arXiv subjects

Toby Wiseman

Publications and source records attributed to Toby Wiseman.

At least 19 recordsLinked to original sources

arXiv2026

Graviton propagation in ghost-free massive gravity

We consider the ghost-free dRGT massive gravity with two of its three possible mass terms. This theory has five gravitational degrees of freedom. On Minkowski spacetime these modes have helicity-2, -1 and -0 and propagate on the Minkowski lightcone in the high-frequency limit. However for a general background the degrees of freedom corresponding to the helicity-1 and -0 modes have characteristics different to that of the metric lightcone. Here we prove in all generality, that the two degrees of freedom corresponding to the helicity-2 mode always propagate on the metric lightcone for any background in the high-frequency limit, which has significant relevance for current and future observational tests of the theory.

hep-th↗

arXiv2025

Ill-posedness of the Cauchy problem for linearized gravity in a cavity with conformal boundary conditions

We consider Lorentzian General Relativity in a cavity with a timelike boundary, with conformal boundary conditions and also a generalization of these boundary conditions. We focus on the linearized gravitational dynamics about the static empty cavity whose boundary has spherical spatial geometry. It has been recently shown that there exist dynamical instabilities, whose angular dependence is given in terms of spherical harmonics $Y_{\ell m}$, and whose coefficient of exponential growth in time goes as $\sim \ell^{1/3}$. We use these modes to construct a sequence of solutions for which the initial data converge to zero as $\ell \rightarrow \infty$ but for which the solution itself does not converge to zero. This implies a lack of continuity of solutions on initial data, which shows that the initial value problem with these boundary conditions is not well-posed. This is in tension with recent mathematical work on well-posedness for such boundary conditions.

gr-qc↗

arXiv2024

Towards a uniqueness theorem for static black holes in Kaluza-Klein theory with small circle size

Kaluza-Klein theory, by which we mean vacuum gravity in 5-dimensions, with asymptotics that are a product of a circle with Minkowski spacetime, has a variety of different static black hole solutions; localized black holes and the homogeneous and inhomogeneous black strings. There is currently no uniqueness theorem for the solutions, and for fixed circle size multiple solutions with the same mass co-exist. Intuitively for small circle sizes we might expect the theory truncates to become 4-dimensional, and correspondingly the only black holes are the homogeneous black strings. Thus we conjecture that for fixed mass and sufficiently small circle size, the only black holes are homogeneous ones. Here we give evidence that this is indeed the case. Firstly we introduce a toy scalar field model with a potential that allows tachyonic behaviour. Putting this theory on a product of Minkowski with a circle gives an analogous set of static homogeneous and inhomogeneous solutions to that of the black holes. We prove that solutions must be homogeneous for small circle sizes, the analog of our conjecture for this toy model. A weaker statement that is straightforward to derive is a bound on how inhomogeneous a solution can be - putting this scalar theory in a large but finite cavity, a norm of the wavefunction of the Kaluza-Klein modes can be shown to vanish in the small circle limit. Turning to the full gravitational theory, we employ a metric ansatz that imposes static axisymmetry, encompasses the homogeneous and inhomogeneous black strings (but not the localized solutions) and allows us to measure inhomogeneity of a solution. Employing a finite cavity and imposing boundary conditions that are compatible with homogeneity we show a similar result; the norm of certain Kaluza-Klein modes is bounded by the circle size, providing evidence that our conjecture is true.

hep-th↗

arXiv2024

Well-posedness of minimal dRGT massive gravity

Ghost-free dRGT massive gravity is a subtle theory, even at the classical level. Its viability depends on Vainshtein screening, which is an intrinsically non-linear phenomenon, and thus understanding the full non-linear dynamics of the theory is crucial. The theory was not expected to have a well-posed hyperbolic formulation as it is usually interpreted as a low energy EFT, and hence its short distance physics would be modified by higher derivative operators. Here we study a new dynamical formulation of the theory for the case of the minimal mass term. This firstly involves using a harmonic formulation of the theory, and then writing it as a first order system. We are able to cast it in a form that is strongly hyperbolic about the Minkowski background. We discuss strong hyperbolicity for backgrounds close to the Minkowski solution, conjecturing that Cauchy evolution remains well-posed. Interestingly, as part of the analysis, we find that the characteristics of the spin two graviton mode are simply governed by the inverse metric on a general background.

