Polarised black holes in AdS
Polarised black holes in AdS
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AdS 中的偏振黑洞
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Jorge E Santos
中科院分区：
文献类型：
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作者：
M. Costa;Lauren Greenspan;Miguel Oliveira;J. Penedones;Jorge E Santos
我们考虑了具有负宇宙学常数的Einstein-Maxwell理论解，该解渐近于具有共形边界S2 × Rt的整体AdS 4.在无限远的球体上，我们打开一个空间相关的静电势，它不会破坏渐近AdS行为。为了简单起见，我们集中在偶极静电势的情况下。我们发现两个新的几何形状：（i）一个AdS孤子，它包括电场对AdS几何的完全反作用;（ii）一个极化的中性黑洞，它被电场变形，在每个半球积累相反的电荷。对于这两种几何形状，我们研究边界数据，如电荷密度和应力张量。对于黑洞，我们还研究了视界电荷密度和面积，并进一步验证了一个Smarr公式。然后，我们考虑这个系统在有限的温度和计算吉布斯自由能的AdS孤子和黑洞阶段。相应的相图推广了Hawking-Page相变。AdS孤子占主导地位的低温阶段和黑洞的高温阶段，随着外部电场的增加而降低的临界温度。最后，我们考虑了S2 × Rt上自由带电标量场共形耦合的简单情形.对于SU（N）伴随表象中的场，我们将相图与上述引力系统进行比较。
We consider solutions in Einstein–Maxwell theory with a negative cosmological constant that asymptote to global AdS4 with conformal boundary S 2 × R t . At the sphere at infinity we turn on a space-dependent electrostatic potential, which does not destroy the asymptotic AdS behaviour. For simplicity we focus on the case of a dipolar electrostatic potential. We find two new geometries: (i) an AdS soliton that includes the full backreaction of the electric field on the AdS geometry; (ii) a polarised neutral black hole that is deformed by the electric field, accumulating opposite charges in each hemisphere. For both geometries we study boundary data such as the charge density and the stress tensor. For the black hole we also study the horizon charge density and area, and further verify a Smarr formula. Then we consider this system at finite temperature and compute the Gibbs free energy for both AdS soliton and black hole phases. The corresponding phase diagram generalizes the Hawking–Page phase transition. The AdS soliton dominates the low temperature phase and the black hole the high temperature phase, with a critical temperature that decreases as the external electric field increases. Finally, we consider the simple case of a free charged scalar field on S 2 × R t with conformal coupling. For a field in the SU(N ) adjoint representation we compare the phase diagram with the above gravitational system.