Horizon Geometry Research Articles

Supersymmetric black hole hair and AdS3× S3

The 4D-5D connection allows us to view the same near horizon geometry as part of a 4D black hole or a 5D black hole. A much studied example of this phenomenon is the BMPV black hole uplifted to 6D with flat base space versus Taub-NUT base space. These black holes have identical near horizon AdS3 × S3 geometry. In this paper, we study modes in AdS3 × S3 and identify those that correspond to supersymmetric hair modes in the full black hole spacetimes. We show that these modes satisfy non-normalisable boundary conditions in AdS3. The non-normalisable boundary conditions are different for different hair modes and for different asymptotic completion. We also discuss how the supersymmetric hair modes on BMPV black holes fit into the classification of supersymmetric solutions of 6D supergravity.

First few overtones probe the event horizon geometry

First few overtones probe the event horizon geometry

Integration of seismic and well log data for evaluating the upper cretaceous reservoirs of Horus oil field, Alamein Basin, Northern Western Desert, Egypt

Horus field stands out as one of the main oil-rich areas in Alamein Basin. Formation and evolution of Horus field were influenced by tectonic processes occurring from Jurassic to Cretaceous periods. The main objectives of this study are to characterize structural elements, identify hydrocarbon potential, and pinpoint promising zones within Early Cretaceous rocks for hydrocarbon accumulations in Horus reservoirs. By utilizing high-quality 2D seismic reflection sections enhanced with structural smoothing attribute, which help eliminate random noise while preserving structural details and horizon geometry, building a 3D structural model becomes facile. Analysis of well logging data provides a comprehensive understanding of Cretaceous reservoirs, simplified by 3D static reservoir modeling to depict their varying ranges and anisotropies. 3D structural model shows that the trap of Horus field is linked to a structural uplift in an ENE-WSW trend, bordered to north and south by sediment-filled lows. This anticlinal ridge within the model is segmented into blocks by a series of NW-SE normal faults. 3D static reservoir models reveal high-quality reservoirs in Upper Bahariya and Abu Roash (G) Dolomite, characterized by substantial thicknesses of net pay zones. 3D static modeling of Cretaceous reservoirs guides the oilfield development and optimizes production strategies in Horus area.

The Asymptotic Expansion of the Spacetime Metric at the Event Horizon

AbstractHawking’s local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degenerate Killing horizon. In this paper, we prove that the full asymptotic expansion of any smooth vacuum metric at a non-degenerate Killing horizon is determined by the geometry of the horizon. This gives a new perspective on the black hole uniqueness conjecture. In spacetime dimension 4, we also prove an existence theorem: Given any non-degenerate horizon geometry, Einstein’s vacuum equations can be solved to infinite order at the horizon in a unique way (up to isometry). The latter is a gauge invariant version of Moncrief’s classical existence result, without any restriction on the topology of the horizon. In the real analytic setting, the asymptotic expansion is shown to converge and we get well-posedness of this characteristic Cauchy problem.

Scalar bosons with gravitational effects near Schwarzschild’s black hole: The Rindler recipe

In this study, we explore the quantum effects in the Schwarzschild spacetime for massive and massless scalar particles in the presence of an external gravitational field. The methodology involves the analytical solution of the Klein–Gordon equation for the scalar particles in the near-horizon spacetime limit, using Rindler approximation. The results show that the quantum effects differ significantly for the massive and massless cases, they possess similar characteristics near the event horizon. Bosons without mass that are distant from the event horizon undergo a reduced gravitational impact and possess a symmetric wave function that remains unchanged when they approach the event horizon. However, the symmetry is lost, indicating that the particle strives for a lower energy state and becomes erratic as it nears the event horizon. This aligns with the anticipated behavior of particles within the Schwarzschild horizon. The particles have an energy spectrum even for tremendous values of the Schwarzschild radius, which entails the validity of the Rindler approximation in the near horizon geometry. We have observed that the quantum effects of massive and massless particles differ based on the mass. Specifically, massive and massless scalars behave differently due to their geometric differences, which results in different eigenstates. Although they both tend to seek lower energy levels when they approach the event horizon, their behavior is not the same.

Matrix models from black hole geometries

Supersymmetric, magnetically charged (and possibly accelerating) black holes in AdS4 that uplift on Sasaki-Einstein manifolds Y7 to M-theory have a dual matrix model description. The matrix model in turn arises by localization of the 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs, dual to the AdS4 vacuum, on the black hole horizon geometry, which is a Riemann surface Σg (or a spindle Σ). We identify the imaginary part t of the continuously distributed eigenvalues in the matrix model, and their density function ρ(t), with natural geometric quantities associated with the M-theory circle action U(1)M on the near-horizon geometry AdS2 × Y9, the internal space Y9 being a Y7 fibration over Σg (or Σ). Moreover, we argue that the points where ρ′(t) is discontinuous match with the classical action of BPS probe M2-branes wrapping AdS2 and the M-theory circle. We illustrate our findings with the ABJM and ADHM theories, whose duals have Y7 = S7/ℤk, and some of their flavoured variants corresponding to other toric Y7.

