Black holes with scalar hair in light of the Event Horizon Telescope (2005.05992v3)

Abstract: Searching for violations of the no-hair theorem (NHT) is a powerful way to test gravity, and more generally fundamental physics, particularly with regards to the existence of additional scalar fields. The first observation of a black hole (BH) shadow by the Event Horizon Telescope (EHT) has opened a new direct window onto tests of gravity in the strong-field regime, including probes of violations of the NHT. We consider two scenarios described by the Einstein-Maxwell equations of General Relativity and electromagnetism, to which we add a scalar field. In the first case we consider a minimally-coupled scalar field with a potential, whereas in the second case the field is conformally-coupled to curvature. In both scenarios we construct charged BH solutions, which are found to carry primary scalar hair. We then compute the shadows cast by these two BHs as a function of their electric charge and scalar hair parameter. Comparing these shadows to the shadow of M87* recently imaged by the EHT collaboration, we set constraints on the amount of scalar hair carried by these two BHs. The conformally-coupled case admits a regime for the hair parameter, compatible with EHT constraints, describing a so-called mutated Reissner-Nordstr\"{o}m BH: this solution was recently found to effectively mimic a wormhole. Our work provides novel constraints on fundamental physics, and in particular on violations of the no-hair theorem and the existence of additional scalar fields, from the shadow of M87*.

• The paper constrains scalar-hairy black hole models by comparing EHT shadow observations with theoretical predictions.
• The analysis examines both minimally-coupled and conformally-coupled scalar fields, revealing deviations from Reissner–Nordström solutions.
• The results refine limits on additional scalar parameters in strong gravitational fields, informing future quantum gravity and cosmology research.

Analysis of Scalar Hair in Black Holes via Event Horizon Telescope Observations

The paper "Black holes with scalar hair in light of the Event Horizon Telescope" explores the investigation of black holes (BHs) possessing scalar hair, an exploration motivated by the discrete violations of the no-hair theorem (NHT). The paper primarily leverages recent observations from the Event Horizon Telescope (EHT) to impose constraints on these deviations. There is a particular focus on two theoretical scenarios—black holes described within the contexts of Einstein-Maxwell theories supplemented by additional scalar fields that are either minimally or conformally coupled.

The NHT posits that a static, asymptotically flat black hole in general relativity (GR), which is also a solution of the Einstein-Maxwell equations, can be uniquely characterized by three primary parameters: mass, charge, and angular momentum. The appearance of "hair," additional parameters governing the black hole's configuration, would thus signify a deviation from traditional GR predictions. These potential deviations carry profound implications for our understanding of gravity, particularly in the strong-field regime.

Methodological Approach

The authors first consider a model with a minimally-coupled scalar field. Here, they introduce a scalar potential that supports the existence of black holes deviating from the standard Reissner-Nordström solutions, characterized by primary scalar hair. The charged black holes in these setups, subsequently referred to as minimally-coupled charged hairy black holes (MCCHBH), reveal modifications in the shadow they cast as a result of the additional scalar parameter.

In a parallel line of inquiry, conformally-coupled scalar fields form the backbone of a separate theoretical investigation. Within this framework, the scalar hair leads to solutions termed conformally-coupled charged hairy black holes (CCCHBH). Of particular interest are configurations that mimic wormhole geometries—a notable example being the mutated Reissner-Nordström black hole—which shows promise in mimicking non-traditional BH behavior.

Results and Implications

The shadows of these BH configurations were calculated numerically to identify variations from the classical BH profiles. Notably, the comparisons between theoretical calculations and the shadow of M87* captured by the EHT enabled setting constraints on these models. For the MCCHBH model, findings suggest an upper limit on the scalar hair parameter. The results for CCCHBH are more nuanced and are contingent upon whether the scalar charge is positive or negative. Such constraints directly inform the extent to which GR might be modified by incorporating additional scalar fields.

Future Prospects and Theoretical Ramifications

Imposing bounds on the possible hair parameter of black holes aids in refining our model of gravitational interactions under extreme conditions. Insights gained from this research could significantly contribute to efforts towards a quantum theory of gravity or in the context of large-scale cosmological models encompassing dark matter and dark energy.

While the paper provides essential bounds and advances the theories that challenge GR, further work is required to explore black holes with rotation, emphasizing on Kerr solutions, since many astrophysical black holes, including M87*, are expected to have significant angular momentum. Additionally, more general model-agnostic constraints could be computed to broaden the impact of such theoretical studies on fundamental physics.

Overall, this research marks an important step in cross-examining the NHT through direct astronomical observations, setting a valuable precedent for future explorations that focus on merging theoretical physics with observational data in the field of astrophysics and fundamental physics.