Massless Gravity Research Articles

Infrared finite scattering theory: scattering states and representations of the BMS group

Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an “out” state with memory which gives rise to infrared divergences in the standard S-matrix. To obtain an infrared-finite scattering theory, one must suitably include states with memory. However, except in the case of QED with massive charged particles, asymptotic states with memory that have finite energy and angular momentum have not been constructed for more general theories (e.g. massless QED, Yang-Mills and quantum gravity). To this end, we construct direct-integral representations over the “Lorentz orbit” of a given memory and classify all “orbit space representations” that have well-defined energy and angular momentum. We thereby provide an explicit construction of a large supply of physical states with memory as well as the explicit action of the BMS charges all states. The construction of such states is a key step toward the formulation of an infrared-finite scattering theory. While we primarily focus on the quantum gravitational case, we outline how the methods presented in this paper can be applied to obtain representations of the Poincaré group with memory for more general quantum field theories.

Subregion independence in gravity

In gravity, spacelike separated regions can be dependent on each other due to the constraint equations. In this paper, we give a natural definition of subsystem independence and gravitational dressing of perturbations in classical gravity. We find that extremal surfaces, non-perturbative lumps of matter, and generic trapped surfaces are structures that enable dressing and subregion independence. This leads to a simple intuitive picture for why extremal surfaces tend to separate independent subsystems. The underlying reason is that localized perturbations on one side of an extremal surface contribute negatively to the mass on the other side, making the gravitational constraints behave as if there exist both negative and positive charges. Our results support the consistency of islands in massless gravity, shed light on the Python’s lunch, and provide hints on the nature of the split property in perturbatively quantized general relativity. We also prove a theorem bounding the area of certain surfaces in spherically symmetric asymptotically de Sitter spacetimes from above and below in terms of the horizon areas of de Sitter and Nariai. This theorem implies that it is impossible to deform a single static patch without also deforming the opposite patch, provided we assume spherical symmetry and an energy condition.

Constraining the graviton mass with the NANOGrav 15 year data set

The recently detected stochastic signal by several pulsar timing array collaborations, offers an opportunity to scrutinize the fundamental properties of gravity, including the potential mass of the graviton. In this study, we analyze the North American Nanohertz Observatory for Gravitational Waves 15 year data set to search for a stochastic gravitational wave background with modified Hellings–Downs correlations predicted by massive gravity. While the Bayesian analysis comparing the massive gravity to massless gravity within the effective searchable mass range of mg∈[3×10−25,8×10−24]eVc−2 does not yield an explicit upper bound as all the Bayes factors are smaller than 3, the combined consideration of the minimum frequency inherent in a massive gravity and the observed spectrum leads to an upper limit of mg<8.2×10−24eVc−2 .

Entanglement island versus massless gravity

Entanglement islands play an essential role in the recent breakthrough in addressing the black hole information paradox. Inspired by double holography, it is conjectured that the entanglement islands can exist only in massive gravity. There are many pieces of evidence but also debates for this conjecture. This paper recovers the massless entanglement island in wedge holography with negative DGP gravity on the brane. However, the spectrum of negative DGP gravity includes a massive ghost, implying the model is unstable. Our work supports the view that there is no entanglement island in a well-defined braneworld model of massless gravity if one divides the radiation and black hole regions by minimizing entanglement entropy. However, such a partition results in a zero radiation region containing no information. Whether there are other physical non-trivial partitions of the radiation region is an open question and deserves further study.

Massive ambitwistor-strings; twistorial models

Ambitwistor-strings are chiral strings whose targets are spaces of complex massless particles, and whose correlation functions directly lead to simple, compact formulae for scattering amplitudes and loop integrands for massless gauge and gravity theories. This article extends the framework to massive particles in 4d, obtained via a symmetry reduction of higher dimensional massless models based on twistors. The target space of the resulting models turns out to be the phase space of 4d massive particles in a twistorial representation, and the worldsheet theory agrees with the two-twistor string previously introduced by the authors. The paper has been written so as to be largely self-contained. We discuss two interesting classes of massive theories in detail. For gauge theories, the reduction procedure is explicitly adapted to supersymmetric gauge theories on the Coulomb branch. For supergravity theories, the reduction is adapted to give theories obtained via Cremmer, Scherk & Schwartz (CSS) reduction, with broken supersymmetry and massive multiplets. The reduction procedure gives explicit and systematic rules to obtain amplitudes for all these theories and their amplitudes from two compact master formulae that have their origins in 6d based on the polarized scattering equations; in the CSS case the formulae are new, and in both cases their derivation is systematic. The freedom to include mass allows the definition of a loop insertion operator, thereby extending the formulae to 1-loop. Unlike the massless 4d twistorial models, these all display a perfect double copy structure, here incorporating massive particles in the relationship between gauge theory and CSS supergravity amplitudes.

