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Pujian Mao

Publications and source records attributed to Pujian Mao.

At least 19 recordsLinked to original sources
arXiv2026

Twisting asymptotically-flat spacetimes

We extend the Bondi formalism to describe asymptotically-flat spacetimes where the outgoing null geodesic congruence is not hypersurface-orthogonal, i.e. has non-vanishing twist. In the Newman-Penrose formulation, the twist $\text{Im}(ρ)$ is sourced by a twist potential sitting in the transverse null dyad $(m,\bar{m})$, while in the metric formulation this potential enters $g_{ra}\neq0$. We explain how to solve the Einstein equations for such generalized line elements, thereby providing an extension of the Bondi hierarchy to asymptotically-flat spacetimes with twist. We work out the twisting generalizations of all the well-known features pertaining to asymptotically-flat spacetimes in Bondi gauge, such as the solution space, the flux-balance laws, the asymptotic symmetries, and the transformation laws. The twist potential has a natural Carrollian interpretation as an Ehresmann connection, and gives rise to Carroll boosts as extra asymptotic symmetries. The supertranslation generators in this gauge with twist have no extension in the bulk and therefore only act at null infinity. This enables us to study finite supertranslations of any given solution. One of the advantages of the Bondi gauge with twist is also that it allows to write algebraically special solutions in a manifestly finite radial expansion, and with a repeated principal null direction such that $Ψ_0=Ψ_1=0$. This is in particular the case for the Kerr-Taub-NUT solution. The asymptotic symmetries of algebraically special solutions also have a finite radial expansion, which enables us to study, for example, the supertranslated Schwarzschild solution and its charges quite straightforwardly. We also study an analogue of the twist in three-dimensional spacetimes with non-vanishing cosmological constant, and find an 8-dimensional solution space which encompasses and generalizes the existing results in the literature.

gr-qc↗
arXiv2026

Four-dimensional Stationary Algebraically Special Solutions, Weyl Invariants, and Soft Hairs Beyond Large Gauge Transformations

We revisit the Ricci-flat metrics in four dimensions that are stationary and algebraically special, together with the locally asymptotically flat conditions in the generalized Bondi-Sachs framework. We show that the Einstein equation is reduced to Laplacian equation on the celestial sphere. The solutions consist of two pairs of arbitrary holomorphic and antiholomorphic functions analogous to the Virasoro modes. We prove that the higher modes of one pair of the (anti-)holomorphic function contain an infinite tower of soft hairs from the perspectives of the asymptotic supertranslation charges. We verify that different modes of the soft hairs are distinct solutions which cannot be connected by diffeomorphism, using the Weyl invariants associated to the solutions. Extending the construction to Einstein-Maxwell theory introduces a third pair of (anti-)holomorphic functions, arising from the Maxwell tensor which generates soft electric hair. We further present an exact soft-hairy solution of Einstein-Maxwell theory with a cosmological constant, offering a potential understanding of soft hair from the AdS/CFT correspondence.

hep-th↗
arXiv2025

Angular momentum and memory effect

It is a long-standing problem in general relativity that the notion of angular momentum of an isolated system has supertranslation ambiguity. In this paper, we argue that the ambiguity is essentially because of the gravitational wave memory. When properly subtracting the memory effect of the observer, one can introduce a supertranslation invariant definition of the angular momentum at null infinity.

gr-qc↗
arXiv2025

Supertranslations in the bulk of spacetime

Supertranslations are usually defined as asymptotic symmetries associated with spacetime boundaries, such as null infinity and black hole horizons. In this Letter, we show that supertranslations admit a natural, coordinate-independent extension into the bulk of spacetime, realized as transitions between families of null hypersurfaces. This construction applies to generic spacetimes admitting null boundaries with residual symmetries and unifies the realizations of supertranslations at null infinity and finite-distance null hypersurfaces such as black hole horizons. The bulk supertranslation is connected to boundary supertranslation by characteristic flows. The associated symmetry algebra at the linearized level can be realized by light-ray operators defined on the null hypersurface and the bulk supertranslation acts as a zero-mode operator in the context of light-cone quantization. Within this framework, the gravitational wave memory effect corresponds to a shift of null hypersurfaces in the bulk. As explicit examples, we compute bulk supertranslations in Minkowski spacetime and four-dimensional Schwarzschild spacetime, where we uncover a novel curvature-dependent memory effect with observable consequences for light propagation.

