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Register a new userGauss-Bonnet Black Holes and Heavy Fermion Metals
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We consider charged black holes in Einstein-Gauss-Bonnet Gravity with Lifshitz boundary conditions. We find that this class of models can reproduce the anomalous specific heat of condensed matter systems exhibiting non-Fermi-liquid behaviour at low temperatures. We find that the temperature dependence of the Sommerfeld ratio is sensitive to the choice of Gauss-Bonnet coupling parameter for a given value of the Lifshitz scaling parameter. We propose that this class of models is dual to a class of models of non-Fermi-liquid systems proposed by Castro-Neto et.al.
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Einsteins General Relativity theory simplifies dramatically in the limit that the spacetime dimension D is very large. This could still be true in the gravity theory with higher derivative terms. In this paper, as the first step to study the gravity with a Gauss-Bonnet(GB) term, we compute the quasi-normal modes of the spherically symmetric GB black hole in the large D limit. When the GB parameter is small, we find that the non-decoupling modes are the same as the Schwarzschild case and the decoupled modes are slightly modified by the GB term. However, when the GB parameter is large, we find some novel features. We notice that there are another set of non-decoupling modes due to the appearance of a new plateau in the effective radial potential. Moreover, the effective radial potential for the decoupled vector-type and scalar-type modes becomes more complicated. Nevertheless we manage to compute the frequencies of the these decoupled modes analytically. When the GB parameter is neither very large nor very small, though analytic computation is not possible, the problem is much simplified in the large D expansion and could be numerically treated. We study numerically the vector-type quasinormal modes in this case.
We construct uniform black-string solutions in Einstein-Gauss-Bonnet gravity for all dimensions $d$ between five and ten and discuss their basic properties. Closed form solutions are found by taking the Gauss-Bonnet term as a perturbation from pure Einstein gravity. Nonperturbative solutions are constructed by solving numerically the equations of the model. The Gregory-Laflamme instability of the black strings is explored via linearized perturbation theory. Our results indicate that new qualitative features occur for $d=6$, in which case stable configurations exist for large enough values of the Gauss-Bonnet coupling constant. For other dimensions, the black strings are dynamically unstable and have also a negative specific heat. We argue that this provides an explicit realization of the Gubser-Mitra conjecture, which links local dynamical and thermodynamic stability. Nonuniform black strings in Einstein-Gauss-Bonnet theory are also constructed in six spacetime dimensions.
Einstein-Gauss-Bonnet theory is a string-generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help to solve the black hole singularity problem. In this work, we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein-Gauss-Bonnet gravity in various spacetime dimensions with both positive and negative couping constant $alpha$. By summarizing the asymptotic behavior of the evaporation process, we find the lifetime of the black holes is dimensional dependent. For $alpha>0$, in $Dgeqslant6$ cases, the black holes will be completely evaporated in a finite time, which resembles the Schwarzschild-AdS case in Einstein gravity. While in $D=4,5$ cases, the black hole lifetime is always infinite, which means the black hole becomes a remnant in the late time. Remarkably, the cases of $alpha>0, D=4,5$ will solve the terminal temperature divergent problem of the Schwarzschild-AdS case. For $alpha<0$, in all dimensions, the black hole will always spend a finite time to a minimal mass corresponding to the smallest horizon radius $r_{min}=sqrt{2|alpha|}$ which coincide with an additional singularity. This implies that there may exist constraint conditions to the choice of coupling constant.
We report the existence of unstable, s-wave modes, for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that in the transverse section are black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single one and its derivatives. For this latter component we find a master equation which admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related with the wave number along the extra direction, as it occurs in General-Relativity. It is known that these configurations suffer from a thermal instability, and therefore the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Due to the non-triviality of the curvature of the background, all the components of the metric perturbation appear in the linearized equations. As it occurs for spherical black holes, these black strings should be obtained as the short distance $r<<alpha^{1/2}$ limit of the black string solution of Einstein-Gauss-Bonnet theory, which is not know analytically, where $alpha$ is the Gauss-Bonnet coupling.
Using the Sens mechanism we calculate the entropy for an $AdS_{2}times S^{d-2}$ extremal and static black hole in four dimensions, with higher derivative terms that comes from a three parameter non-minimal Einstein-Maxwell theory. The explicit results for Gauss-Bonnet in the gauge-gravity sector are shown.
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