Boson stars in massless and massive scalar-tensor gravity

Boson stars in massless and massive scalar-tensor gravity

Page curves on codim-m and charged branes

This paper investigates Page curves on the branes with higher codimensions and charges. We study two kinds of doubly holographic modes, the AdS/dCFT and cone holography. In AdS/dCFT, the gravitations on the brane are massive, and the black hole on the codim-m brane is coupled with the non-gravitational bath on the AdS boundary. Following the standard approach, we derive the Page curve for eternal black holes. On the other hand, cone holography includes massless graviton on the brane, and the bath becomes gravitating. By adding suitable DGP gravity on the end-of-the-world brane, we recover non-trivial entanglement islands and Page curves, which strongly support that the island is consistent with massless gravity. Finally, we analyze the effects of charges and find that, as the charges increase, the Page time increases, and the parameter space for non-trivial Page curves widens.

Holography of information in massive gravity using Dirac brackets

The principle of holography of information states that in massless gravity, it is possible to extract bulk information using asymptotic boundary operators. In our work, we study this principle in a linearized setting about empty flat space and formulate it using Dirac brackets between boundary Hamiltonian and bulk operators. We then address whether the storage of bulk information in flat space linearized massive gravity resembles that of massless gravity. For linearized massless gravity, using Dirac brackets, we recover the necessary criteria for the holography of information. In contrast, we show that the Dirac bracket of the relevant boundary observable with bulk operators vanishes for massive gravity. We use this important distinction to outline the canonical Hilbert space. This leads to split states, and consequently, one cannot use asymptotic boundary observables to extract bulk information in massive gravity. We also argue the split property directly without an explicit reference to the Hilbert space. The result reflects that we can construct local bulk operators in massive gravity about the vacuum, which are obscured from boundary observables due to the lack of diffeomorphism invariance. Our analysis sheds some light on evaporating black holes in the context of the islands proposal.

Massless entanglement islands in cone holography

It is controversial whether entanglement islands can exist in massless gravity theories. Recently, it is found that the massless entanglement island appears in wedge holography with DGP gravity on the branes. In this paper, we generalize the discussions to the codim-n holography named cone holography. For simplicity, we focus on the case with a codim-2 E brane and a codim-1 Q brane. We discuss the effective action, mass spectrum and holographic entanglement entropy for cone holography with DGP terms. We verify that there is massless gravity on the branes, and recover non-trivial entanglement islands and Page curves. Besides, we work out the parameter space which allows entanglement islands and Page curves. Compared with wedge holography, there are several new features. First, one can not add DGP gravity on the codim-2 E brane. That is because the energy density has to be a constant on codim-2 branes for Einstein gravity in bulk. Second, the Hartman- Maldacena surface ends only on the codim-1 Q brane. Third, the Hartman-Maldacena surface can be defined only in a finite time. We notice that this unusual situation also appears in AdS/dCFT and even in AdS/CFT. Fortunately, it does not affect the Page curve since it happens after Page time. Our results provide more support that the entanglement island is consistent with massless gravity theories.

Entanglement island and Page curve in wedge holography

Entanglement islands play an essential role in the recent breakthrough in resolving the black hole information paradox. However, whether entanglement islands can exist in massless gravity theories is controversial. It is found that entanglement islands disappear in the initial model of wedge holography with massless gravity on the brane. As a result, the entanglement entropy of Hawking radiation becomes a time-independent constant, and there is no Page curve. In this paper, we recover massless entanglement islands in wedge holography with suitable DGP gravity or higher derivative gravity on the branes. We study two typical cases. In the first case, we consider a black hole on the strong-gravity brane and a bath on the weak-gravity brane. It is similar to the usual double holography with non-gravitational baths. In the second case, we discuss two black holes on the two branes with the same gravitational strength. We recover massless entanglement islands and non-trivial Page curves in both cases. We also argue that the entanglement island is consistent with massless gravity. Our results strongly support that entanglement islands can exist in long-range theories of gravity.

