# Dilaton Mass Formulas in a Hairy Binary Black Hole Model

## TL;DR

This paper derives an analytic formula for the scalar-field-dependent mass in a hairy binary black hole model within Einstein--Maxwell--dilation theory, revealing a universal attractor solution in the large-dilaton-field limit.

## Contribution

It provides the first closed-form analytic solution for the mass function in a hairy binary black hole model, including an attractor solution in the large-dilaton-field regime.

## Key findings

- Analytic integration of the mass differential equation achieved.
- Identification of a universal attractor solution.
- Closed-form formula for the mass function derived.

## Abstract

In this note an analytic integration is obtained for the differential equation governing the scalar-field-dependent mass in a hairy binary black hole model, in the context of the Einstein--Maxwell--dilation theory, which gives a closed-form formula-level description of the mass function. We also identify a particular solution which attracts all solutions of the mass-governing equation exponentially rapidly in large-dilaton-field limit.