In this dissertation, we review work presented in arXiv:0906.2015, arXiv:0907.1663, arXiv:1002.3132, arXiv:1003.2746, and arXiv:1007.2202 on the D1D5 system. We begin with some motivational material for black holes in string theory. In Chapter 2, we review the D1D5 system, including the gravity and CFT descriptions. In Chapter 3, we show how to perturbatively relax the decoupling limit in a general AdS-CFT setting. This allows one to compute the emission out of the AdS/CFT into the asymptotic flat space. In Chapter 4, we apply that formalism to some particular geometries, and exactly reproduce the emission spectrum. These geometries are interpreted as fuzzball microstates of a black hole, and the emission as the microscopic analogue of the Hawking radiation. In Chapter 5, we discuss how to deform the D1D5 CFT off of its orbifold point. In particular, we present full off-shell expressions for first-order corrections to the CFT states. One can see how high-energy states can fragment into many lower-energy states. In the conclusion, we discuss some opportunities for future work.
We present a new method for reconstructing CFT duals of states excited by the bulk local operators in the three dimensional AdS black holes in the AdS/CFT context. As an important procedure for this, we introduce a map between the bulk points in AdS and those on the boundary where CFT lives. This gives a systematic and universal way to express bulk local states even inside black hole interiors. Our construction allows us to probe the interior structures of black holes purely from the CFT calculations. We analyze bulk local states in the single-sided black holes as well as the double-sided blac…
We study the near horizon geometry of black ring solutions in five-dimensional U(1)^3 supergravity with three electric dipole charges and one angular momentum. We consider the extremal vanishing horizon (EVH) limit of these solutions and show that the near horizon geometries develop locally AdS_3 throats which at the near-EVH near horizon limit the AdS_3 factor turns to a BTZ black hole. By analysing the first law of thermodynamics for black rings we show that at EVH limit it reduces to the first law of thermodynamics for BTZ black holes. Using the AdS3/CFT2 duality, we propose a dual CFT to d…
We demonstrate that Kerr-CFT duality can be extended to super-entropic black holes, which have non-compact horizons with finite area. We demonstrate that this duality is robust insofar as the ultra-spinning limit of a Kerr-AdS black hole (which yields the super-entropic class)commutes with the near-horizon limit (which yields the Kerr-CFT duality). Consequently the Bekeinstein-Hawking and the CFT entropies are equivalent. We show that the duality holds for both singly-spinning super-entropic black holes in 4 dimensions and for doubly-spinning super-entropic black holes of gauged supergravity i…
It has been shown by A. Sen that logarithmic corrections to the black hole area-entropy law are entirely determined macroscopically from the massless particle spectrum. They therefore serve as powerful consistency checks on any proposed enumeration of quantum black hole microstates. Sen's results include a macroscopic computation of the logarithmic corrections for a five-dimensional near extremal Kerr-Newman black hole. Here we compute these corrections microscopically using a stringy embedding of the Kerr/CFT correspondence and find perfect agreement.
We compute thermal 2-point correlation functions in the black brane $AdS_5$ background dual to 4d CFT's at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.
We study RN/CFT correspondence for four dimensional extremal Reissner-Nordstrom black hole. We uplift the 4d RN black hole to a 5d rotating black hole and make a geometric regularization of the 5d space-time. Both hands central charges are obtained correctly at the same time by Brown-Henneaux technique.
In this paper, we study the thermodynamic properties of Kiselev black hole and its holographic dual. We obtain the thermodynamic product formula for the Kiselev black hole. We consider Kiselev Black hole surrounded by both dust and radiation. We find that the area (or entropy) product formula for both cases is mass-independent as well as the case in the Einstein gravity, which interpreted as universal quantity. Moreover, we calculate the black hole entropy bound for both the inner and outer horizons. Furthermore, we show that the central charges of the left and right moving sectors are not the…
We show that the very near horizon region of nonextreme black holes, which can be described by horizon CFTs, are related to $AdS_2$ Rindler spaces. The latter are $AdS_2$ black holes with specific masses and can be described by states of either $D=1$ or $D=2$ CFTs. The central charges of these CFTs and the conformal weights of their states that correspond to the nonextreme black holes exactly match those predicted by the horizon CFTs, providing supporting evidence for this description.
We study the thermodynamic properties of warped AdS$_3$ black hole within the framework of thermodynamic information geometry. Our analysis focuses on finding the set of proper thermodynamic Riemannian metrics on the space of equilibrium states, together with the conditions for local and global thermodynamic stability. We use our findings to constrain the values of left and right central charges from the dual CFT theory and the parameters of the bulk gravitational theory.
We extend the conjectured Kerr/CFT correspondence to the case of extremal Kerr black holes immersed by an magnetic field, namely the extremal Melvin-Kerr black holes. We compute the central charge which appears in the associated Virasoro algebra generated by a class of diffeomorphisms that satisfies a set of boundary conditions in the near horizon of an extremal Melvin-Kerr black hole. Our results support the Kerr/CFT conjecture, where the macroscopic Bekenstein-Hawking entropy for an extremal Melvin-Kerr black hole matches the result obtained from a dual 2D CFT microscopic computation using C…
Recently a new class of asymptotically AdS ultra-spinning black holes has been constructed with a noncompact horizon of finite area [1], in which the asymptotic rotation is effectively boosted to the speed of light. We employ this technique for four-dimensional $U(1)^4$ and five-dimensional $U(1)^3$ gauged supergravity black holes. The obtained new exact black hole solutions for both cases possess a noncompact horizon; their topologies are a sphere with two punctures. We then demonstrate that the ultra-spinning limit commutes with the extremality condition as well as the near horizon limit for…
Kaluza-Klein theory, AdS/CFT correspondence and black hole entropy
通过反演卡鲁扎-克莱因约化得到的提升（近极值）Reissner-Nordstrom黑洞的近视界几何的渐近对称性解释了贝肯斯坦-霍金熵偏离极值的原因。我们指出的事实是，额外的维度使我们能够证明使用Virasoro模式分解沿类时边界的近视界几何，AdS $_2\times$ S $^n$，低维（Reissner-Nordstrom）时空。
$AdS_5$ type IIb supergravity compactifications on five-dimensional Einstein manifolds ${\cal V}_5$ realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black holes become sufficiently small in (global) $AdS_5$, they are expected to suffer Gregory-Laflamme instability with respect to localization on ${\cal V}_5$. Previously, the instability was demonstrated for gravitational dual of ${\cal N}=4$ SYM, where ${\cal V}_5=S^5$. We extend stability analysis to arbitrary ${\cal V}_5$. We point out that t…
We revisit the holographic calculation of the decay modes of the BTZ blackhole perturbed by a scalar probe. We carry out a finite temperature expansion of the torus two point function of large central charge $(c)$ CFTs in order to obtain the corrections to blackhole quasinormal modes. We take the contribution of the lightest primary above the vacuum, with dimension $Δ_χ$ and upper bound of $c/6$, in the torus two point function. We exploit the modular properties of 2D CFT on the torus to connect the expression of thermal two point function at high temperature with the same at low temperature. …
