[Paper Review] Dynamical descalarization in Einstein-Maxwell-scalar theory

Chao Niu, Wei Xiong+3 more|arXiv (Cornell University)|Sep 25, 2022

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates nonlinear dynamical descalarization in asymptotically flat Einstein-Maxwell-scalar black holes, showing that scalar hair can be shed when the black hole absorbs sufficient energy, reducing its effective charge-to-mass ratio below a critical threshold. The descalarization process is continuous, indicating a second-order phase transition, with the effective charge-to-mass ratio being the decisive parameter.

ABSTRACT

For an asymptotically flat hairy black hole in the Einstein-Maxwell-scalar (EMS) theory, we study the possibility of shedding off its scalar hair via nonlinear scalar perturbation fully interacting with the background spacetime. We examine the effect of the perturbation strength on the descalarization. The results show that the effective charge to mass ratio of the black hole plays the key role in the dynamical descalarization. The descalarization at the threshold is continuous. This indicates a second order phase transition.

Motivation & Objective

• To study the dynamical descalarization of scalarized black holes in the Einstein-Maxwell-scalar (EMS) theory within asymptotically flat spacetime.
• To investigate whether a single black hole can shed its scalar hair through nonlinear perturbations without binary mergers.
• To determine the role of the effective charge-to-mass ratio in triggering descalarization.
• To analyze the nature of the phase transition during descalarization (continuous vs. discontinuous).
• To examine the impact of perturbation strength and energy dissipation on the descalarization outcome.

Proposed method

• Numerical evolution of the full nonlinear equations of motion in the Einstein-Maxwell-scalar theory with exponential coupling $ f( heta) = e^{-b heta^2} $, $ b < 0 $.
• Initial data constructed as a Reissner-Nordström black hole plus a finite outgoing scalar perturbation, with total mass fixed at $ M = 1 $.
• Use of the Misner-Sharp mass $ M_{\text{MS}} $ to track energy evolution and monitor mass loss to infinity.
• Analysis of the scalar field amplitude $ \phi_h $ at the horizon over time to detect descalarization.
• Investigation of the effective charge-to-mass ratio $ q = Q/M_s $, where $ M_s $ is the black hole's effective mass after energy loss.
• Comparison of descalarization outcomes across varying initial perturbation strengths $ B $, with fixed $ b = -4 $, $ Q = 0.8 $.

Experimental results

Research questions

• RQ1 Can a single scalarized black hole in asymptotically flat EMS spacetime shed its scalar hair through nonlinear perturbations without binary merger?
• RQ2 What determines the threshold for descalarization—specifically, is it the perturbation amplitude or the effective charge-to-mass ratio?
• RQ3 Is the descalarization process continuous or discontinuous, and what does this imply about the phase transition type?
• RQ4 How does energy dissipation to infinity affect the final state of the black hole and its ability to remain scalarized?
• RQ5 Does the coupling structure $ f( heta) = e^{-b heta^2} $ lead to second-order descalarization dynamics in flat spacetime, as observed in AdS?

Key findings

• Scalar hair can be shed from a scalarized black hole in asymptotically flat EMS spacetime via nonlinear perturbations, even without binary mergers.
• The effective charge-to-mass ratio $ q = Q/M_s $ is the decisive parameter for descalarization: descalarization occurs only when $ q $ drops below a critical value.
• For fixed $ b = -4 $, $ Q = 0.8 $, and total mass $ M = 1 $, descalarization occurs only for sufficiently strong initial perturbations ($ B = 4, 5 $), where energy loss increases the effective $ Q/M_s $ ratio.
• The descalarization process is continuous at the threshold, indicating a second-order phase transition, consistent with findings in AdS spacetime.
• Energy dissipation to infinity is non-negligible despite compactification; it accounts for a significant fraction of total energy due to grid spacing near spatial infinity.
• The final black hole state transitions from scalarized to bald only when the effective mass $ M_s $ of the black hole decreases sufficiently due to energy loss, lowering $ q $ below the critical threshold.