北京雁栖湖应用数学研究院

The multipolar post-Minkowskian formalism describes the external gravitational field outside sources such as a compact binary merger. In this formalism, the metric is expanded in harmonic gauge, also known as de Donder gauge. In radiation zone, at length scales above the gravitational wave typical wavelength, the metric is best studied in Bondi or Newman-Unti gauge where an infinite set of flux-balance laws describe much physics of interest. In this talk, I will describe how to transfer known results from de Donder gauge to Bondi gauge, first at linear order and then at quadratic order in the post-Minkowskian expansion. I will discuss the tail and memory effects from this point of view, as well the description of recently defined w(1+\infty) charges in terms of canonical multipole moments.

In this talk, we will present a holographic description of gravity in 4d asymptotically flat spacetime in terms of a 3d sourced conformal Carrollian field theory. The external sources encode the leaks of gravitational radiation at null infinity. The Ward identities of this theory are shown to reproduce those of the 2d celestial CFT after relating Carrollian to celestial operators. This suggests a new set of interplays between gravity in asymptotically flat spacetime, sourced conformal Carrollian field theory and celestial CFT.

We identify the reduced phase space of causal diamonds with fixed edge length in pure 2+1 dimensional gravity with a negative cosmological constant, which turns out to be the cotangent bundle of the homogeneous space Diff^+(S^1)/PSL(2,R). Isham’s group theoretic quantization scheme is applied to this nonlinear phase space. We find that the twist of the boundary curve (which is also the ``spin” of the diamond) is quantized in integer or half-integer multiples of the ratio of the Planck length to the diamond edge length. We identify the reduced phase space of causal diamonds with fixed edge length in pure 2+1 dimensional gravity with a negative cosmological constant, which turns out to be the cotangent bundle of the homogeneous space Diff^+(S^1)/PSL(2,R). Isham’s group theoretic quantization scheme is applied to this nonlinear phase space. We find that the twist of the boundary curve (which is also the ``spin” of the diamond) is quantized in integer or half-integer multiples of the ratio of the Planck length to the diamond edge length.

I will present an analysis of 4d gravity in a partial Bondi gauge, where only three conditions instead of the usual four are imposed on the metric. The so-called determinant condition usually imposed on the angular metric is in particular dropped. This partial gauge still enables to construct a solution space, which can accommodate an arbitrary cosmological constant, boundary sources, the ''trace of the shear'', and polyhomogeneous terms. After presenting this solution space I will discuss the asymptotic symmetries. The partial gauge is in particular adapted to treating in a unified manner and contrasting the celebrated Bondi-Sachs gauge, and the Newman-Unti gauge, which we find to be inequivalent. This latter does indeed enable to access a new asymptotic symmetry. This construction generalizes previous work in 3d gravity, which I will also present as further motivation for the 4d extension. (Based on upcoming work with Céline Zwikel.)

In this talk, I'm going to formulate the D-dimensional Einstein gravity in presence of a codimension one null boundary. As we will see in addition to the bulk degrees of freedom that propagate into the bulk we also have to account for the boundary degrees of freedom that reside at the boundary. A suitable way to label these boundary degrees of freedom is using the surface charges associated with large diffeomorphisms. Surprisingly, we will also observe these boundary degrees of freedom describe a thermodynamic system with local laws of thermodynamics. This thermodynamical system is generally an open system and can be closed only when there is no flux of gravitons through the null surface. Local laws of thermodynamics are a manifestation of diffeomorphism invariance of the theory at the boundary and account for the dynamics of the part of spacetime behind the boundary. Our analysis extends the usual black hole thermodynamics to a universal feature of any area element on a generic null surface in a generic diffeomorphism invariant theory of gravity

Arguments are given that time evolution in an expanding universe is a non-unitary isometry.

Physics at null boundaries is relevant in flat space holography and for black holes. I focus on the latter, reviewing near horizon symmetries and their implications for soft hair, black hole entropy, phase space slicings, and memory effects.

In this talk, I will consider a universal group of symmetries that are associated to embedded surfaces in a classical spacetime. In the codimension-2 case, we refer to these surfaces as corners, and the symmetry as the extended corner symmetry. In the context of the Einstein-Hilbert theory, we show that the Noether charges supported by such a corner coincide precisely with the extended corner symmetry. The inclusion of the embedding map into the phase space of the theory allows for a calculation of the algebra of charges. We then show that within the covariant phase space formalism, there is a precise way of extending the phase space such that all charges are integrable and associated with Hamiltonian vector fields on field space. The algebra of charges is then consistently represented in terms of the Poisson brackets of this extended phase space theory. This resolves an old conundrum in gravity, separating the notion of non-integrability from non-conservation. Finally, we discuss some recent work employing the orbit method which relates corners to certain symplectic reductions. This gives an entirely group theoretical characterization of corners without reference to an underlying classical spacetime, and thus might be regarded as the building blocks of a quantum theory.

In this talk, I will present an analysis, based on symmetries, of Einstein's equation in Asymptotically flat spacetime that simplifies the asymptotic gravitational dynamics drastically. I will show that the asymptotic Einstein's equation can be recast as conservations equations for a Carrollian fluid. These conservation equations contain a spin-zero (the mass), spin 1 (the momenta) and spin 2 charge aspects. I will show that the spin 2 conservation equation finally gives a symmetry interpretation to the subsub-leading soft theorems. It also reveals a higher spin symmetry in gravity acting on the gravitational phase space. If time permits, I will explain the connection with the Celestial CFT derivation of a global version of the symmetry algebra and the challenges that lie ahead.

I will start with a brief review some of the problems associated with the information paradox. I will then move on to a discussion of gravitational collapse and the formation of singularities in classical general relativity. We then look at quantum gravity and the Wheeler-DeWitt equation. We use this to make deductions about the nature of singularities quantum mechanically. Finally, we suggest that our results lead to a possible route to a resolution of the information paradox.

I will explain how one can derive dual asymptotic gravitational charges using the first-order tetrad formalism. I will then explain why such dual charges are important.

After deriving the modular covariant partition function of photons and gravitons with perfectly conducting boundary conditions in a slab geometry, we infer consequences for the behavior of these gases at criticality.

We present an explicit formula for Lorentz boosts and rotations that commute with BMS supertranslations in asymptotically flat spacetimes. Key to the construction is the use of infrared regularizations and of a unitary transformation that makes observables commute with the soft degrees of freedom. We explicitly verify that our charges satisfy the Lorentz algebra and we check that they are consistent with expectations by evaluating them on the supertranslated Minkowski space and on the boosted Kerr black hole.

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. We provide explicit constructions in the boundary theory of Kruskal-like time evolutions which can take bulk observers behind the horizon. The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III1 von Neumann algebraic structure and the half-sided modular translation structure associated with it.

I will argue that apparent ensemble averaging in gravity even when there is actually no ensemble reflects two facts: 1) black hole physics is chaotic, and 2) the Hamiltonian H_N that describes black holes has no regular behavior for large N except what follows from thermodynamics. This interpretation predicts that the gravitational path integral does not show signs of ensemble averaging if one computes the energies and couplings of states that are not black holes. In D=3, this prediction can be checked by studying classical solutions, and passes the test. (Based on arXiv:2202.01372 with J.-M. Schlenker.)