Einstein observers in flat space-time are inertial observers which use light to synchronize their clocks. For such observers, speed of light is a constant by construction. However, one can use super-translations to change coordinates from Einstein to BMS coordinates. From the point of view of BMS observers, speed of light is not a constant all over the space-time and in all directions. So in general, clocks which are synchronized for Einstein observers are not synchronized for BMS observers, and vice versa. Based on this fact, we propose a local observable for detecting the soft hairs, which is the variations in speed of light for such observers. We also investigate the relation of this observable to gravitational memory, which is a permanent change of position of test particles at infinity, after a gravitational wave passes completely from them. It is shown that the BMS time coordinate is the physical time after a gravitational wave, and it is the legitimate time to be used to calculate the light speed. Based on this argument, the analysis predicts a permanent change in the speed of light rays which propagate in asymptotics after a gravitational wave. Moreover, it is explained how this change is related to the gravitational memory by comparing their significance in observations.
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.
Treating Maxwell soft hair as a transition function that relates U(1) gauge fields living in the asymptotic region and near-horizon region, the U(1) gauge parameter $ϕ$ naturally becomes a good label of those Maxwell soft hair degrees of freedom. This interpretation also builds the connection between Maxwell soft hair and U(1) edge modes living in the intermediate region, which admits a well-defined effective action description. We study the statistical properties by Euclidean path integral, which concludes that the soft hair density of state increases with black hole temperature. Hawking radi…
The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einstein's field equations, are related to the fluid dynamics, governed by the relativistic Navier-Stokes equations. In this work the correspondence is extended, where the duality between incompressible fluids and gravitational backgrounds with soft hair excitations is implemented. This construction is set through appropriate boundary conditions to the gravitational background, leading to a correspondence between generalized incompressible Navier-Stokes equations and soft hairy horizons.
The membrane paradigm posits that black hole microstates are dynamical degrees of freedom associated with a physical membrane vanishingly close to the black hole's event horizon. The soft hair paradigm postulates that black holes can be equipped with zero-energy charges associated with residual diffeomorphisms that label near horizon degrees of freedom. In this essay we argue that the latter paradigm implies the former. More specifically, we exploit suitable near horizon boundary conditions that lead to an algebra of `soft hair charges' containing infinite copies of the Heisenberg algebra, ass…
We calculate log corrections to the entropy of three-dimensional black holes with "soft hairy" boundary conditions. Their thermodynamics possesses some special features that preclude a naive direct evaluation of these corrections, so we follow two different approaches. The first one exploits that the BTZ black hole belongs to the spectrum of Brown-Henneaux as well as soft hairy boundary conditions, so that the respective log corrections are related through a suitable change of the thermodynamic ensemble. In the second approach the analogue of modular invariance is considered for dual theories …
We develop a unified framework for the construction of soft dressings at boundaries of spacetime, such as the null infinity of Minkowski spacetime and the horizon of a Schwarzschild black hole. The construction is based on an old proposal of Mandelstam for quantizing QED and considers matter fields dressed by Wilson lines. Along time-like paths, the Wilson lines puncturing the boundary are the analogs of flat space Faddeev-Kulish dressings. We focus on the Schwarzschild black hole where our framework provides a quantum-field-theoretical perspective of the Hawking-Perry-Strominger viewpoint tha…
We explore the spacetime structure near non-extremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. 2. The near horizon algebra of a set of boundary conditions, labeled by a parameter $s$, is given by the semi-direct sum of diffeomorphisms at the horizon with "spin-$s$ supertranslations". For $s=1$ we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. …
We study the near horizon geometry of both static and stationary extremal Oliva Tempo Troncoso (OTT) black holes. For each of these cases, a set of consistent asymptotic conditions is introduced. The canonical generator for the static configuration is shown to be regular. For the rotating OTT black hole, the asymptotic symmetry is described by the time reparametrization, the chiral Virasoro and centrally extended $u(1)$ Kac-Moody algebras.