Localization and attraction

We use equivariant localization to construct off-shell entropy functions for supersymmetric black holes in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2, D = 4 gauged supergravity coupled to matter. This allows one to compute the black hole entropy without solving the supergravity equations of motion and provides a novel generalization of the attractor mechanism. We consider magnetically charged black holes in AdS4 which have an AdS2 × M2 near horizon geometry, where M2 is a sphere or a spindle, and we also obtain entropy functions for ungauged supergravity as a simple corollary. We derive analogous results for black strings and rings in D = 5 supergravity which have an AdS3 × M2 near horizon geometry, and in this setting we derive an off-shell expression for the central charge of the dual \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = (0, 2), d = 2 SCFT.

Revisiting logarithmic correction to five dimensional BPS black hole entropy

We compute logarithmic correction to the entropy of BPS black holes in asymptotically flat five dimensional space-time using finite temperature black hole geometry and find perfect agreement with the microscopic results and macroscopic computations based on zero temperature near horizon geometry. We also reproduce the Bekenstein-Hawking term for zero temperature black hole entropy from the corresponding term for finite temperature black hole.

Dyonic Taub-NUT-AdS spaces: Phase structures of all horizon geometries

Dyonic Taub-NUT-AdS spaces: Phase structures of all horizon geometries

Tensionless strings on AdS3 orbifolds

The bound state of one NS5 brane (wrapped on a \U0001d54b4) and N NS1-branes has two dual descriptions: its low-energy dynamics is described by the symmetric orbifold of \U0001d54b4, while the near horizon geometry is captured by string theory on AdS3 × S3 × \U0001d54b4 with one unit of NS flux. The latter theory is exactly solvable in the hybrid formalism, and this allows one to prove the equivalence of the two descriptions. In this paper we extend this duality to ℤk orbifolds of this AdS3 × S3 background. In particular, we show that the corresponding worldsheet spectrum reproduces exactly the perturbative excitations on top of a certain non-perturbative state in the dual symmetric orbifold theory. Since the AdS/CFT duality map is exact for these models, we obtain an interesting picture of how the duality relates boundary and bulk descriptions.

Holographic two-point functions in medium

In this paper, we study two-point correlation function in a medium composed of two kinds of matter, which is the dual of a three-dimensional generalized p-brane gas geometry. Following the holographic prescription, we calculate temporal and spatial two-point functions in the medium. In general, the screening effect of the medium makes two-point functions decreases more rapidly than the CFTs two-point function. In the extremal limit, however, we find that a temporal two-point function is still conformal. This indicates that a two-dimensional UV CFT flows into a one-dimensional quantum mechanics in the IR limit. This is consistent with the fact that the near horizon geometry in the extremal limit reduces to AdS2. We also investigate holographic mutual information representing the correlation between two subsystems. We show that a critical distance in the IR region, where the mutual information vanishes, leads to a similar behavior to the correlation length of a two-point function.

Deformations of the Kerr-(A)dS near horizon geometry

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński (2013 Gen. Rel. Grav. 45 987–1004) to eliminate all but a finite number of Fourier modes of linear perturbations. In the second part, we give an argument using analyticity to prove that there are no odd Fourier modes.

On spinning strings in I-brane background

We revisit semiclassical strings, in particular we focus on rigidly rotating strings, in the near horizon geometry of two orthogonal stacks of NS5-branes (I-branes) using the string sigma model. We determine the conserved charges for the probe string moving in the resulting ℝt×Sθ13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\ heta_1}^3 $$\\end{document}×Sθ23\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {S}_{\ heta_2}^3 $$\\end{document} background supported by NS-NS two-forms and find a regularized dispersion relation for different values of integration constants. Using configurations that move simultaneously on both spheres, we obtain the giant magnon like dispersion relation for one particular set of parameters, while other consistent set of values gives us a dispersion relation reminiscent of the single spike.

Discontinuities of free theories on AdS2

The partition functions of free bosons as well as fermions on AdS2 are not smooth as a function of their masses. For free bosons, the partition function on AdS2 is not smooth when the mass saturates the Breitenlohner-Freedman bound. We show that the expectation value of the scalar bilinear on AdS2 exhibits a kink at the BF bound and the change in slope of the expectation value with respect to the mass is proportional to the inverse radius of AdS2. For free fermions, when the mass vanishes the partition function exhibits a kink. We show that expectation value of the fermion bilinear is discontinuous and the jump in the expectation value is proportional to the inverse radius of AdS2. We then show the supersymmetric actions of the chiral multiplet on AdS2 × S1 and the hypermultiplet on AdS2 × S2 demonstrate these features. The supersymmetric backgrounds are such that as the ratio of the radius of AdS2 to S1 or S2 is dialled, the partition functions as well as expectation of bilinears are not smooth for each Kaluza-Klein mode on S1 or S2. Our observation is relevant for evaluating one-loop partition function in the near horizon geometry of extremal black holes.