Novel features of Schwarzschild-like black hole of Lorentz violating bumblebee gravity

A possible avenue for observing quantum gravity (QG) effects at low energy scales is to introduce spontaneous Lorentz violation (LV) in new models of gravity theories. One such model in the literature is bumblebee gravity yielding Schwarzschild-like black hole and weak field Solar System observations involve LV corrections characterized by the parameter ℓ. Here we first show that these LV corrections have a novel genesis in the conical angle Δ = πb subtended at the origin of the spacetime of massless bumblebee gravity. Exploiting the resultant asymptotic light deflection angle πb −1 as a new input in the exact deflection formula, we next study the strong field lensing properties of the Schwarzschild-like black hole exploring how they differ from those of the Schwarzschild black hole of general relativity. It is shown that the angular image separation and ratio of fluxes could respectively be s ∼ e πℓ and r ∼ e−πℓ times those of the Schwarzschild black hole (ℓ = 0). However, the shadow of the Schwarzschild-like black hole is independent of ℓ suggesting that observations of shadow radii cannot reveal QG effects. Finally, we raise an interesting issue about the measurability of the LV corrections caused by strong field lensing. An appendix briefly outlines lensing by the spinning bumblebee black hole.

Effective action, spectrum and first law of wedge holography

In this paper, we study the effective action, the mass spectrum and the first law of entanglement entropy for a novel doubly holographic model called wedge holography. We work out the effective action of quantum gravity on the branes. In the perturbative formulation, it is given by an infinite sum of Pauli-Fierz actions. In the non-perturbative formulation, the effective action is composed of a higher derivative gravity and a matter action. Usually, a higher derivative gravity can be renormalizable but suffers the ghost problem. For our case, since the effective theory on the brane is equivalent to Einstein gravity in the bulk, it must be ghost-free. We notice that the matter action plays an important role in eliminating the ghost. We also provide evidences that the higher derivative gravity on the brane is equivalent to a ghost-free multi-gravity. Besides, we prove that the effective action yields the correct Weyl anomaly. Interestingly, although the effective action on the brane is an infinite tower of higher derivative gravity, the holographic Weyl anomaly is exactly the same as that of Einstein gravity. We also analyze the mass spectrum of wedge holography. Remarkably, there is always a massless mode of gravitons on the end-of-the-world branes in wedge holography. This happens because one imposes Neumann boundary condition on both branes. On the other hand, the massless mode disappears if one imposes Dirichlet boundary condition on one of the branes as in brane world theory and AdS/BCFT. Finally, we verify the first law of entanglement entropy for wedge holography. Interestingly, the massive fluctuations are irrelevant to the first order perturbation of the holographic entanglement entropy. Thus, in many aspects, the effective theory on the brane behaves like massless Einstein gravity.

Inconsistency of islands in theories with long-range gravity

In ordinary gravitational theories, any local bulk operator in an entanglement wedge is accompanied by a long-range gravitational dressing that extends to the asymptotic part of the wedge. Islands are the only known examples of entanglement wedges that are disconnected from the asymptotic region of spacetime. In this paper, we show that the lack of an asymptotic region in islands creates a potential puzzle that involves the gravitational Gauss law, independently of whether or not there is a non-gravitational bath. In a theory with long-range gravity, the energy of an excitation localized to the island can be detected from outside the island, in contradiction with the principle that operators in an entanglement wedge should commute with operators from its complement. In several known examples, we show that this tension is resolved because islands appear in conjunction with a massive graviton. We also derive some additional consistency conditions that must be obeyed by islands in decoupled systems. Our arguments suggest that islands might not constitute consistent entanglement wedges in standard theories of massless gravity where the Gauss law applies.

Zwanziger\u2019s pairwise little group on the celestial sphere

We generalize Zwanziger’s pairwise little group to include a boost subgroup. We do so by working in the celestial sphere representation of scattering amplitudes. We propose that due to late time soft photon and graviton exchanges, matter particles in the asymptotic states in massless QED and gravity transform under the Poincaré group with an additional pair of pairwise celestial representations for each pair of matter particles. We demonstrate that the massless abelian and gravitational exponentiation theorems are consistent with the proposed pairwise Poincaré transformation properties. For massless QED we demonstrate that our results are consistent with the effects of the Faddeev-Kulish dressing and the abelian exponentiation theorem for celestial amplitudes found in arXiv:2012.04208. We discuss electric and magnetic charges simultaneously as it is especially natural to do so in this formalism.

Hidden relations of central charges and OPEs in holographic CFT

It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation c = 1/3ℓeff∂a/∂ℓeff and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.