hep-th↗

arXiv2024

Dynamics of dRGT ghost-free massive gravity in spherical symmetry

We focus on dRGT massive gravity in spherical symmetry in the limit of small graviton mass. Firstly we examine the minimal model. This does not exhibit a Vainshtein mechanism in spherical symmetry, but one may still ask what happens for spherical dynamics. We show that there are no regular time-dependent spherically symmetric solutions unless the matter has sufficiently large pressure. For matter that does not satisfy this, such as non-relativistic matter, any Cauchy slice of such a solution must necessarily have a point where the metric becomes singular. Only a weak assumption on the asymptotics is made. We then consider the next-to-minimal model. This has been argued to have a good Vainshtein mechanism in spherical symmetry, and hence be phenomenologically viable, provided the relative sign of the minimal and next-to-minimal mass terms is the same, and we restrict attention to this case. We find that regular behaviour requires the matter at the origin of symmetry to have positive pressure -- in particular a massive scalar field fails to satisfy this condition. Furthermore it restricts non-relativistic matter so that the pressure is bounded from below in terms of the density and graviton mass in a manner that is at odds with a reasonable phenomenology. This suggests that realistic phenomenology will either require a resolution of singularities, or will require dynamics beyond the non-generic setting of spherical symmetry.

hep-th↗

arXiv2024

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity

We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of these. Focussing on static Euclidean solutions, we derive a thermodynamic first law. Restricting to a spherical spatial boundary, the infillings are flat space or the Schwarzschild solution, and have similar thermodynamics to the Dirichlet case. We consider smooth Euclidean fluctuations about the flat space saddle; for $p > 1/6$ the spectrum of the Lichnerowicz operator is stable -- its eigenvalues have positive real part. Thus we may regard large $p$ as a regularization of the ill-posed Dirichlet boundary conditions. However for $p < 1/6$ there are unstable modes, even in the spherically symmetric and static sector. We then turn to Lorentzian signature. For $p < 1/6$ we may understand this spherical Euclidean instability as being paired with a Lorentzian instability associated with the dynamics of the boundary itself. However, a mystery emerges when we consider perturbations that break spherical symmetry. Here we find a plethora of dynamically unstable modes even for $p > 1/6$, contrasting starkly with the Euclidean stability we found. Thus we seemingly obtain a system with stable thermodynamics, but unstable dynamics, calling into question the standard assumption of smoothness that we have implemented when discussing the Euclidean theory.

hep-th↗

arXiv2023

Analog gravity and the continuum effective theory of the graphene tight binding lattice model

We consider the tight-binding model of graphene with slowly spatially varying hopping functions. We develop a low energy approximation as a derivative expansion in a Dirac spinor that is perturbative in the hopping function deformation. The leading description is the Dirac equation in flat 2+1-d spacetime with (strain-)gauge field. Prior work considered subleading corrections written as non-trivial frame and spin connection terms. We previously argued that such corrections cannot be considered consistently without taking all the terms at the same order of approximation, which due to the unconventional power counting originating from the large gauge field, involve also higher covariant derivative terms. Here we confirm this, explicitly computing subleading terms. To the order we explore, the theory is elegantly determined by the gauge field and frame, both given by the hopping functions, the torsion free spin connection of the frame, together with coefficients for the higher derivative terms derived from lattice invariants. For the first time we compute the metric that the Dirac field sees - the `electrometric' - to quadratic order in the deformation allowing us to describe the subleading corrections to the dispersion relation for inhomogeneous deformations originating from corrections to the frame. Focussing on in-plane inhomogeneous strain, we use a simple model to relate the hopping functions to the strain field, finding the electrometric becomes curved at this quadratic order. Thus this lattice model yields an effective analog gravity description as a curved space Dirac theory, with large magnetic field, and Lorentz violating higher covariant derivative terms. We check this by comparison to numerical diagonalization. From this we conjecture a form for the effective theory for monolayer graphene in terms of the strain tensor, consistent up to quadratic order in the deformation.

