Binary Black Hole Coalescence and the Dynamics of Scalar Hair in Einstein-Maxwell-Scalar Theory

Abstract: We investigate the head-on coalescence of charged binary black holes in Einstein-Maxwell-Scalar (EMS) theory using numerical relativity. The binaries are built from charged puncture initial data representing two Reissner-Nordström black holes immersed in a purely kinetic scalar perturbation: the scalar field initially vanishes, while its conjugate momentum provides a small seed for the instability. We evolve the coupled gravitational, electromagnetic, and scalar sectors and monitor the apparent horizons, the emitted radiation, and the scalar field on the horizons. Our simulations show that the nonminimal electromagnetic-scalar coupling can dynamically trigger the growth of scalar hair even when the individual black holes are initially scalar-free. The subsequent evolution depends on the coupling strength and on the charge retained by the remnant. For weak coupling, or when charge cancellation suppresses the electromagnetic source after merger, the scalar field is radiated away or absorbed by the final horizon and the system dynamically descalarizes. For sufficiently strong coupling and nonzero remnant charge, the scalar field remains finite and the final black hole approaches a scalarized configuration. The coalescence also excites scalar radiation whose time profile is qualitatively correlated with the dominant gravitational-wave mode during the nonlinear stage of the collision. These results provide a binary realization of scalarization/descalarization transitions in EMS theory and show that the fate of scalar hair is controlled by the interplay between the scalar coupling and the charge content of the remnant.

• The paper demonstrates that scalar hair formation during BBH coalescence in EMS theory hinges on the remnant's charge and the strength of the scalar-electromagnetic coupling.
• It employs advanced numerical relativity simulations using the CCZ4 formulation in GRChombo with adaptive mesh refinement to capture nonlinear merger dynamics.
• The study reveals a multi-field correlation among gravitational, electromagnetic, and scalar radiation, offering insights that can refine gravitational waveform templates for beyond-GR tests.

Binary Black Hole Coalescence and Scalar Hair Dynamics in Einstein-Maxwell-Scalar Theory

Theoretical Framework and Scalarization Mechanism

The paper investigates head-on binary black hole (BBH) coalescence in Einstein-Maxwell-Scalar (EMS) theory, characterized by a nonminimal coupling between the electromagnetic field and a scalar field. The action incorporates a quadratic scalar-electromagnetic coupling $f(\phi) = 1 + a_0 \phi^2$, allowing for the Reissner–Nordström branch to remain a solution but enabling spontaneous scalarization via tachyonic instability when $a_0$ exceeds a critical threshold. Under these couplings, electromagnetic invariants (not curvature) source scalar field amplification. The scalar-puncture initial data, consisting of two charged Reissner-Nordström black holes and a purely kinetic scalar perturbation (vanishing scalar field, nonzero conjugate momentum), initiates the nonlinear dynamical process.

The evolution employs the CCZ4 formulation implemented in GRChombo, with adaptive mesh refinement and fourth-order finite-difference schemes, ensuring robust monitoring of constraint violations and horizon dynamics. The binary initial data construction extends the TwoPunctures method for charged systems, ensuring the electromagnetic and scalar momentum constraints are compatible with the prescribed gauge and slicing.

Numerical Relativity Simulations: Scalarization and Descalarization in BBH Mergers

The numerical simulations focus on several scenarios: equal-charge and opposite-charge binaries, and varying scalar-electromagnetic couplings ($a_0$). The main diagnostic is the horizon-averaged scalar field, monitored pre- and post-merger. For weak coupling ($a_0 = 300$), scalar hair generated during infall is radiated away or absorbed post-merger, and the remnant dynamically descalarizes. For strong coupling ($a_0 = 3000$), the remnant retains nonzero scalar hair, stabilizing toward a scalarized configuration.

A critical outcome is the dependence of scalarization on the remnant’s charge. Equal-charge binaries retain net charge post-merger, allowing the scalar field to persist via the electromagnetic source. In contrast, opposite-charge binaries undergo charge cancellation, suppressing the electromagnetic invariant, leading to rapid descalarization and a bald remnant. Despite pre-merger scalarization of individual horizons, only remnants with sufficiently high charge-to-mass ratios sustain scalar hair.

Multi-Channel Radiation and Correlation with Gravitational Waveforms

The simulations demonstrate excitation of scalar radiation correlated with the dominant gravitational-wave mode during the nonlinear merger stage. The extraction of Newman-Penrose scalar $\Psi_4$ alongside electromagnetic and scalar field channels reveals the multi-field dynamical imprint. This correlation accentuates the scalar channel as dynamically sourced during coalescence, not merely as a vestige of pre-merger perturbation. The scalar field distribution post-merger confirms spatial localization near the common horizon for scalarized remnants, decreasing toward spatial infinity.

Implications and Theoretical Significance

The results provide a binary realization of scalarization/descalarization transitions, clarifying that the survival of scalar hair in EMS theory is controlled by scalar coupling strength and remnant charge content. The interplay between electromagnetic invariants and scalar field instabilities replaces curvature-driven mechanisms found in scalar-Gauss-Bonnet gravity or Horndeski models. The findings align with and extend prior studies of isolated black holes [33-35], revealing threshold phenomena and dynamical transitions in strongly nonlinear, binary spacetime configurations.

Practically, the presence or absence of scalar hair modifies radiative channels, potentially affecting gravitational waveform templates used in parameter estimation and tests of fundamental physics with gravitational wave data. Binary EMS systems exemplify environments where scalar field observables are dynamically tied to merger remnants, highlighting distinct signatures compared to GR or pure Einstein-Maxwell frameworks. This has implications for searches of beyond-GR phenomena in gravitational wave astronomy and for theoretical models involving additional degrees of freedom.

Future Directions

Further exploration is warranted across a broader parameter space, especially mapping the boundary between scalarized and descalarized remnants in $(q_1, q_2, a_0)$ space. The study motivates analyses of quasi-circular binaries and rotating charged black holes to probe the impact of orbital angular momentum and spin on scalarization mechanisms. Enhanced waveform extraction and systematic studies of radiated fluxes will enhance quantitative assessments of scalar and electromagnetic imprints on gravitational signals. Such efforts could clarify the measurable deviations from GR in realistic astrophysical scenarios and refine the understanding of scalar hair in alternative gravity theories.

Conclusion

This work robustly demonstrates that binary black hole mergers in EMS theory can dynamically generate and sustain scalar hair, contingent on nonminimal coupling strength and remnant charge. The fate of the scalar field is not universal; it depends on the merger remnant’s electromagnetic content. Opposite-charge binaries exhibit efficient descalarization, while equal-charge binaries can maintain scalarized states, thereby providing multidimensional radiative signatures. The results establish the binary scenario as a powerful probe of scalarization dynamics, with implications for theoretical modeling and observational searches for non-GR physics in the strong-field regime.