Notes on ten-dimensional localized black holes and deconfined states in two-dimensional SYM

We study phases of equilibrium Hawking radiation in d-dimensional holographic CFTs on spatially compact spacetimes with two black holes. In the particular phases chosen the dual (d + 1)-dimensional bulk solutions describe a variety of black funnels and droplets. In the former the CFT readily conducts heat between the two black holes, but it in the latter such conduction is highly suppressed. While the generic case can be understood in certain extreme limits of parameters on general grounds, we focus on CFTs on specific geometries conformally equivalent to a pair of d ≥ 4 AdS d -Schwarzschild black holes of radius R. Such cases allow perturbative analyses of non-uniform funnels associated with Gregory-Laflamme zero-modes. For d = 4 we construct a phase diagram for pure funnels and droplets by constructing the desired bulk solutions numerically. The fat non-uniform funnel is a particular interesting phase that dominates at small R (due to having lowest free energy) despite being sub-dominant in the perturbative regime. The uniform funnel dominates at large R, and droplets and thin funnels dominate at certain intermediate values. The thin funnel phase provides a mystery as it dominates over our other phases all that way to a critical R turn beyond which it fails to exist. The free energy of the system thus appears to be discontinuous at R turn , but such discontinuities are forbidden by the 2nd law. A new more-dominant phase is thus required near R turn but the nature of this phase remains unclear.

Section: Discussionmentioning

confidence: 52%

“…As in that case, the short droplets have smaller ∆F as may be seen by comparing figures 8 and 14. The behavior is again akin to that of localized black holes in Kaluza-Klein theory [67,39,40,41,68,66,69,70,71].…”

Section: Diagnosticsmentioning

confidence: 88%

Phases of holographic Hawking radiation on spatially compact spacetimes

Marolf

Santos

2019

“…These geometries are not asymptotically flat, and the horizons extend indefinitely as ρ → ∞. The conjecture that they arise locally at the connection between black string and black hole phases when p = 2, and black ring and black hole phases when p = 3, has been verified numerically in [9,10,[12][13][14][15][16]. Ref.…”

Section: Exact Critical Conesmentioning

confidence: 85%

“…Although the exactly self-similar conical geometry is simple, its split and fused deformations to the black hole and the black string phases are only known through approximate perturbative or numerical solutions [9][10][11][12][13][14][15][16]. Furthermore, the connection of the local model to the overall geometry of the black hole or black string horizon away from the self-similar region is poorly understood.…”

Section: Contentsmentioning

confidence: 99%

“…The KR conifold can also be described using concepts of statistical mechanics and field theory. 16 Namely, the scale-breaking induced by the parameter µ can be regarded as a relevant perturbation of the exact cone at short distances, while the critical KR cone (with µ = 0) is a relevant perturbation of the cone at long distances. The solution is therefore an attractor.…”

Section: Rigidity Of Compact Ancient Flowsmentioning

confidence: 99%

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Topology-changing horizons at large D as Ricci flows

Suzuki

2019

The topology-changing transition between black strings and black holes localized in a Kaluza-Klein circle is investigated in an expansion in the inverse of the number of dimensions D. Performing a new kind of large-D scaling reduces the problem to a Ricci flow of the near-horizon geometry as it varies along the circle direction. The flows of interest here simplify to a non-linear logarithmic diffusion equation, with solutions known in the literature which are interpreted as the smoothed conifold geometries involved in the transition, namely, split and fused cones, which connect to black holes and non-uniform black strings away from the conical region. Our study demonstrates the adaptability of the 1/D expansion to deal with all the regimes and aspects of the static black hole/black string system, and provides another instance of the manner in which the large D limit reduces the task of solving Einstein's equations to a simpler but compelling mathematical problem. arXiv:1905.01062v3 [hep-th] 22 Jul 20191 See [1, 2] for early reviews, and the book monograph [3] for a more up to date view. 2 The evolution of black strings to black holes in solution space seems to be unrelated to the dynamical evolution of black strings towards (and across) a naked singularity. Although the change in topology is expected to be the same in both cases, the dynamical evolution appears to be at all moments strongly time-dependent, and occurs far from the static configurations around the transition in solution space. The singularities also appear to be very different in the two cases.3 Again, these black hole mergers in solution space are rather different than the dynamical mergers of event horizons. The latter admit simple local models studied in [6] and do not involve naked singularities. The evolution in solution space is adiabatic, while the dynamical merger is irreversible.

Critical lumpy black holes in AdSp×Sq

Cardona

Figueras

2021

In this paper we study lumpy black holes with AdSp × Sq asymptotics, where the isometry group coming from the sphere factor is broken down to SO(q). Depending on the values of p and q, these are solutions to a certain Supergravity theory with a particular gauge field. We have considered the values (p, q) = (5, 5) and (p, q) = (4, 7), corresponding to type IIB supergravity in ten dimensions and eleven-dimensional supergravity respectively. These theories presumably contain an infinite spectrum of families of lumpy black holes, labeled by a harmonic number ℓ, whose endpoints in solution space merge with another type of black holes with different horizon topology. We have numerically constructed the first four families of lumpy solutions, corresponding to ℓ = 1, 2+, 2− and 3. We show that the geometry of the horizon near the merger is well-described by a cone over a triple product of spheres, thus extending Kol’s local model to the present asymptotics. Interestingly, the presence of non-trivial fluxes in the internal sphere implies that the cone is no longer Ricci flat. This conical manifold accounts for the geometry and the behavior of the physical quantities of the solutions sufficiently close to the critical point. Additionally, we show that the vacuum expectation values of the dual scalar operators approach their critical values with a power law whose exponents are dictated by the local cone geometry in the bulk.