Quasi-normal modes of rotating black holes and neutron stars: gravitational waves and AdS/CFT correspondence

这项研究计划的主题是在广义相对论和广义引力理论的背景下研究黑洞和中子星。我们建议在弦理论和其他量子引力候选理论的激励下，在存在附加场，如标量场和规范场，或额外维度的情况下，研究这种致密物体的性质。我们提出的研究有两个主要目的。-第一个方向将集中于不同天体物理相关物体的引力波发射，如黑洞和中子星。LIGO的合作最近探测到了引力波。分析表明，这些探测的来源是聚合的天体物理黑洞。灵敏度的不断提高将允许探测到来自其他来源的引力波，如中子星合并、白矮星碰撞，以及可能的其他未知现象。其目的是研究广义引力理论中的引力波发射。我们将研究给定理论的现象学特征在物理对象的几个可观察性质中的存在，例如引力波的振铃频率与一些整体参数、旋转性质以及可能打破的宇宙关系(Eikonal极限，I-Love-Q)之间的关系。通过将探测到的引力波与每个理论的预测进行比较，我们可以约束该理论的参数和场内容。-第二个方向将侧重于研究更高维的黑洞。这些天体在弦理论的背景下很有趣，弦理论预测了额外维度的存在，以及ADS/CFT的对应关系。对应猜想D维引力理论中传播的场与在其(D-1)维边界上传播的量子场是对偶的。特别地，5维黑洞可以用来描述4维共形场理论中的热态。这种对应关系允许使用像黑洞这样的几何对象来探索强相互作用量子系统的性质。目的是研究新黑洞的性质和已知解在超引力背景下的可能推广，特别是渐近ADS解和超对称性。我们将研究这些黑洞的热力学性质，不同解族的存在范围和稳定性，以及这些解与粒子理论和凝聚态模型的可能联系。

The topic of this research proposal is the investigation of black holes and neutron stars in the context of General Relativity and in generalized theories of gravity. We propose to study the properties of such compact objects in the presence of additional fields, like scalars and gauge fields, or extra dimensions, as motivated by string theory and other candidate theories of quantum gravity. The research we propose has two main objectives. -The first direction will focus on the gravitational wave emission of different astrophysically relevant objects, like black holes and neutron stars. Gravitational waves have been detected recently by the LIGO collaboration. The analysis indicates that the sources of these detections are coalescing astrophysical black holes. The continuous enhancement of sensitivity will allow to detect gravitational waves from other sources as well, like neutron stars mergers, white dwarf collisions, and possibly other unknown phenomena. The objective is to study gravitational wave emission in generalized theories of gravity. We shall study the presence of phenomenological signatures of a given theory in several observable properties of the physical objects, such as the relation between the ringdown frequencies of gravitational waves with some global parameters, rotational properties, and possible breaking of universal relations (Eikonal limit, I-love-Q). By comparing the detected gravitational waves with the predictions of each theory we can constrain the parameters and field content of the theory. -The second direction will focus on the study of higher dimensional black holes. These objects are interesting in the context of string theory, which predicts the existence of extra dimensions, and the AdS/CFT correspondence. The correspondence conjectures that fields propagating in a D-dimensional gravitational theory are dual to quantum fields propagating on its (D-1)-dimensional boundary. In particular black holes in 5 dimensions can be used to describe thermal states in a 4 dimensional conformal field theory. This correspondence allows to use geometrical objects like black holes to explore the properties of strongly interacting quantum systems. The purpose is to study the properties of new black holes and possible generalizations of known solutions in the context of supergravity, especially asymptotically AdS solutions and supersymmetry. We will study the thermodynamic properties of these black holes, the domain of existence and stability of the different families of solutions, and possible connections of these solutions with particle theory and condensed matter models.