Soft Hair on Black Holes

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   Soft Hair, Memory, and the Quantum Structure of Black-Hole Horizonsxt

   Arthur Li-Wang · 2026 · Highlights in Science Engineering and Technology · Not summarized yet

   Abstract

   This paper studies the theoretical foundations and observational prospects of soft hair and gravitational memory related to the quantum structure of black-hole horizons. It starts by putting the black-hole information paradox with its historical context, which outlines how classical general relativity and quantum mechanics rises to bright contradictions regarding unitarity and information conversation. Against this backdrop, the concept of soft hair, which is low energy excitations associated with asymptotic symmetries, emerges as a potential means of including and taking back information otherwise between soft theorems. The Bondi-Metzner-Sachs (BMS) symmetries, for example, highlights how t…

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   Dynamical horizons and black hole soft hair

   A. Huber · 2025 · Annals of Physics · cited 1 time · Not summarized yet

   Abstract

   In the present work, quasilocal Brown-York charges are derived that coincide in the large sphere limit with the conserved supertranslation hair and superrotation charges introduced by Hawking, Perry and Strominger in [45, 46]. Given these charges, a general scenario is outlined in which a non-rotating black hole completely evaporates after its collapse due to particle creation effects, whereby a genuine one-way traversable event horizon is never formed, but merely a two-way traversable dynamical (resp. future trapping) horizon. The formation of such a dynamical horizon has the consequence, as is demonstrated, that quasilocal energy transported by the considered charges, and thus information,…

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   Superrotation charge and supertranslation hair on black holes

   Stephen William Hawking, Malcolm J. Perry, Andrew Strominger · 2017 · Journal of High Energy Physics · cited 333 times · Not summarized yet

   Abstract

   It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentum $$ \overrightarrow{P} $$ , angular momentum $$ \overrightarrow{J} $$ and boost charge $$ \overrightarrow{K} $$ , an infinite head of supertranslation hair. The distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with super-translation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. A leading-order Bondi-gaug…

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   Shaving off soft hairs and black hole image memory effect

   Shao-Qi Hou, Zong-Hong Zhu · 2026 · Physical Review D · Not summarized yet

   Abstract

   Soft hairs of black holes are the Noether charges associated with the generalized Bondi-Metzner-Sachs symmetries. In this work, the images of soft-haired Kerr black holes are studied. For an eternal black hole, the image is rotated, dilated, and drifting compared to that of the bald counterpart in the celestial plane. The rotation and the dilation are independent of time, while the drifting occurs at a constant speed and in a fixed direction. These effects all depend on angular directions. The soft hair of an astronomical black hole can change due to the emission of gravitational or electromagnetic waves from various physical processes occurring in the vicinity of the horizon. Then, the imag…

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   The No-Short Hair Theorem for Black Holes and Wormholes in Extra-Dimension

   Mandas Biswas · 2026 · cited 1 time · Not summarized yet

   Abstract

   The no-short hair theorem for static spherically symmetric black holes in general theory of relativity asserts that if a black hole has hair, that hair must extend beyond the lowest photon sphere radius of the black hole. This report generalizes the theorem to various extra-dimensional cases of black holes and wormholes in post-Einstein gravity and shows how the observational satisfaction of the no-short hair theorem may lead to a probe for the existence of extra-dimensions. We also show how we may lead to argue that this no-short hair theorem is satisfied for black holes in theories of quantum gravity that naturally precludes extra-dimensional cases, like string theory.

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   Dressed Tunneling in Soft Hair

   Wen Wen · 2021 · cited 3 times · Not summarized yet

   Abstract

   We revisit the Parikh-Wilczek's tunneling model of Hawking radiation in the Schwarzschild black hole with soft hair. Unlike the no-hair black hole, tunneling through the degenerate event horizon generated by supertranslation hair picks up an angular dependence, which suggests a hairy modification to the Bekenstein-Hawking entropy. At last, we discuss several implications and possible observable of soft hair.

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   HPS meets AMPS: how soft hair dissolves the firewall

   Sabrina Pasterski, H. Verlinde · 2020 · Journal of High Energy Physics · cited 30 times · Not summarized yet

   Abstract

   We build on the observation by Hawking, Perry and Strominger that a global black hole space-time supports a large number of soft hair degrees of freedom to shed new light on the firewall argument by Almheiri, Marolf, Polchinski, and Sully. We propose that the soft hair Goldstone mode is encoded in a classical transition function that connects the asymptotic and near horizon region. The entropy carried by the soft hair is part of the black hole entropy and encoded in the outside geometry. We argue that the infalling observer automatically measures the classical value of the soft mode before reaching the horizon and that this measurement implements a code subspace projection that enables the r…

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   Black hole entropy from soft hair

   M. Perry · 2020 · International Journal of Modern Physics D · cited 4 times · Not summarized yet

   Abstract

   We start by looking at why we believe that black holes have entropy. According to Boltzmann, the entropy is a measure of the number of microstates of a system. We suggest here that the entropy arises from a holographic conformal field theory on the black hole horizon. Finally, we discuss some of the implications for the information paradox.

Prior work it builds on

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   Perturbative gravity at null infinity

   T. Adamo, Eduardo Casali, D. Skinner · 2014 · Classical and Quantum Gravity · cited 122 times · Not summarized yet

   Abstract

   We describe a theory that lives on the null conformal boundary I ?> of asymptotically flat space-time, and whose states encode the radiative modes of (super)gravity. We study the induced action of the BMS group, verifying that the Ward identity for certain BMS supertranslations is equivalent to Weinbergʼs soft graviton theorem in the bulk. The subleading behaviour of soft gravitons may also be obtained from a Ward identity for certain superrotation generators in the extended BMS algebra proposed by Barnich and Troessaert. We show that the theory computes the complete classical gravitational S-matrix, perturbatively around the Minkowski vacuum.

