Registration Room: Applebey Lecture Theatre (Geography)

Opening Remarks

• Simon Ross

Room: Applebey Lecture Theatre (Geography)

Accelerating Horizons and Thermodynamics

• Ruth Gregory

Room: Applebey Lecture Theatre (Geography) The C-metric in GR is a fascinating spacetime with a deformed horizon and a cosmic string connecting the black hole to asymptotic infinity meaning the black hole is not isolated. In spite of this, the thermodynamics of these composite solutions is well defined and can even include changes in the string tension as I will show, however the holography of such solutions is a bit more subtle. To explore such questions in a simpler set-up I've been working on 3D solutions in AdS. I will describe recent progress on acceleration and rotation in three dimensions, including accelerating "point particles" as well as BTZ-like solutions.

Lorentzian Slicings of Euclidean Wormholes

• Alexandre Belin (Universita & INFN, Milano-Bicocca (IT))

Room: Applebey Lecture Theatre (Geography) Euclidean wormholes are understood to encode important non-perturbative information of gravitational physics, coming from the chaotic nature of the dual CFT. In this talk, I will discuss the Lorentzian slicings of such geometries. Slicing a Euclidean geometry, in terms of the path integral, is a method often used to prepare states. In this case, the nature of the state is radically different depending on whether the cut intersects the AdS boundary or not. If it does, the bulk geometry should have an interpretation as a state in the CFT. If it does not, the geometry prepares a state in a closed universe. We discuss both cases and discuss the interpretation from the point of view of the dual CFT.

Symmetries of extremal horizons

• Alex Colling (University of Cambridge)

Room: Applebey Lecture Theatre (Geography) Extremal horizons in a spacetime can be studied through their near-horizon geometry. Building on work by Dunajski and Lucietti, we prove a near-horizon analogue of Hawking’s rigidity theorem: any rotating near-horizon geometry admits a Killing field tangent to the horizon cross-sections. This result holds in spacetimes of arbitrary dimension and with general matter content, assuming only that the cross-sections are compact. As a consequence, any near-horizon geometry admits an enhanced symmetry group containing either SO(2,1) or the two-dimensional Poincaré group. The rigidity theorem enables a complete classification of four-dimensional near-horizon geometries in Einstein-Maxwell theory. We further construct new families of extremal horizons in five dimensions carrying charge and two independent angular momenta.

Detecting black hole microstates

• William Chan (University of Pennsylvania)

Room: Applebey Lecture Theatre (Geography) A step towards probing the black hole interior and its structure is being able to detect the black hole microstate. We demonstrate that the Euclidean two-point function of an appropriately chosen probe operator can detect the microstate of an asymptotically AdS black hole. This detection, which requires a tuned, state-dependent choice of probe, is the result of a new gravitational saddle, which dominates over the usual saddles. The gravitational result can be explicitly reproduced in the dual boundary CFT if we assume the eigenstate thermalization hypothesis. We also discuss a binary search protocol to detect the black hole microstate from a candidate list.

Revisiting near-extremal and near-BPS black holes in AdS3 supergravity

• Adam Bac (University of Cambridge)

Room: Applebey Lecture Theatre (Geography) Despite the archetypal status of the BTZ background in quantifying quantum aspects of black holes, several features at low temperatures remain imprecise and incomplete. Here, we systematically investigate the behaviour of the Euclidean path integral at low temperatures in the context of AdS3 supergravity, including an analysis of quantum fluctuations in both the near-horizon and asymptotic regions. We clarify and rectify aspects of the bosonic fluctuations, highlighting the role of boundary conditions in AdS3, and show in particular that the gravitational path integral in the near-horizon region is inequivalent to that around BTZ at low temperature. We further account in detail for the contributions of Chern–Simons fields and spin-3/2 modes, thereby refining the disparities between the near-extremal and near-BPS limits at low temperature. Altogether, our analysis sharpens the distinction between near- and far-region dynamics and demonstrates a disagreement in the gravitational path integral at the quantum level.

Quantum Gravity and Spacetime Singularities

• Leonardo Modesto (Cagliari University)

Room: Applebey Lecture Theatre (Geography) We present a unified (gravity and matter) weakly nonlocal theory unitary, causal, and finite at quantum level in the quantum field theory framework. As a consequence of finiteness, there is no Weyl anomaly and the theory turns out to be conformal invariant at classical as well at quantum level. Therefore, nonlocal quantum gravity is a conformal invariant theory in the spontaneously broken phase of the Weyl symmetry. Accordingly, following and extending the seminal paper by Narlikar and Kembhavi, we are able to provide explicit examples of singularity-free black hole exact solutions. The absence of singularities is based on the finiteness of the curvature invariants and, more important, on the geodesic completion. It tuns out that, no massive or massless particle can reach the singularity domains of the spacetime. Finally, we will present new results about unitarity in curved spacetime.