hep-th↗

arXiv2023

A dynamical formulation of ghost-free massive gravity

We present a formulation of ghost-free massive gravity with flat reference metric that exhibits the full non-linear constraint algebraically, in a way that can be directly implemented for numerical simulations. Motivated by the presence of higher order operators in the low-energy effective description of massive gravity, we show how the inclusion of higher-order gradient (dissipative) terms leads to a well-posed formulation of its dynamics. While the formulation is presented for a generic combination of the minimal and quadratic mass terms on any background, for concreteness, we then focus on the numerical evolution of the minimal model for spherically symmetric gravitational collapse of scalar field matter. This minimal model does not carry the relevant interactions to switch on an active Vainshtein mechanism, at least in spherical symmetry, thus we do not expect to recover usual GR behaviour even for small graviton mass. Nonetheless we may ask what the outcome of matter collapse is for this gravitational theory. Starting with small initial data far away from the centre, we follow the matter through a non-linear regime as it falls towards the origin. For sufficiently weak data the matter disperses. However for larger data we generally find that the classical evolution breaks down due to the theory becoming infinitely strongly coupled without the presence of an apparent horizon shielding this behaviour from an asymptotic observer.

hep-th↗

arXiv2022

Gradient flow of Einstein-Maxwell theory and Reissner-Nordstr\"om black holes

Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field. We argue that this flow is well-posed for static spacetimes with pure electric or magnetic potentialsand show it preserves both non-extremal and extremal black hole horizons. In the latter case we find the flow of the near horizon geometry decouples from that of the exterior. The Schwarzschild black hole is an unstable fixed point of Ricci flow for static spacetimes. Here we consider flows of the Reissner-Nordstr\"om (RN) fixed point. The magnetic RN solution becomes a stable fixed point of the flow for sufficient charge. However we find that the electric RN black hole is always unstable. Numerically solving the flow starting with a spherically symmetric perturbation of a non-extremal RN solution, we find similar behaviour in the electric case to the Ricci flows of perturbed Schwarzschild, namely the horizon shrinks to a singularity in finite time or expands forever. In the magnetic case, a perturbed unstable RN solution has a similar expanding behaviour, but a perturbation that decreases the horizon size flows to a stable black hole solution rather than a singularity. For extremal RN we solve the near horizon flow for spherical symmetry exactly, and see in the electric case two unstable directions which flow to singularities in finite flow time. However, even turning these off, and fixing the near horizon geometry to be that of RN, we numerically show that the flows appear to become singular in the vicinity of its horizon.

hep-th↗

arXiv2021

Curved-space Dirac description of elastically deformed monolayer graphene is generally incorrect

Undistorted monolayer graphene has energy bands which cross at protected Dirac points. It elastically deforms and much research has assumed the Dirac description persists, now in a curved space and coupled to a gauge field related to lattice strain. We show this is incorrect by using a real space gradient expansion to study how the Dirac equation derives from the tight binding model. Generic spatially varying hopping functions give rise to large magnetic fields which spoil the truncation in derivatives. In the perturbative regime, the only consistent truncation to Dirac is one with nontrivial gauge field but in flat space. One can instead fine tune the magnetic field to be small, and we derive the resulting differential condition that the hopping functions must satisfy to yield a consistent truncation to Dirac in curved space. We consider whether mechanical effects might impose this fine tuning, but find this is not the case for a simple elastic membrane model.

