Charged Deformation of a Hairy Black Brane: Perturbative Solution and Thermodynamics
Abstract
We study electrically charged black branes in four-dimensional Einstein-Maxwell-scalar theory with Maxwell coupling Z(ϕ)=e3ϕ/√7, whose potential has an AdS4 fixed point only in the infrared. For nonzero hair parameter α the scalar grows logarithmically at large radius and the geometry is not asymptotically AdS, so the holographic dictionary is a working assumption. With the scale-invariant multi-trace boundary condition of the neutral branes, giving conformal thermodynamics, we work to second order in the charge, obtaining the Maxwell field and susceptibility in closed form, plus the thermodynamics, condensate, incoherent conductivity and cumulant ratio T2χ4/χ2=6c(α)<0 for all α considered. Independent perturbative computations and first-law closed forms agree within 4×10−6; nonlinear solutions reproduce second-order results to 1.2×10−5 and c to 6×10−4. They are locally thermodynamically stable where constructed, and the pressure is analytic in (μQ/T)2 near zero density. No regular extremal horizon exists at finite scalar value, and ρ/s<√(21)/(2π) exactly. The extremal limit is an AdS2×ℝ2 throat where the scalar grows as lnln(1/u) in the AdS2 radial coordinate u; the bound is saturated there, and extremal values are approached as powers of 1/ln(μQ/T). With a Dirichlet condition on the scalar source, the same solutions describe a non-conformal theory with scale Λ, whose charged branes exist only below Tmax(μQ), which falls from 0.194Λ at zero density to zero at μQ=0.506Λ. This boundary is a diffusive instability where the charge susceptibility diverges at nonzero density, and the bulk viscosity violates Buchel's bound at all densities. Quasinormal modes with the normalizable large-radius condition reproduce its hydrodynamics.
Related
- Particle Dynamics and Thermodynamics of a Charged-Like Hairy Black Hole in Extended Gravitational Decoupling
- Perturbative Hairy Black Branes in the G2-Invariant Sector of Dyonic ISO(7) Gauged Supergravity
- Hairy Taub-NUT solution in gauged supergravity
- First law of thermodynamics for interacting charged black holes and applications
- Astrophysical Signatures of Charged Anisotropic Compact Star in f(R,T) Gravity via Minimal Geometric Deformation
BibTeX
@misc{yun2026charged,
title = {{Charged Deformation of a Hairy Black Brane: Perturbative Solution and Thermodynamics}},
author = {Sangheon Yun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14929},
eprint = {2610.14929},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14929},
}
RIS
TY - UNPB
TI - Charged Deformation of a Hairy Black Brane: Perturbative Solution and Thermodynamics
AU - Sangheon Yun
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14929
UR - https://arxiv.org/abs/2610.14929
AB - We study electrically charged black branes in four-dimensional Einstein-Maxwell-scalar theory with Maxwell coupling Z(ϕ)=e^3ϕ/√7, whose potential has an AdS_4 fixed point only in the infrared. For nonzero hair parameter α the scalar grows logarithmically at large radius and the geometry is not asymptotically AdS, so the holographic dictionary is a working assumption. With the scale-invariant multi-trace boundary condition of the neutral branes, giving conformal thermodynamics, we work to second order in the charge, obtaining the Maxwell field and susceptibility in closed form, plus the thermodynamics, condensate, incoherent conductivity and cumulant ratio T^2χ_4/χ_2=6c(α)<0 for all α considered. Independent perturbative computations and first-law closed forms agree within 4×10^−6; nonlinear solutions reproduce second-order results to 1.2×10^−5 and c to 6×10^−4. They are locally thermodynamically stable where constructed, and the pressure is analytic in (μ_Q/T)^2 near zero density. No regular extremal horizon exists at finite scalar value, and ρ/s<√(21)/(2π) exactly. The extremal limit is an AdS_2×ℝ^2 throat where the scalar grows as lnln(1/u) in the AdS_2 radial coordinate u; the bound is saturated there, and extremal values are approached as powers of 1/ln(μ_Q/T). With a Dirichlet condition on the scalar source, the same solutions describe a non-conformal theory with scale Λ, whose charged branes exist only below T_max(μ_Q), which falls from 0.194Λ at zero density to zero at μ_Q=0.506Λ. This boundary is a diffusive instability where the charge susceptibility diverges at nonzero density, and the bulk viscosity violates Buchel's bound at all densities. Quasinormal modes with the normalizable large-radius condition reproduce its hydrodynamics.
ER -