Regular black holes from pure (nonlocal) gravity

• Pablo Bueno

Room: Applebey Lecture Theatre (Geography) Resolving spacetime singularities within an effective classical description has motivated two complementary approaches. One is based on nonlocal gravities, which are able to smear localized matter sources over finite regions. The other is based on infinite towers of higher-curvature corrections to the Einstein--Hilbert action belonging to the Quasitopological class, which have recently been shown to possess vacuum regular black holes (RBHs) as their unique spherically symmetric solutions. Within these models, such RBHs arise from gravitational collapse, although singular matter distributions can still produce singular geometries. In this talk, I will review the features and shortcomings of both approaches. I will then combine them by presenting new nonlocal completions of Quasitopological gravities that admit exact, spherically symmetric vacuum RBHs, satisfy a perturbative Birkhoff theorem, and overcome several of the limitations of the individual frameworks.

The third law of black hole mechanics

• Harvey Reall (University of Cambridge)

Room: Applebey Lecture Theatre (Geography) The third law of black hole mechanics asserts that it is impossible for a non-extremal black hole to become extremal in finite time (in classical General Relativity). Counterexamples were found recently: gravitational collapse of a massless charged scalar field can produce an exactly extremal Reissner-Nordstrom black hole in finite time, passing through an intermediate phase in which the solution is exactly Schwarzschild at the horizon. These examples involve matter with a large charge to mass ratio. I will describe how if the charge to mass ratio of matter is suitably bounded then one cannot form an extremal Reissner-Nordstrom black hole in finite time. It is conjectured that one can form an extremal rotating black hole via gravitational collapse of gravitational waves. I shall describe recent work showing that this conjecture is true in five spacetime dimensions.

Cosmological pole-skipping and quantum chaotic dynamics of de Sitter horizons

• Juan Pedraza (Madrid IFT)

Room: Applebey Lecture Theatre (Geography) Pole-skipping has emerged as a sharp, near-horizon signature of many-body quantum chaos in holography. In this talk, I will demonstrate how it generalizes to cosmological spacetimes and what it reveals about the microscopic dynamics of de Sitter horizons. First, in empty de Sitter and Schwarzschild-de Sitter geometries, I will map the tower of pole-skipping points for scalar, Maxwell, and gravitational perturbations and explain the constraints they impose on bulk two-point functions. Focusing on the gravitational sound channel, I will then relate this calculation to the scrambling of quanta skimming the horizons and extract lessons about the structure of a hypothetical dual description. I will conclude by proposing microscopic toy models based on long-range and non-Hermitian deformations of DSSYK-type chains that reproduce the qualitative features observed in these settings.

The third law of black hole mechanics and gravitational collapse to supersymmetric AdS black holes

• Aidan McSharry (University of Cambridge)

Room: Applebey Lecture Theatre (Geography) Recently it has been shown that the third law of black hole mechanics can be violated: an exactly extremal Reissner-Nordström black hole can form in finite time in the gravitational collapse of matter with a large charge to mass ratio. However, it has also been proved that this cannot happen if the matter satisfies a “supersymmetric” lower bound on its energy in terms of its charge. In this talk, I will discuss related results for gravity with a negative cosmological constant in both three and four spacetime dimensions. In the four-dimensional case, a supersymmetric Kerr-Newman-AdS black hole cannot be formed in the gravitational collapse of matter satisfying the aforementioned bound. Likewise, one can prove that it satisfies the third law. In three dimensions, the situation is rather different: assuming the dominant energy condition, although one can prove a third law for the extremal BTZ black hole, one can still form it in collapse.

A Reverse Black Hole Information Problem

• Andrew Rolph (VUB)

Room: Applebey Lecture Theatre (Geography) In this talk, I will discuss the formation, detection and coarse-graining of black holes in AdS/CFT, with an emphasis on the tension between boundary unitarity and the production of mixed state Hawking radiation in the bulk. I will construct CFT states dual to black hole formation and evaporation by colliding bulk particle wavepackets at trans-Planckian energy. I will propose boundary probes which are able to distinguish small AdS black holes from other states within the microcanonical ensemble. I will discuss different coarse-graining prescriptions acting on the evolving CFT state, including averaging over CFT data, Hamiltonians and time windows, and compare their purities to those expected from the bulk semiclassical description. These results clarify how semiclassical black hole behaviour can arise from an ensemble-averaging of the exact unitary dynamics, and take a step towards a better understanding of coarse-graining in the single-sided black hole information problem. Based on arXiv:2601.22077 with Jan de Boer and Jildou Hollander.