Partially massless theory as a quantum gravity candidate

We study partially massless gravity theory (PM gravity theory) and suggest an alternative way to add higher order interaction vertices to the theory. Rather than introducing self-interaction vertices of the gravitational fields to the partially massless gravity action, we consider interactions with matter fields, since it is well known that addition of the self-interaction terms necessarily breaks the [Formula: see text] gauge symmetry that PM gravity theory enjoys. For the coupling with matter fields, we consider two different types of interaction vertices. The first one is given by an interaction Lagrangian density, [Formula: see text], where [Formula: see text] is the PM gravity field and [Formula: see text] is the stress-energy tensor of the matter fields. To retain the [Formula: see text] gauge symmetry, the matter fields also transform accordingly and it turns out that the transform must be nonlocal in this case. The second type of interaction is obtained by employing a gauge covariant derivative with the PM gravity field, where the PM gravity fields play a role of a gauge connection canceling the phase shift of the matter fields. We also study the actions and the equations of motion of the partially massless gravity fields. As expected, it shows 4 unitary degrees of freedom — 2 of them are traceless tensor modes and they are light-like fields and the other 2 are transverse vector modes and their dispersion relation changes as background space–time (de Sitter) evolutes. In the very early time, they are light-like but in the very late time, their velocities become a half of speed of light. The vector mode dispersion relation shows momentum-dependent behavior. In fact, the higher (lower) frequency modes show the faster (slower) velocity. We call this effect “conformal (or de Sitter) prism”. We suggest their quantization, compute Hamiltonians to present their exited quanta and construct their free propagators.

No-go theorems on localization of gravity around higher codimensional branes in noncompact extra dimensions

We study the brane world scenario of a single brane (or a single stack of branes) with codimension higher than one. When the extra dimensions are not small, localization of gravity around the brane is needed in order to reproduce the observable four-dimensional gravity. We focus on the case of noncompact extra dimensions, where the possibility of localized gravity becomes non-trivial. We show that in large class of gravity models, localization of massless gravity is not possible for codimension-2 branes with at least one noncompact extra dimension. With additional mild assumptions on field backgrounds, we also show that it is not possible for higher codimensional branes with two or more noncompact extra dimensions.

Tidal effects in Schwarzschild black hole in holographic massive gravity

We investigate tidal effects produced in the spacetime of Schwarzschild black hole in holographic massive gravity, which has two additional mass parameters due to massive gravitons. As a result, we have obtained that massive gravitons affect the angular component of the tidal force, while the radial component has the same form with the one in massless gravity. On the other hand, by solving the geodesic deviation equations, we have found that radial components of two nearby geodesics keep tightening while falling into the black hole and after passing the event horizons get abruptly infinitely stretched due to massive gravitons. However, angular components of two nearby geodesics get stretched firstly, reach a peak and then get compressed while falling into the black hole. Moreover, we have also shown that the angular components are more easily deformed near the departure position as the mass of a black hole is smaller for a fixed graviton mass.

Massive islands

We comment on the role of the graviton mass in recent calculations of the Page curve using holographic ideas. All reliable calculations of the Page curve in more than 2+1 spacetime dimensions have been performed in systems with massive gravitons. A crucial ingredient in these calculations is the formation of islands, regions that contribute to the entropy of degrees of freedom located elsewhere. While most often simply ignored, it is indeed true that mass of the graviton does not appear to significantly affect the calculations that appeared in the literature. We use the freedom to change the graviton mass to give an extremely simple model of analytically tractable island formation in general dimensions. We do however note that if one attempts to take the limit of zero graviton mass, any contribution from the islands disappears. This raises the question to what extent entanglement islands can play a role in standard massless gravity.

New massless and massive infinite derivative gravity in three dimensions

In this paper we will consider the most general quadratic curvature action with infinitely many covariant derivatives of massless gravity in three spacetime dimensions. The action is parity invariant and torsion-free and contains the same off-shell degrees of freedom as the Einstein-Hilbert action in general relativity. In the ultraviolet, with an appropriate choice of the propagator given by the exponential of an entire function, the point-like curvature singularity can be smoothened to a Gaussian distribution, while in the infrared the theory reduces to general relativity. We will also show how to embed new massive gravity in ghost-free infinite derivative gravity in Minkowski background as one of the infrared limits. Finally, we will provide the tree-level unitarity conditions for infinite derivative gravity in presence of a cosmological constant in deSitter and Anti-deSitter spacetimes in three dimensions by perturbing the geometries.