Dynamical hair growth in black hole binaries in Einstein-scalar-Gauss-Bonnet gravity

TL;DR

This work investigates dynamical scalarization of binary black holes in Einstein-scalar-Gauss-Bonnet gravity, showing that BBHs initially described by General Relativity can acquire scalar charges once their separation crosses a DS radius $d_{\rm DS}$. A semi-analytic model based on adiabatic conservation of the Wald entropy $\mathcal{S}_{\rm W}$ is developed to estimate scalar-charge evolution, and fully nonlinear NR simulations validate the approach in suitable regimes. The authors quantify the GW dephasing with respect to GR and assess detectability for third-generation detectors, finding that DS could be observable in nearly equal-mass BBHs within a narrow mass window near the DS threshold, particularly for ET with appropriate couplings $\lambda$ and $\beta$. The results highlight a concrete, testable signature of EsGB gravity in the strong-field regime and provide a framework for rapid exploration of parameter space, while noting limitations when the adiabatic approximation breaks down near merger.

Abstract

Within the framework of scalar-tensor theories of gravity, certain models can evade classical black hole no-hair theorems. A well-known example is Einstein-scalar-Gauss-Bonnet gravity, where black holes carrying a scalar charge can exist. We find that, within this theory, binary black holes initially described by General Relativity can acquire scalar charges once they reach a critical orbital separation ("dynamical scalarization"). We develop a simple semi-analytic model, based on the adiabatic conservation of the total Wald entropy, to estimate the scalar charge evolution during the binary inspiral. We also run fully nonlinear numerical-relativity simulations for different configurations, finding consistent results. The gravitational-wave phase difference between Einstein-scalar-Gauss-Bonnet and General Relativity waveforms, which we use to assess detectability, is also computed. We find that dynamical scalarization might be observable in nearly equal-mass binary black hole mergers with third-generation ground-based gravitational-wave detectors, in a narrow range of the dimensional coupling of the theory.

Figures (12)

• Figure 1: Scalar field at the event horizon $\varphi_{\rm EH}$ as a function of separation for $\beta = 800$ and different values of $\lambda$, computed with the semi-analytic approach described in the main text. The scalarization radius increases for larger values of the coupling.
• Figure 2: Scalar field at the event horizon (EH) as a function of separation for $(\lambda/M)^2 = 0.703$ and different values of $\beta$, computed with the semi-analytic approach described in the main text. The scalarization radius is constant, while the scalar charge increases for decreasing $\beta$.
• Figure 3: Effect of a slight mass asymmetry ($m_1/m_2 = 0.98$) on the scalar field evolution. Dot-dashed lines show the unequal-mass case, while solid lines correspond to equal-mass binaries with individual masses $m_1$ and $m_2$. The scalarization radius is the same for both BHs and lies between the equal-mass cases, though the scalar field growth differs at each horizon.
• Figure 4: The scalar field development for $(\lambda/M)^2=0.688$, $\beta=48$ with initial data ID1, i.e. a uniform initial scalar field with an amplitude of $10^{-5}$ throughout all the space. The initial puncture distance is different for the two simulations, namely $d/M=11$ and $d/M=13$. Both simulations stop shortly after the merger when the scalar field drops to zero because the newly formed BH is too massive to sustain scalar field hair. (top) The average value of the scalar field at the apparent horizon (AH) of one of the two BHs as a function of the distance between the BHs throughout inspiral. When the merger occurs (which happens at $t\sim 1350\,M$), we compute it instead at the horizon of the remnant. (bottom) The scalar field as a function of simulation time on a logarithmic scale.
• Figure 5: The scalar field development for $(\lambda/M)^2=0.712$, $\beta=800$, and the two types of initial data described before. (top) The average value of the scalar field at the apparent horizon as a function of the distance between the BHs. (middle) The scalar field as a function of simulation time. (bottom) The average value (with the $L^2$ norm) of the Hamiltonian constraint throughout the whole space.