Three-dimensional Einstein gravity with negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near horizon region of these black holes that lead to a surprisingly simple near horizon symmetry algebra consisting of two affine u(1) current algebras. The symmetry algebra is essentially equivalent to the Heisenberg algebra. The associated charges give a specific example of "soft hair" on the horizon, as defined by Hawking, Perry and Strominger. We show that soft hair does not contribute to the Bekenstein-…
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 …
We present a paradox for evaporating black holes, which is common in most schemes trying to avoid the firewall by decoupling early and late radiation. At the late stage of the black hole evaporation, the decoupling between early and late radiation can not be realized because the black hole has a very small coarse-grained entropy, then we are faced with the firewall again. We call the problem hair-loss paradox as a pun on losing black hole soft hair during the black hole evaporation and the situation that the information paradox has put so much pressure on researchers.
We consider large gauge transformations of gravity and electromagnetism in D=4 asymptotically flat spacetime. Already at the classical level, we identify a canonical transformation that decouples the soft variables from the hard dynamics. We find that only the soft dynamics is constrained by BMS or large U(1) charge conservation. Physically this corresponds to the fact that sufficiently long-wavelength photons or gravitons that are added to the in-state will simply pass through the interaction region; they scatter trivially in their own sector. This implies in particular that the large gauge s…
We propose a model with multiple qubits that reproduces the thermal properties of 4-dimensional (4-dim) Schwarzschild black holes (BHs) by simultaneously taking account of the emission of Hawking particles and the zero-energy soft hair evaporation at horizon. The results verify that the entanglement entropy between a qubit and other subsystems, including emitted radiation, is much larger than the BH entropy analogue of the qubit, as opposed to the Page curve prediction. Our result suggests that early Hawking radiation is entangled with soft hair, and that late Hawking radiation can be highly e…
We construct a new set of boundary conditions for higher spin gravity, inspired by a recent "soft Heisenberg hair"-proposal for General Relativity on three-dimensional Anti-de Sitter. The asymptotic symmetry algebra consists of a set of affine $\hat u(1)$ current algebras. Its associated canonical charges generate higher spin soft hair. We focus first on the spin-3 case and then extend some of our main results to spin-$N$, many of which resemble the spin-2 results: the generators of the asymptotic $W_3$ algebra naturally emerge from composite operators of the $\hat u(1)$ charges through a twis…
We provide the first explicit proposal for all microstates of generic black holes in three dimensions (of Banados-Teitelboim-Zanelli-type): black hole microstates, termed "horizon fluffs", are a particular class of near horizon soft hairs which have zero energy as measured by the horizon observer and cannot be distinguished by observers at finite distance from the horizon. These states are arranged in orbits of the two-dimensional conformal algebra associated with the asymptotic black hole geometry. We count these microstates using the Hardy-Ramanujan formula for the number of partitions of a …
General covariance is the cornerstone of Einstein's General Relativity (GR) and implies that any two metrics related by diffeomorphisms are physically equivalent. There are, however, many examples pointing to the fact that this strict statement of general covariance needs refinement. There are a very special (measure-zero) subset of diffeomorphisms, the residual diffeomrphisms, to which one can associate well-defined conserved charges. This would hence render these diffeomorphic geometries physically distinct. We discuss that these symmetries may be appropriately called "symplectic symmetries"…
We demonstrate within the quantum field theoretical framework that an asymptotic particle falling into the black hole implants soft graviton hair on the horizon, conforming with the classical proposal of Hawking, Perry and Strominger. A key ingredient to this result is the construction of gravitational Wilson line dressings of an infalling scalar field, carrying a definite horizon supertranslation charge. It is shown that a typical Schwarzschild state is degenerate, and can be labeled by different soft supertranslation hairs parametrized for radial trajectories by the mass and energy of the in…