cond-mat.mes-hall↗

arXiv2021

Rotating black holes in Einstein-aether theory

We introduce new methods to numerically construct for the first time stationary axisymmetric black hole solutions in Einstein-aether theory and study their properties. The key technical challenge is to impose regularity at the spin-2, 1, and 0 wave mode horizons. Interestingly we find the metric horizon, and various wave mode horizons, are not Killing horizons, having null generators to which no linear combination of Killing vectors is tangent, and which spiral from pole to equator or vice versa. Existing phenomenological constraints result in two regions of coupling parameters where the theory is viable and some couplings are large; region I with a large twist coupling and region II with also a (somewhat) large expansion coupling. Currently these constraints do not include tests from strong field dynamics, such as observations of black holes and their mergers. Given the large aether coupling(s) one might expect such dynamics to deviate significantly from general relativity, and hence to further constrain the theory. Here we argue this is not the case, since for these parameter regions solutions exist where the aether is "painted" onto a metric background that is very close to that of general relativity. This painting for region I is approximately independent of the large twist coupling, and for region II is also approximately independent of the large expansion coupling and normal to a maximal foliation of the spacetime. We support this picture analytically for weak fields, and numerically for rotating black hole solutions, which closely approximate the Kerr metric.

gr-qc↗

arXiv2020

A Surprising Similarity Between Holographic CFTs and a Free Fermion in $(2+1)$ Dimensions

We compare the behavior of the vacuum free energy (i.e. the Casimir energy) of various $(2+1)$-dimensional CFTs on an ultrastatic spacetime as a function of the spatial geometry. The CFTs we consider are a free Dirac fermion, the conformally-coupled scalar, and a holographic CFT, and we take the spatial geometry to be an axisymmetric deformation of the round sphere. The free energies of the fermion and of the scalar are computed numerically using heat kernel methods; the free energy of the holographic CFT is computed numerically from a static, asymptotically AdS dual geometry using a novel approach we introduce here. We find that the free energy of the two free theories is qualitatively similar as a function of the sphere deformation, but we also find that the holographic CFT has a remarkable and mysterious quantitative similarity to the free fermion; this agreement is especially surprising given that the holographic CFT is strongly-coupled. Over the wide ranges of deformations for which we are able to perform the computations accurately, the scalar and fermion differ by up to 50% whereas the holographic CFT differs from the fermion by less than one percent.

hep-th↗

arXiv2020

Three-dimensional super-Yang--Mills theory on the lattice and dual black branes

In the large-$N$ and strong-coupling limit, maximally supersymmetric SU($N$) Yang--Mills theory in $(2 + 1)$ dimensions is conjectured to be dual to the decoupling limit of a stack of $N$ D$2$-branes, which may be described by IIA supergravity.We study this conjecture in the Euclidean setting using nonperturbative lattice gauge theory calculations.Our supersymmetric lattice construction naturally puts the theory on a skewed Euclidean 3-torus. Taking one cycle to have anti-periodic fermion boundary conditions, the large-torus limit is described by certain Euclidean black holes. We compute the bosonic action---the variation of the partition function---and compare our numerical results to the supergravity prediction as the size of the torus is changed, keeping its shape fixed. Our lattice calculations primarily utilize $N = 8$ with extrapolations to the continuum limit, and our results are consistent with the expected gravity behavior in the appropriate large-torus limit.

hep-th↗

arXiv2020

Does the Round Sphere Maximize the Free Energy of (2+1)-Dimensional QFTs?

