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arxiv: 2606.24215 · v1 · pith:73BK5EFBnew · submitted 2026-06-23 · 🌀 gr-qc

Nonlinear Stability of Kerr-Sen Black Holes in Merging Binaries

Andrew Carroll , Eric W. Hirschmann , Hyun Lim , David Neilsen , David F. Van Komen , Sebastian Vander Ploeg Fallon This is my paper

Pith reviewed 2026-06-25 23:09 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Kerr-Sen black holesnonlinear stabilitybinary black hole mergernumerical relativityEinstein-Maxwell-dilaton-axiondilaton fieldaxion fieldscalar hair
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The pith

Kerr-Sen black holes keep dilaton and axion fields after head-on mergers in Einstein-Maxwell-dilaton-axion theory.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests the nonlinear stability of Kerr-Sen black holes by running numerical relativity simulations of head-on binary mergers with approximate initial data. For cases with electric charge the dilaton field survives the merger, and for spinning cases the remnant keeps an axion field long afterward. The authors also show that black holes sitting in a scalar background acquire and retain scalar hair, including Kerr-Newman solutions that start without it and later scalarize. These outcomes are offered as evidence that the black holes remain stable inside the theory.

Core claim

Head-on binary black hole simulations in Einstein-Maxwell-dilaton-axion theory show that Kerr-Sen solutions with nontrivial electric charge preserve a dilaton field through merger while spinning remnants preserve an axion field. Black holes immersed in a scalar background retain scalar hair, and initially unscalarized Kerr-Newman black holes scalarize and stay scalarized throughout the evolution.

What carries the argument

Numerical relativity evolution of head-on binary collisions that tracks the survival of dilaton and axion fields after merger.

Load-bearing premise

Simulations that use approximate initial data for head-on collisions over a limited parameter space are sufficient to establish long-term nonlinear stability.

What would settle it

A longer simulation in which the dilaton or axion field amplitude falls to zero after merger would show the claimed stability does not hold.

Figures

Figures reproduced from arXiv: 2606.24215 by Andrew Carroll, David F. Van Komen, David Neilsen, Eric W. Hirschmann, Hyun Lim, Sebastian Vander Ploeg Fallon.

Figure 1
Figure 1. Figure 1: shows the waveforms from one such represen￾tative head-on collision of two identical Kerr–Sen black holes. For this system, both BHs have χ = 0.4 and q/m = 0.1, are initially separated by 16M and fall to￾gether from rest. The waveforms are of the gravitational radiation, Ψ4 and electromagnetic radiation,Φ1 and Φ2. The radiated energy as a function of time is shown in [PITH_FULL_IMAGE:figures/full_fig_p004… view at source ↗
Figure 2
Figure 2. Figure 2: In this case, the GW is clearly the dominant [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Plot of the radiated energy for the case [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The scalar fields on the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Percent deviation of the remnant black hole’s horizon [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The scalar fields on the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The Hamiltonian constraint [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The volume weighted [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The sum of the volume weighted Hamiltonian [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

We investigate the stability of Kerr-Sen black holes, which arise in Einstein-Maxwell-dilaton-axion theory. Within a numerical relativity framework, we perform head-on binary black hole simulations with approximate initial data across a portion of the parameter space. We find that for nontrivial electric charge, a dilaton field persists through merger and that in the presence of spin, the remnant will also retain an axion field. The persistence of these fields for long times after merger strongly suggests the stability of these black holes within this alternative gravity theory. We further test whether initially unscalarized black holes will acquire hair in the presence of a scalar background. We find that black holes immersed in such a background retain scalar hair. Furthermore, we find that even initially unscalarized Kerr-Newman black holes will scalarize and remain scalarized throughout the evolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper investigates nonlinear stability of Kerr-Sen black holes in Einstein-Maxwell-dilaton-axion theory via numerical relativity simulations of head-on binary mergers using approximate initial data over a limited parameter space. It reports persistence of dilaton fields for charged cases and axion fields for spinning cases after merger, interprets this as evidence of stability, and additionally finds that initially unscalarized black holes acquire and retain scalar hair when immersed in a scalar background or via scalarization of Kerr-Newman solutions.

