Abstract

We investigate general features of charged Lovelock black branes by giving a detailed description of geometrical, thermodynamic and holographic properties of charged Gauss-Bonnet (GB) black branes in five dimensions. We show that when expressed in terms of effective physical parameters, the thermodynamic behaviour of charged GB black branes is completely indistinguishable from that of charged Einstein black branes. Moreover, the extremal, near-horizon limit of the two classes of branes is exactly the same as they allow for the same AdS$_2\times R_3$, near-horizon, exact solution. This implies that, although in the UV the associated dual QFTs are different, they flow in the IR to the same fixed point. The calculation of the shear viscosity to entropy ratio $\eta/s$ confirms these results. Despite the GB dual plasma has in general a non-universal temperature-dependent $\eta/s$, it flows monotonically to the universal value $1/4\pi$ in the IR. For negative (positive) GB coupling constant, $\eta/s$ is an increasing (decreasing) function of the temperature and the flow respects (violates) the KSS bound.

Highlights

  • Derive exact black hole solutions of the theory

  • We investigate general features of charged Lovelock black branes by giving a detailed description of geometrical, thermodynamic and holographic properties of charged Gauss-Bonnet (GB) black branes in five dimensions

  • In the GB black brane solutions (BB) case, we have seen that the same thermodynamic relations (5.1) hold for M, T given by the effective values in eq (2.8) and we will get from eqs. (5.4)

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Summary

Black brane solutions of Lovelock gravity

Let us consider black branes that are solutions of Lovelock higher curvature gravity in d-dimensional spacetime. Electrically charged, radially symmetric AdS Lovelock BB, we use the following line element and electromagnetic (EM) field ds. Where dΣ2d−2 denotes the (d − 2)-dimensional space with zero curvature and planar topology, whereas L is related to the cosmological constant α(0) by L−2 = α(0)/(d − 1)(d − 2). Where GN is the d-dimensional Newton’s constant and each of the Einstein-like tensors. For d = 2k the higher-curvature corrections are topological, and they vanish identically in lower dimensions. Where V d−2 is the volume of the (d − 2)-dimensional space with curvature κ = 0.

Universality of black brane thermodynamics in Lovelock gravity
Gauss-Bonnet solution
Singularities
Near horizon extremal solution
Near horizon metric as exact solution of equations of motion
Charged GB black brane thermodynamics
Large temperature
Small temperature
Shear viscosity to entropy ratio
Large TH
Small TH
Dependence on the time rescaling factor N
Summary and outlook
A The black hole case

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