Condensation for non-relativistic matter in Hořava-Lifshitz gravity

Jiliang Jing; Songbai Chen; Qiyuan Pan

doi:10.1016/j.physletb.2015.08.009

paper

Condensation for non-relativistic matter in Hořava-Lifshitz gravity

arXiv:1410.7847 · doi:10.1016/j.physletb.2015.08.009

Abstract

We study condensation for non-relativistic matter in a Hořava-Lifshitz black hole without the condition of the detailed balance. We show that, for the fixed non-relativistic parameter $α_{2}$ (or the detailed balance parameter $ε$ ), it is easier for the scalar hair to form as the parameter $ε$ (or $α_{2}$ ) becomes larger, but the condensation is not affected by the non-relativistic parameter $β_{2}$ . We also find that the ratio of the gap frequency in conductivity to the critical temperature decreases with the increase of $ε$ and $α_{2}$ , but increases with the increase of $β_{2}$ . The ratio can reduce to the Horowitz-Roberts relation $ω_{g} / T_{c} \approx 8$ obtained in the Einstein gravity and Cai's result $ω_{g} / T_{c} \approx 13$ found in a Hořava-Lifshitz gravity with the condition of the detailed balance for the relativistic matter. Especially, we note that the ratio can arrive at the value of the BCS theory $ω_{g} / T_{c} \approx 3.5$ by taking proper values of $ε$ , $α_{2}$ , $β_{2}$ and $m$ .

16 pages, 5 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1001.1472; and text overlap with arXiv:0911.4867 by other authors

Condensation for non-relativistic matter in Hořava-Lifshitz gravity

Abstract

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