Recent studies of asymptotic symmetries suggest, that a Hamiltonian phase space analysis in gravitational theories might be able to account for black hole microstates. In this context we explain, why the use of conventional Bondi fall-off conditions for the gravitational field is too restrictive in the presence of an event horizon. This implies an enhancement of physical degrees of freedom ($\mathcal{A}$-modes). They provide new gravitational hair and are responsible for black hole microstates. Using covariant phase space methods, for the example of a Schwarzschild black hole, we give a propos…
The Hawking-Perry-Strominger (HPS) work [1] states a new controversial idea about the black hole (BH) information paradox [2-5] where BHs maximally entropize and encode information in their event horizon area [6,7], with no "hair" were thought to reveal information outside but angular momentum, mass and electric charge only [8,9] in a unique quantum gravity (QG) vacuum state. This new idea invokes new conservation laws involving gravitation and electromagnetism [10,11], to generate different QG vacua and preserve more information in hair implants. In the context of black holes and the HPS prop…
One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the b…
Motivated by the lack of a general parametrization for exotic compact objects, we construct a class of perturbative solutions valid for small (but otherwise generic) multipolar deviations from a Schwarzschild metric in general relativity. We introduce two classes of exotic compact objects, with "soft" and "hard" hair, for which the curvature at the surface is respectively comparable to or much larger than that at the corresponding black-hole horizon. We extend the Hartle-Thorne formalism to relax the assumption of equatorial symmetry and to include deformations induced by multipole moments hig…
We show that the existence of black holes with classical skyrmion hair invalidates standard proofs that global charges, such as the baryon number, cannot be conserved by a black hole. By carefully analyzing the standard arguments based on a Gedankenexperiment in which a black hole is seemingly-unable to return the baryon number that it swallowed, we identify inconsistencies in this reasoning, which does not take into the account neither the existence of skyrmion black holes nor the baryon/skyrmion correspondence. We then perform a refined Gedankenexperiment by incorporating the new knowledge a…
In [1] the horizon fluffs proposal is put forward to identify microstates of generic non-extremal three-dimensional Banados-Teitelboim-Zanelli (BTZ) black holes. The proposal is that black hole microstates, which were dubbed as horizon fluffs, are states labelled by the conserved charges associated with non-trivial diffeomorphisms on the near horizon geometry and these states are not in the coadjoint orbits of the asymptotic Virasoro algebra at the Brown-Henneaux central charge, associated with the BTZ black holes. It is also known that AdS3 Einstein gravity has more general black hole solutio…
We revisit Carlip's approach to entropy counting. This analysis reemerged in a recently obtained Schwarzschild/CFT-correspondence as Sugawara-construction of a 2D stress-tensor. Here, for the example of a Schwarzschild black hole, we show how to single out diffeomorphisms forming in contrast to Carlip's analysis the full 2D local conformal algebra. We provide arguments, why their Hamiltonian generators are expected to be the symmetry generators of a possible conformal field theory describing the part of phase space responsible for black hole microstates. Then, we can infer central charges and …
We study the existence and nature of Aretakis "hair" and its potentially observable imprint at a finite distance from the horizon (Ori-coefficient) in near-extremal black hole backgrounds. Specifically, we consider the time evolution of horizon penetrating scalar and gravitational perturbations with compact support on near-extremal Reissner-Nordstrom (NERN) and Kerr (NEK). We do this by numerically solving the Teukolsky equation and determining the Aretakis charge values on the horizon and at a finite distance from the black hole. We demonstrate that these values are no longer strictly conserv…
The gravitational Gauss law requires any addition of energy to be accompanied by the addition of gravitational flux. The possible configurations of this flux for a given source may be called gravitational hair, and several recent works discuss gravitational observables (`gravitational Wilson lines') which create this hair in highly-collimated `combed' configurations. We construct and analyze time-symmetric classical solutions of 2+1 Einstein-Hilbert gravity such as might be created by smeared versions of such operators. We focus on the AdS$_3$ case, where this hair is characterized by the prof…
We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; information that is analogous to the mass and angular momentum of asymptotically flat spacetimes and that characterizes how an AFdS spacetime approaches its asymptotic form. We define new 'cosmological tension' charges associated with future asymptotic spatial translation symmetries, which are analytic continuations of the ADM mass and tensions of asymptotically planar AdS spacetimes, and which measure the leading anisotropic corrections to the isotropic, exponential deSitter expansion rate. A cosmologic…