Significance. Numerical tests of stability for charged, spinning black holes in modified gravity via binary mergers could provide useful evidence if the simulations are shown to be robust; the persistence results, if confirmed, would support the viability of Kerr-Sen solutions as end states and motivate further study of scalar hair in dynamical settings.

major comments (3)
  1. [Abstract] Abstract and concluding section: the claim that 'persistence of these fields for long times after merger strongly suggests the stability' is not justified by the reported setup, as head-on collisions with approximate initial data exclude orbital angular momentum and generic perturbation directions that could excite unstable modes.
  2. [Numerical Methods] Numerical setup section: no convergence tests, resolution studies, or error bars are described, leaving the reliability of late-time field persistence unverified and open to contamination from constraint violations in the approximate initial data.
  3. [Results] Results section: the restricted parameter scan (head-on only, portion of charge/spin/mass-ratio space) does not rule out instabilities for other configurations, undermining the inference from observed persistence to general nonlinear stability.
minor comments (2)
  1. [Introduction] Notation for the dilaton and axion fields should be defined explicitly at first use to aid readability.
  2. [Figures] Figure captions could include more detail on the plotted quantities and simulation parameters for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. We address each major comment below, agreeing where revisions are needed to better reflect the scope of our work and proposing changes to the abstract, numerical methods, and results sections.

read point-by-point responses

  1. Referee: [Abstract] Abstract and concluding section: the claim that 'persistence of these fields for long times after merger strongly suggests the stability' is not justified by the reported setup, as head-on collisions with approximate initial data exclude orbital angular momentum and generic perturbation directions that could excite unstable modes.

    Authors: We agree that the original phrasing overstates the generality of the conclusion. Head-on mergers with approximate initial data do not include orbital angular momentum and cannot excite all possible perturbation modes. We will revise the abstract and concluding section to state that the observed persistence provides supporting evidence for stability against the perturbations realized in these specific head-on simulations, rather than claiming it strongly suggests general nonlinear stability. revision: yes

  2. Referee: [Numerical Methods] Numerical setup section: no convergence tests, resolution studies, or error bars are described, leaving the reliability of late-time field persistence unverified and open to contamination from constraint violations in the approximate initial data.

    Authors: This point is correct and represents a clear gap in the current manuscript. We will add convergence tests at multiple resolutions, resolution studies for the scalar fields, and error estimates in a revised numerical methods section to demonstrate that the late-time persistence is robust and not an artifact of constraint violations or numerical errors. revision: yes

  3. Referee: [Results] Results section: the restricted parameter scan (head-on only, portion of charge/spin/mass-ratio space) does not rule out instabilities for other configurations, undermining the inference from observed persistence to general nonlinear stability.

    Authors: The manuscript already notes that only a portion of parameter space is explored with head-on mergers. We do not claim to have ruled out instabilities in unexamined regimes. We will revise the results section to emphasize these restrictions and qualify the interpretation as applying to the simulated configurations, avoiding any implication of comprehensive nonlinear stability. revision: partial

Circularity Check

0 steps flagged

No circularity in numerical simulation results

full rationale

The paper's conclusions rest on direct numerical relativity evolutions of head-on mergers with approximate initial data, where observed persistence of dilaton and axion fields after merger is taken to suggest stability. No analytical derivation chain, self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations are present; the results are generated by evolving the underlying field equations rather than reducing to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on the field equations of Einstein-Maxwell-dilaton-axion theory and standard numerical relativity assumptions for evolving black hole spacetimes; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Einstein-Maxwell-dilaton-axion theory field equations govern the dynamics
    All simulations are performed within this modified gravity theory as stated in the abstract.
  • domain assumption Approximate initial data can be used to evolve head-on binary mergers
    The paper explicitly uses approximate initial data across a portion of parameter space.

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