Higher-dimensional BKL dynamics in AdS black holes

• Ángel Murcia (Instituto de Física Teórica)

Room: Applebey Lecture Theatre (Geography) Chaotic BKL dynamics provides a canonical description of the approach to spacelike singularities as a sequence of Kasner epochs grouped into eras. While this paradigm is well established for cosmological singularities, explicit realizations inside black holes have been scarce, despite renewed interest from holography. Here, we construct a broad class of asymptotically AdS black holes in D ≥ 4 whose interiors exhibit bona fide BKL dynamics as the singularity is approached. In the near-singularity regime, the evolution reduces to billiard-like motion in a compact domain that forms a regular (D − 2)-simplex. We derive closed-form bouncing rules for the Kasner exponents in arbitrary dimension and prove the ensuing chaotic dynamics. A key novelty for D ≥ 5 is a richer internal organization of eras: inequivalent transitions between epochs lead to distinct Kasner seasons, yielding new patterns of epoch/era structure for both electric and gravitational walls. Finally, we investigate a holographic diagnostic, the thermal a-function, whose monotonic flow captures individual epochs and eras and can display near-walking behavior in suitable Kasner regimes.

A strengthened Quantum Null Energy Condition

• Victor Franken (Ghent University)

Room: Applebey Lecture Theatre (Geography) The quantum null energy condition (QNEC) is a well-known and proven information-theoretic lower bound on the expectation value of energy density in quantum field theory. The bound can be predicted simply as a consequence of a conjectured quantum gravity principle called the restricted quantum focusing conjecture (RQFC). Here, we show that for conformal field theories in spacetime of dimension greater than two, a stronger-than-QNEC bound is predictable from the RQFC. This strengthened QNEC says that $T_{kk} -\frac{S''}{\mathcal{A}} \geq \kappa \mathcal{A} \left(\frac{S'}{\mathcal{A}}\right)^2$, where derivatives denote null variations of a Rindler wedge in region of area $\mathcal{A}$.

Bulk observers near quantum black holes

• Thomas Mertens (Ghent University)

Room: Applebey Lecture Theatre (Geography) In this talk, I will construct a definition of diff-invariant bulk observables in lower-dimensional JT gravity. I will use these to define quantum accelerated observers and a generalization of the Unruh effect. After the gravity path integral, this leads to a finite matter thermal entropy of bulk quantum fields. Finally, I will discuss a definition of infalling observers, and derive how quantum gravity effects lead to a violation of the equivalence principle, but an absence of a firewall. Based on constructions started in 1902.11194, and revisited more recently in 2507.20983 and 2607.XXXXX.

Spacetime singularities and the Bruhat-Tits tree

• Sean Hartnoll

Room: Applebey Lecture Theatre (Geography) I will review how the Einstein equations in a near-singularity 'BKL' regime map onto hyperbolic billiard dynamics. Solutions to the Wheeler-DeWitt equation, i.e. the quantum wavefunctions of this system, are thus odd automorphic forms. I will explain how these quantum wavefunctions can be expressed as Green's functions for hopping dynamics on the Bruhat-Tits tree. This suggests a possible adelic dual description of spacetime singularities.

Nonlocality induces isometry and factorisation in holography

• Johanna Erdmenger (Julius Maximilians University Würzburg)

Room: Applebey Lecture Theatre (Geography) In AdS/CFT holography, two manifestations of the black hole information paradox are given by the nonisometric nature of the bulk-boundary map and by the factorisation puzzle. By considering time-shifted microstates of the eternal black hole, we have demonstrated that both puzzles may be simultaneously resolved by taking into account nonlocal quantum corrections that correspond to wormholes arising from state averaging. This is achieved by showing, using a resolvent technique, that the resulting Hilbert space for an eternal black hole is finite-dimensional with a discrete energy spectrum. Moreover, I will discuss how geometric phases may be used to describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of their Hilbert space. We find a direct relation between geometric phases and von Neumann algebras, and show that a vanishing geometric phase implies the existence of a well-defined trace functional on the algebra. We discuss how this is realised within the AdS/CFT correspondence for the eternal black hole.

