 is also found to be excluded at the 99% confidence interval, reinforcing the preference for the Kerr solution.
• The results are robust across multiple statistical metrics, including modified forms of the Nash-Sutcliffe efficiency and index of agreement.
• The study notes limitations due to unmodeled components in the SED (e.g., corona, jet, dusty torus), which may affect parameter estimation, and suggests future work with alternative observables like black hole shadows or iron K-alpha lines.