hep-th↗
arXiv2025

Character of the highest weight module of BMS algebra realized on codimensional-two boundary

In this paper, we investigate the highest weight representation (HWR) of the three and four-dimensional Bondi-Metzner-Sachs (BMS) algebra realized on the codimension-two boundary of asymptotic flat spacetime (AFS). In such a realization, the action of supertranslation shifts the conformal weight of the highest-weight states. As a result, there is no extra quantum number relating to the supertranslation. We construct the highest-weight BMS modules and compute their characters. We show that the BMS$_3$ highest-weight vacuum character with special value of central charges coincides with the 1-loop partition function of three-dimensional asymptotic flat gravity, up to an overall phase factor ``$i$''. We expect the vacuum character of BMS$_4$ may shed light on the flat holography in four dimensions.

hep-th↗
arXiv2025

Note on identifying four-dimensional vacuum solutions from Weyl invariants

The diffeomorphism covariance is a fundamental property of General Relativity which leads to the fact that the same solution of Einstein equation can be given in completely distinct forms in different coordinate systems. Distinguishing or identifying two metrics as solutions of Einstein equation is particularly challenging. In a recent paper arXiv:2503.14586 [hep-th], it is proposed to apply the relations of different Weyl invariants to distinguish solutions. In this note, we present a complementary application of the Weyl invariants. We verify from Weyl invariants that two metrics with completely different forms are the same solution. We also present the coordinates transformation that connects the two metrics.

gr-qc↗
arXiv2025

Note on post-Minkowskian expansion and Bondi coordinates

In this note, we transform the linear order (at order $G$) metric from a system of pointlike bodies source in the post-Minkowskian expansion to the Bondi coordinates. We show that the Bondi 4-momentum and angular momentum coincide with the relativistic definitions of 4-momentum and angular momentum for the system of pointlike bodies. The angular momentum computed at the null infinity is free of supertranslation ambiguity.

gr-qc↗
arXiv2025

Twisting asymptotic symmetries and algebraically special vacuum solutions

In this paper, we study asymptotic symmetries and algebraically special exact solutions in the Newman-Penrose formalism. Removing the hypersurface orthogonal condition in the well studied Newman-Unti gauge, we obtain a generic asymptotic solution space which includes all possible origins of propagating degree of freedom. The asymptotic symmetry of the generalized system extends the Weyl-BMS symmetry by two independent local Lorentz transformations with non-trivial boundary charges, which reveals new boundary degrees of freedom. The generalized Newman-Unti gauge includes algebraically special condition in its most convenient form. Remarkably, the generic solutions satisfying the algebraically special condition truncate in the inverse power of radial expansions and the non-radial Newman-Penrose equations are explicitly solved at any order. Hence, we provide the most general algebraically special solution space and the derivation is self-contained in the Newman-Penrose formalism. The asymptotic symmetry with respect to the algebraically special condition is the standard Weyl-BMS symmetry and the symmetry parameters consist only the integration constant order. We present the Kerr solution and Taub-NUT solution in the generalized Newman-Unti gauge in a simple form.

gr-qc↗
arXiv2025

Supertranslation ambiguity in post-Minkowskian expansion

The supertranslation ambiguity of angular momentum is a long-standing problem in general relativity, which arises the puzzle of the angular momentum loss in the post-Minkowskian (PM) expansion. The angular momentum loss in gravitational scattering is of order $G^2$ in the linear response theory but of order $G^3$ in the amplitudes-based methods. In this paper, we propose a generic prescription to fix the supertranslation ambiguity in the PM expansion which will uniquely determine the angular momentum loss. The proposal is self-contained and involves only the null infinity data.

gr-qc↗
arXiv2024

Loop corrections versus marginal deformation in celestial holography

Four-dimensional all-loop amplitudes in QED and gravity exhibit universal Infrared (IR) singularities with a factorization structure. This structure is governed by tree amplitudes and a universal IR-divergent factor representing the exchange of soft particles between external lines. This letter offers a precise dual interpretation of these universal IR-divergent factors within celestial holography. Considering the tree amplitude as the foundation of the celestial conformal field theory (CCFT), these universal factors correspond to marginal deformations with a \textit{double-current} construction in the CCFT. Remarkably, a novel geometric representation of these deformations through topological gauging provides an exact description of transitions within bulk vacuum moduli spaces which extends the celestial holography beyond the perturbative level. Our findings establish a concrete dictionary for celestial holography and offer a holographic lens to understand loop corrections in scattering amplitudes.