We examine the renormalized free energy of the free Dirac fermion and the free scalar on a (2+1)-dimensional geometry $\mathbb{R} \times \Sigma$, with $\Sigma$ having spherical topology and prescribed area. Using heat kernel methods, we perturbatively compute this energy when $\Sigma$ is a small deformation of the round sphere, finding that at any temperature the round sphere is a local maximum. At low temperature the free energy difference is due to the Casimir effect. We then numerically compute this free energy for a class of large axisymmetric deformations, providing evidence that the round sphere globally maximizes it, and we show that the free energy difference relative to the round sphere is unbounded below as the geometry on $\Sigma$ becomes singular. Both our perturbative and numerical results in fact stem from the stronger finding that the difference between the heat kernels of the round sphere and a deformed sphere always appears to have definite sign. We investigate the relevance of our results to physical systems like monolayer graphene consisting of a membrane supporting relativistic QFT degrees of freedom.

hep-th↗

arXiv2019

A new energy upper bound for AdS black holes inspired by free field theory

We consider the toroidally compactified planar AdS-Schwarzschild solution to 4-dimensional gravity with negative cosmological constant. This has a flat torus conformal boundary metric. We show that if the spatial part of the boundary metric is deformed, keeping it static and the temperature and area fixed, then assuming a static bulk solution exists, its energy is less than that of the AdS-Schwarzschild solution. The proof is non-perturbative in the metric deformation. While we expect the same holds for the free energy for black hole solutions we are so far are not able to prove it. In the context of AdS-CFT this implies a 3-dimensional holographic CFT on a flat spatial torus whose bulk dual is AdS-Schwarzschild has a greater energy than if the spatial geometry is deformed in any way that preserves temperature and area. This work was inspired by previous results in free field theory, where scalars and fermions in 3-dimensions have been shown to energetically disfavour flat space.

hep-th↗

arXiv2018

Free energy dependence on spatial geometry for (2+1)-dimensional QFTs

We consider (2+1)-QFT at finite temperature on a product of time with a static spatial geometry. The suitably defined difference of thermal vacuum free energy for the QFT on a deformation of flat space from its value on flat space is a UV finite quantity, and for reasonable fall-off conditions on the deformation is IR finite too. For perturbations of flat space we show this free energy difference goes quadratically with perturbation amplitude and may be computed from the linear response of the stress tensor. As an illustration we compute it for a holographic CFT finding that at any temperature, and for any perturbation, the free energy decreases. Similar behaviour was previously found for free scalars and fermions, and for unitary CFTs at zero temperature, suggesting (2+1)-QFT may generally energetically favour a crumpled spatial geometry. We also treat the deformation in a hydrostatic small curvature expansion relative to the thermal scale. Then the free energy variation is determined by a curvature correction to the stress tensor and for these theories is negative for small curvature deformations of flat space.

hep-th↗

arXiv2018

What spatial geometry does the (2+1)-dimensional QFT vacuum prefer?

We consider relativistic (2+1)-QFTs on a product of time with a two-space and study the vacuum free energy as a functional of the temperature and spatial geometry. We focus on free scalar and Dirac fields on arbitrary perturbations of flat space, finding that the free energy difference from flat space is finite and always \textit{negative} to leading order in the perturbation. Thus free (2+1)-QFTs appear to always energetically favor a crumpled space on all scales; at zero temperature this is a purely quantum effect. Importantly, we show that this quantum effect is non-negligible for the relativistic Dirac degrees of freedom on monolayer graphene even at room temperature, so we argue that this vacuum energy effect should be included for a proper analysis of the equilibrium configuration of graphene or similar materials.

hep-th↗

arXiv2017

Testing the holographic principle using lattice simulations

The lattice studies of maximally supersymmetric Yang-Mills (MSYM) theory at strong coupling and large N is important for verifying gauge/gravity duality. Due to the progress made in the last decade, based on ideas from topological twisting and orbifolding, it is now possible to study these theories on the lattice while preserving an exact supersymmetry on the lattice. We present some results from the lattice studies of two-dimensional MSYM which is related to Type II supergravity. Our results agree with the thermodynamics of different black hole phases on the gravity side and the phase transition (Gregory--Laflamme) between them.

hep-lat↗