The Rindler horizon in Minkowski spacetime can be implanted with supertranslation hair by a matter shock wave without planar symmetry, and the hair is observable as a supertranslation memory on the Rindler family of uniformly linearly accelerated observers. We show that this classical memory is accompanied by a supertranslation quantum memory that modulates the entanglement between the opposing Rindler wedges in quantum field theory. A corresponding phenomenon across a black hole horizon may play a role in Hawking, Perry and Strominger's proposal for supertranslations to provide a solution to …
Perturbations of black holes with primary hair: time evolutions, quasinormal modes and greybody factors
CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学技术学院物理系CENTRA）
An old result ({\tt astro-ph/9905303}) by Jacobson implies that a black hole with Schwarzschild radius $r_s$ acquires scalar hair, $Q \propto r_s^2 μ$, when the (canonically normalized) scalar field in question is slowly time-dependent far from the black hole, $\partial_t ϕ\simeq μM_p$ with $μr_s \ll 1$ time-independent. Such a time dependence could arise in scalar-tensor theories either from cosmological evolution, or due to the slow motion of the black hole within an asymptotic spatial gradient in the scalar field. Most remarkably, the amount of scalar hair so induced is independent of the s…
We show that large gauge transformations in asymptotically flat spacetime can be implemented by sandwiching a shell containing the ingoing hard particles between two finite-width shells of soft gauge excitations. Integration of the graviton Dirac bracket implies that our observable soft degrees of freedom obey the algebra imposed by Strominger on unobservable boundary degrees of freedom. Thus, we provide both a derivation and an observable realization of this algebra. The conservation laws associated with asymptotic symmetries are seen to arise physically from free propagation of infrared mode…
The gravitational shock waves have provided crucial insights into entanglement structures of black holes in the AdS/CFT correspondence. Recent progress on the soft hair physics suggests that these developments from holography may also be applicable to geometries beyond negatively curved spacetime. In this work, we derive a remarkably simple thermodynamic relation which relates the gravitational shock wave to a microscopic area deformation. Our treatment is based on the covariant phase space formalism and is applicable to any Killing horizon in generic static spacetime which is governed by arbi…
Conformal invariance is spontaneously broken in many physical systems leading to the appearance of a single massless Goldstone mode in the spectrum, the dilaton. The dilaton soft limit is shown to generically encode the action of both the dilatation and the special conformal transformation on observables. For massive on-shell legs these take the form of sub-leading soft theorems. At loop level, we show how anomalous dimensions for coupling constants and fields can be included. We illustrate the general analysis with a variety of formal and phenomenological applications.
In gauge theories and gravity, field variables are generally not gauge-invariant observables, but such observables may be constructed by "dressing" these or more general operators. Dressed operators create particles, together with their gauge or gravitational fields which typically extend to infinity. This raises an important question of how well quantum information can be localized; one version of this is the question of whether soft charges fully characterize a given localized charge or matter distribution. This paper finds expressions for the non-trivial soft charges of such dressed operato…
It is shown that a tensor-to-scalar ratio close to r = 0.03, which can be observed by Planck, is realized in supersymmetric hybrid inflation models with TeV-scale soft supersymmetry breaking terms. This extends our previous analysis, which also found r <~ 0.03 but employed intermediate scale soft terms. Other cosmological observables such as the scalar spectral index are in good agreement with the WMAP data.
Neutron stars and quark stars are ideal laboratories to study fundamental physics at supra nuclear densities and strong gravitational fields. Astrophysical observables, however, depend strongly on the star's internal structure, which is currently unknown due to uncertainties in the equation of state. Universal relations, however, exist among certain stellar observables that do not depend sensitively on the star's internal structure. One such set of relations is between the star's moment of inertia ($I$), its tidal Love number (Love) and its quadrupole moment ($Q$), the so-called I-Love-Q relat…