hep-th↗
arXiv2024

Gravitational vacua in the Newman-Penrose formalism

In this paper, we derive the generic solution of the Newman-Penrose equations in the Newman-Unti gauge with vanishing curvature tensor. The obtained solutions are the vacua of the gravitational theory which are connected to the derivations in metric formalism from exponentiating the infinitesimal BMS generators in the BMS gauge in \cite{Compere:2016jwb,Compere:2016hzt} by a radial transformation. The coordinate transformations in the Newman-Unti gauge connecting each vacuum are also obtained. We confirm that the supertranslation charge of the gravitational vacua with respect to global considerations vanishes exactly not only in the Einstein theory but also when including the Holst, Pontryagin, and Gauss-Bonnet terms which verifies that the gravitational vacua are not affected by those trivial or boundary terms.

hep-th↗
arXiv2024

Linearized gravity and soft graviton theorem in de Sitter spacetime

We study the linearized gravity theory in the Newman-Unti gauge in the near horizon region of the de Sitter spacetime. The linearized Einstein equation involves the cosmological constant. The near horizon symmetry consists of near horizon supertranslation and near horizon superrotation. We compute the near horizon supertranslation charge and find the proper near horizon fall-off conditions which uncover a soft graviton theorem from the Ward identity of the near horizon supertranslation.

hep-th↗
arXiv2024

Notes on no black hole theorem in three dimensional gravity

In this paper, we revisit the no black hole theorem in three dimensional (3D) gravity in the Newman-Penrose formalism in a generalized Newman-Unti gauge. After adapting the well established 4D NP formalism and its gauge and coordinates system to 3D gravity, we show that the no black hole theorem is manifest in the NP equations. We further study in detail the horizon properties of the 3D charged rotating solutions and confirm that a black hole solution requires a negative cosmological constant.

gr-qc↗
arXiv2024

Notes on Wormhole Cancellation and Factorization

In AdS/CFT, partition functions of decoupled CFTs living on separate asymptotic boundaries factorize. However, the presence of bulk wormholes connecting different boundaries tends to spoil the factorization of the bulk partition function, which leads to a disagreement between the two sides. In this paper, we present two examples where wormhole contributions cancel each other in bulk partition function calculations, thus the bulk factorization can be realized. The first example is in 2-dimensional Jackiw-Teitelboim (JT) gravity, where the proposed way of realizing the cancellation resides in the extra complex phases associated with different wormholes. The phases arise due to the degenerate vacua structure. In the example of the Sachdev-Ye-Kitaev (SYK) model, the cancellation can be achieved due to the distribution of the wormhole saddles on a complex plane. The two examples demonstrate a way of realizing bulk partition function factorization by extending the Hilbert space and dressing wormhole saddles with extra phases.

hep-th↗
arXiv2024

Near horizon linearized gravity and soft theorem

In this paper, we study the linearized gravity theory in the near horizon region of the Schwarzschild black hole in four dimensional spacetime. Under the Newman-Unti gauge, we derive the most general near horizon symmetry and solution space without any near horizon fall-off condition. There are four towers of surface charges that are generic functions on the horizon associated to the near horizon symmetry. With suitable near horizon fall-off conditions, we reveal a soft graviton theorem from the Ward identity of the near horizon supertranslation in both coordinates space and momentum space.

hep-th↗
arXiv2024

Asymptotic Weyl double copy in Newman-Penrose formalism

In this paper, we provide a self-contained investigation of the Weyl double copy in the Newman-Penrose formalism. We examine the Weyl double copy constraints for the general asymptotically flat solution in the Newman-Unti gauge. We find that two transparent solutions of the asymptotic Weyl double copy constraints lead to truncated solutions for both linearized and Einstein gravity theory where the solutions are in the manifest form of Petrov type N or type D in the Newman-Unti gauge.

hep-th↗
arXiv2024

Soft theorems in de Sitter spacetime

In this paper, we derive a soft photon theorem and a soft gluon theorem in the de Sitter spacetime from the Ward identity of the near cosmological horizon large gauge transformation. Taking the flat limit of the de Sitter spacetime, the soft theorems naturally recover the corresponding flat spacetime soft theorems.

hep-th↗