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   Evidence for a New Soft Graviton Theorem

   F. Cachazo, A. Strominger · 2014 · arXiv: High Energy Physics - Theory · preprint, not peer reviewed · cited 528 times · Not summarized yet

   Abstract

   The single-soft-graviton limit of any quantum gravity scattering amplitude is given at leading order by the universal Weinberg pole formula. Gauge invariance of the formula follows from global energy-momentum conservation. In this paper evidence is given for a conjectured universal formula for the finite subleading term in the expansion about the soft limit, whose gauge invariance follows from global angular momentum conservation. The conjecture is non-trivially verified for all tree-level graviton scattering amplitudes using a BCFW recursion relation. One hopes to understand this infinity of new soft relations as a Ward identity for a new superrotation Virasoro symmetry of the quantum gravi…

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   Asymptotic symmetries of gravity and soft theorems for massive particles

   Miguel Campiglia, Alok Laddha · 2015 · Journal of High Energy Physics · cited 180 times · Not summarized yet

   Abstract

   A bstractThe existing equivalence between (generalized) BMS Ward identities with leading and subleading soft graviton theorems is extended to the case where the scattering particles are massive scalars. By extending the action of generalized BMS group off null infinity at late times, we show that there is a natural action of such group not only on the radiative data at null infinity but also on the scattering data of the massive scalar field. This leads to a formulation of Ward identities associated to the generalized BMS group when the scattering states are massive scalars or massless gravitons and we show that these Ward identities are equivalent to the leading and subleading soft graviton…

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   BMS supertranslations and Weinberg’s soft graviton theorem

   T. He, V. Lysov, P. Mitra et al. · 2014 · Journal of High Energy Physics · cited 783 times · Not summarized yet

   Abstract

   Recently it was conjectured that a certain infinite-dimensional “diagonal” subgroup of BMS supertranslations acting on past and future null infinity ( and ) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg’s soft graviton theorem. Along the way we construct the canonical generators of supertranslations at , including the relevant soft graviton contributions. Boundary conditions at the past and future of and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of…

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   Supertranslations and Superrotations at the Black Hole Horizon.

   L. Donnay, G. Giribet, H. González et al. · 2015 · Physical Review Letters · cited 282 times · Not summarized yet

   Abstract

   We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.

Papers that cite it

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   Soft theorems in curved spacetime

   Pengyu Cheng, P. Mao · 2022 · Physical Review D · cited 15 times · Not summarized yet

   Abstract

   In this paper, we derive a soft photon theorem in the near horizon region of the Schwarzschild black hole from the Ward identity of the near horizon large gauge transformation. The flat spacetime soft photon theorem can be recovered as a limiting case of the curved spacetime. The soft photons on the horizon are indeed soft electric hairs. This accomplishes the triangle equivalence on the black hole horizon.

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   Soft-photon theorem near static spherical horizons in generic dimensions

   Kai-Yu Zhang · 2026 · Not summarized yet

   Abstract

   We study Maxwell theory near a nonextremal bifurcate Killing horizon in a general static, spherically symmetric spacetime of dimension $D>3$. We impose near-horizon boundary conditions in a regular Eddington--Finkelstein chart that retain both radiative and Coulombic data, and construct the associated horizon phase space and large-$U(1)$ charge. At null infinity, the radiative falloff depends on the spacetime dimension and involves half-integer powers in odd $D$, whereas a nonextremal horizon at finite radius supports radiative data with an ordinary integer-power expansion. Expanding the horizon fields in Killing frequency and spherical harmonics, we derive the associated soft-photon relatio…

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   Testing the black hole ‘no-hair’ hypothesis

   Vítor Cardoso, Leonardo Gualtieri · 2016 · Classical and Quantum Gravity · cited 237 times · Not summarized yet

   Abstract

   Abstract Black holes (BHs) in general relativity (GR) are very simple objects. This property, that goes under the name of ‘no-hair’, has been refined in the last few decades and admits several versions. The simplicity of BHs makes them ideal testbeds of fundamental physics and of GR itself. Here we discuss the no-hair property of BHs, how it can be measured in the electromagnetic or gravitational window, and what it can possibly tell us about our Universe.

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   Black hole shadow with soft hairs

   Feng-Li Lin, Avani Patel, H. Pu · 2022 · Journal of High Energy Physics · cited 16 times · Not summarized yet

   Abstract

   Light bending by the strong gravity around the black hole will form the so-called black hole shadow, the shape of which can shed light on the structure of the near-horizon geometry to possibly reveal novel physics of strong gravity and black hole. In this work, we adopt both analytical and ray-tracing methods to study the black hole shadow in the presence of the infrared structure of gravity theory, which manifests the asymptotic symmetries of spacetime as the supertranslation soft hairs of the black hole. Though the black hole metrics with and without the soft hair are related by large gauge transformations, the near horizon geometries relevant for the shape of the shadow are quite differen…

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   Soft graviton exchange and the information paradox

   Nava Gaddam, N. Groenenboom · 2020 · Physical Review D · cited 31 times · Not summarized yet

   Abstract

   We show that there is a remarkable soft limit in quantum gravity where the information paradox is readily resolved due to virtual soft graviton exchange on the black hole horizon. This regime is where collision energies satisfy $\sqrt{s}\gg \gamma M_{Pl}$ (with $\gamma \sim M_{Pl}/M_{BH}$) near the horizon. We call this the black hole eikonal phase, in contrast to its flat space analogue where collisions are trans-Planckian. Hawking's geometric optics approximation neglects gravitational interactions near the horizon, and results in thermal occupation numbers in the Bogoliubov coefficients. We show that these interactions are mediated by graviton exchange in $2 \rightarrow 2$ scattering near…