Complexity and the Hilbert space dimension of 3D gravity

• Jonathan Karl (University of Würzburg)

Room: Applebey Lecture Theatre (Geography) A central problem in formulating a theory of quantum gravity is to determine the size and structure of the Hilbert space of black holes. Here we use a quantum dynamical Krylov complexity approach to calculate the Hilbert space dimension of a black hole in 2+1-dimensional Anti-de Sitter space. We achieve this by obtaining the spread of an initial thermofield double state over the Krylov basis. The associated Lanczos coefficients match those for chaotic motion on the *SL*(2,R) group. By including non-perturbative effects in the path integral, which computes coarse-grained ensemble averages, we find that the complexity saturates at late times. The saturation value is given by the exponential of the Bekenstein-Hawking entropy. Our results introduce a new way to compute the Hilbert space dimension of complex interacting systems from the saturating value of spread complexity.

Wheeler–DeWitt Quantisation of BKL Billiards

• Ming Yang (DAMTP)

Room: Applebey Lecture Theatre (Geography) Near a spacelike singularity, the BKL approximation reduces gravitational dynamics to the motion of logarithmic scale factors in a Lorentzian minisuperspace. In the late-time limit, this becomes a billiard motion on a hyperbolic domain. Quantisation then gives a Wheeler–DeWitt equation which can be interpreted as a Laplace-type spectral problem on the corresponding hyperbolic billiard. This talk focuses on the four- and five-dimensional cases. In these cases, the Wheeler–DeWitt eigenfunctions are naturally organised as Maass-type waveforms. I will then describe an auxiliary Fock-space representation of the Mellin-transformed wavefunction, where the wavefunction is written as a trace over charged harmonic oscillators whose modes are labelled by primes in the four-dimensional case, and by the relevant complex primes in the five-dimensional case. This gives a “dual” primon-gas picture of the Wheeler–DeWitt wavefunction near a cosmological singularity. I will also briefly describe ongoing work in seven dimensions, where the BKL billiard may serve as a quaternionic bridge between the commutative arithmetics and the octonionic structures associated with the maximal-supergravity billiard.

A complete mode decomposition of black hole perturbations

• Javier Carballo (University of Southampton)

Room: Applebey Lecture Theatre (Geography) It is well known that quasinormal modes (QNMs) do not form a complete basis for linear black hole perturbations. In particular, retarded Green's functions of black holes can only be decomposed as a convergent sum of QNMs at sufficiently late times. In this talk, I will show that Green's functions can be expanded as a convergent mode sum everywhere in spacetime. When QNMs fail at early times, a sum of Matusbara modes associated to the horizon temperature converges instead. Based on 2510.18956.

Holographic Banners

• Matthew Blacker (University of Cambridge)

Room: Applebey Lecture Theatre (Geography) The goal of this talk is to probe the future interior of an eternal AdS black hole. The quantum cosmological future and past interior states of the black hole may be placed on an equal footing to the left and right AdS boundary data by considering the on-shell bulk action as a function of the left/right/future/past data. We call this object a holographic banner, and it obeys the Hamilton-Jacobi equation with respect to all four of its arguments. We compute the holographic banner for a scalar field in an AdS black hole background explicitly and use it to construct the semiclassical state in the future interior obtained from a thermofield double state in the past evolved by arbitrary time- and space-dependent boundary sources. Time permitting, we will discuss how (when the spacetime itself is dynamical) the holographic banner gives, in principle, a map from boundary data to near-singularity semiclassical quantum cosmology following chaotic BKL dynamics.

Conformal boundaries near extremal black holes

• Andrew Svesko

Room: Applebey Lecture Theatre (Geography) In this talk I examine four dimensional, near-extremal black holes in the presence of a finite boundary obeying conformal boundary conditions, where the conformal class of the induced metric and the trace of the extrinsic curvature are fixed. Working in Euclidean signature, I will describe the quasi-local gravitational thermodynamics, where the near-extremal regime is dominated by a double-scaling limit which reveals new scaling laws for the entropy at low temperatures. Upon spherical dimensional reduction, the effective two-dimensional dilaton-gravity theory that describes the near-extremal regime is shown not to be Jackiw-Teitelboim gravity (as is the case for finite Dirichlet boundaries). Working in Lorentzian signature, I will review the system’s linearized dynamics, characterizing the modes of metric perturbations. When the finite boundary is near the horizon of a near-extremal black hole, the system is rendered linearly stable. This provides the first example of a black hole in the presence of conformal boundaries that is well-posed, and both thermodynamically and (linearly) dynamically stable.