Topological black holes in Einstein-Maxwell and 4D conformal gravities revisited

The thermodynamics of charged topological black holes (TBHs) with different horizon geometries in d-dimensional Einstein-Maxwell and 4-dimensional conformal gravities is revisited using the restricted phase space formalism. The concept of subsystems for black holes is introduced, which enables a precise description for the thermodynamic behaviors of (non-compact) black holes with infinitely large horizon area. The concrete behaviors can be different for TBHs in the same underlying theory but with different horizon geometries, or for those with the same horizon geometry but from different underlying theories. The high and low temperature limits of the TBHs are also considered, and the high temperature limits behave universally as low temperature phonon gases. Finally, using the concept of subsystems, some conceptual issues in the description for thermal fluctuations in black hole systems are clarified, and the relative thermal fluctuations for finite subsystems are also analyzed in some detail.

Extremal Kerr Black Holes as Amplifiers of New Physics.

We show that extremal Kerr black holes are sensitive probes of new physics. Stringy or quantum corrections to general relativity are expected to generate higher-curvature terms in the gravitational action. We show that in the presence of these terms, asymptotically flat extremal rotating black holes have curvature singularities on their horizon. Furthermore, near-extremal black holes can have large yet finite tidal forces for infalling observers. In addition, we consider five-dimensional extremal charged black holes and show that higher-curvature terms can have a large effect on the horizon geometry.

Flows of rotating extremal attractor black holes

We investigate the attractor mechanism of five-dimensional extremal rotating black holes in Einstein gravity minimally coupled with a multiplet complex scalar. By imposing regularity on the horizon, we show that the only possible attractor value of the scalar field is zero in our setup and that the local geometry is determined by the Myers-Perry black hole solution. We numerically obtain the extremal AdS black hole solutions interpolating the near horizon geometry to the asymptotic AdS spacetime under the existence of a bare potential of the scalar field. The black hole energy and the angular momenta are discretized for the usual Dirichlet boundary condition. Under the general boundary condition, we also find hairy extremal AdS black holes in which the energy is smaller than that of the extremal Myers-Perry AdS black hole solution for the same angular momentum.

The attractor flow for AdS5 black holes in mathcal{N} = 2 gauged supergravity

We study the flow equations for BPS black holes in mathcal{N} = 2 five-dimensional gauged supergravity coupled to any number of vector multiplets via FI couplings. We develop the Noether-Wald procedure in this context and exhibit the conserved charges as explicit integrals of motion, in the sense that they can be computed at any radius on the rotating spacetime. The boundary conditions needed to solve the first order differential equations are discussed in great detail. We extremize the entropy function that controls the near horizon geometry and give explicit formulae for all geometric variables at their supersymmetric extrema. We have also considered a complexification of the near-horizon variables that elucidates some features of the theory from the near-horizon perspective.

TCFHs and hidden symmetries of type IIA AdS backgrounds

We present the twisted covariant form hierarchies (TCFHs) of warped (massive) IIA AdS backgrounds. As a consequence we demonstrate that all Killing spinor form bilinears satisfy a generalisation of the conformal Killing-Yano equation with respect to the TCFH connections. We also explore some of the properties of TCFHs which include the reduced holonomy of the minimal TCFH connections for generic backgrounds. Furthermore, we investigate the interplay between TCFHs and hidden symmetries of probes propagating on IIA AdS backgrounds. We find that some of the Killing spinor form bilinears of near horizon geometries of a class of IIA intersecting brane configurations are Killing-Yano forms and so generate hidden symmetries for spinning particle probes.

Thermodynamic stability of black holes in five-dimensional Yang-Mills massive gravity

In this paper, we consider the Einstein-massive gravity coupled to the Yang-Mills gauge field in five dimensions. Concentrating on the static solutions with planar horizon geometry, we explore the thermodynamic behavior in the extended phase space and examine the validity of the first law of thermodynamics besides local thermal stability by the Hessian matrix. We observe that although the topology of boundary is planar, there exists the van der Waals like phase transition for this kind of solution. We find the critical quantities and discuss how the massive and Yang-Mills parameters affect them. Furthermore, some signatures of the first order phase transition such as the swallow-tail behavior of the Gibbs free energy and divergencies of the specific heat are given in detail.