arXiv subjects

Ted Jacobson

Publications and source records attributed to Ted Jacobson.

At least 37 records · Page 2Linked to original sources

arXiv2021

Scrambling and the black hole atmosphere

We argue that the scrambling time is the same, up to a numerical factor in three or more spacetime dimensions, as the time for the atmosphere to fall across the horizon or escape, to be replaced by new atmosphere. We propose that these times agree because the physical scrambling process is part and parcel of the atmosphere refreshment process. We provide some support for this relation also in two dimensions, but the atmosphere is not as localized, so the argument is less justified.

hep-th↗

arXiv2021

Area deficits and the Bel-Robinson tensor

The first law of causal diamonds relates the area deficit of a small ball relative to flat space to the matter energy density it contains. At second order in the Riemann normal coordinate expansion, this energy density should receive contributions from the gravitational field itself. In this work, we study the second-order area deficit of the ball in the absence of matter and analyze its relation to possible notions of gravitational energy. In the small ball limit, any proposed gravitational energy functional should evaluate to the Bel-Robinson energy density $W$ in vacuum spacetimes. A direct calculation of the area deficit reveals a result that is not simply proportional to $W$. We discuss how the deviation from $W$ is related to ambiguities in defining the shape of the ball in curved space, and provide several proposals for fixing these shape ambiguities.

gr-qc↗

arXiv2021

Particle on the sphere: group-theoretic quantization in the presence of a magnetic monopole

The problem of quantizing a particle on a 2-sphere has been treated by numerous approaches, including Isham's global method based on unitary representations of a symplectic symmetry group that acts transitively on the phase space. Here we reconsider this simple model using Isham's scheme, enriched by a magnetic flux through the sphere via a modification of the symplectic form. To maintain complete generality we construct the Hilbert space directly from the symmetry algebra, which is manifestly gauge-invariant, using ladder operators. In this way, we recover algebraically the complete classification of quantizations, and the corresponding energy spectra for the particle. The famous Dirac quantization condition for the monopole charge follows from the requirement that the classical and quantum Casimir invariants match. In an appendix we explain the relation between this approach and the more common one that assumes from the outset a Hilbert space of wave functions that are sections of a nontrivial line bundle over the sphere, and show how the Casimir invariants of the algebra determine the bundle topology.

quant-ph↗

arXiv2021

Phonon redshift and Hubble friction in an expanding BEC

We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot{\cal V}/{\cal V}$, where $\cal{V}$ is the volume of the background condensate. This behavior is analogous to the redshifting and "Hubble friction" for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.

cond-mat.quant-gas↗

arXiv2019

Gravitational Thermodynamics of Causal Diamonds in (A)dS

The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a "first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the "entanglement equilibrium" result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.

hep-th↗

arXiv2019

Spacetime Equilibrium at Negative Temperature and the Attraction of Gravity

We derive the Einstein equation from the condition that every small causal diamond is a variation of a flat empty diamond with the same free conformal energy, as would be expected for a near-equilibrium state. The attractiveness of gravity hinges on the negativity of the absolute temperature of these diamonds, a property we infer from the generalized entropy.

gr-qc↗

arXiv2019

Diffeomorphism invariance and the black hole information paradox

We argue that the resolution to the black hole information paradox lies in a proper accounting of the implications of diffeomorphism invariance for the Hilbert space and observables of quantum gravity. The setting of asymptotically Anti-de Sitter spacetime is adopted for most of the paper, but in the framework of canonical quantum gravity, without invoking AdS/CFT duality. We present Marolf's argument that boundary unitarity is a consequence of diffeomorphism invariance, and show that its failure to apply in the classical limit results from a lack of analyticity that has no quantum counterpart. We argue that boundary unitarity leads to a {\it boundary information paradox}, which generalizes the black hole information paradox and arises in virtually any scattering process. We propose a resolution that involves operators of the boundary algebra that redundantly encode information about physics in the bulk, and explain why such redundancy need not violate the algebraic no cloning theorem. We also argue that the infaller paradox, which has motivated the firewall hypothesis for black hole horizons, is ill-posed in quantum gravity, because it ignores essential aspects of the nature of the Hilbert space and observables in quantum gravity.

gr-qc↗

arXiv2019

Blandford-Znajek process in vacuo and its holographic dual

Blandford and Znajek discovered a process by which a spinning black hole can transfer rotational energy to a plasma, offering a mechanism for energy and jet emissions from quasars. Here we describe a version of this mechanism that operates with only vacuum electromagnetic fields outside the black hole. The setting, which is not astrophysically realistic, involves either a cylindrical black hole or one that lives in 2+1 spacetime dimensions, and the field is given in simple, closed form for a wide class of metrics. For asymptotically Anti-de Sitter black holes in 2+1 dimensions the holographic dual of this mechanism is the transfer of angular momentum and energy, via a resistive coupling, from a rotating thermal state containing an electric field to an external charge density rotating more slowly than the thermal state. In particular, the entropy increase of the thermal state due to Joule heating matches the Bekenstein-Hawking entropy increase of the black hole.

hep-th↗

arXiv2018

Entropy from Carnot to Bekenstein

The second half of this essay tells the story of the genesis and early development of the notion of black hole entropy, in the style of an after dinner talk (apart from a long technical footnote). The first half sketches the development of the concept of entropy, beginning with Carnot, passing via Thomson, Clausius, Boltzmann, Planck, von Neumann, and Shannon on the way to Bekenstein, and the essay ends with a retrospective on Lemaître. The central theme is the fault-tolerant way that profound insights have emerged from simple (yet subtle) thermodynamic reasoning.

physics.hist-ph↗

arXiv2018

Holographic Complexity and Volume

The previously proposed "Complexity=Volume" or CV-duality is probed and developed in several directions. We show that the apparent lack of universality for large and small black holes is removed if the volume is measured in units of the maximal time from the horizon to the "final slice" (times Planck area). This also works for spinning black holes. We make use of the conserved "volume current", associated with a foliation of spacetime by maximal volume surfaces, whose flux measures their volume. This flux picture suggests that there is a transfer of the complexity from the UV to the IR in holographic CFTs, which is reminiscent of thermalization behavior deduced using holography. It also naturally gives a second law for the complexity when applied at a black hole horizon. We further establish a result supporting the conjecture that a boundary foliation determines a bulk maximal foliation without gaps, establish a global inequality on maximal volumes that can be used to deduce the monotonicity of the complexification rate on a boost-invariant background, and probe CV duality in the settings of multiple quenches, spinning black holes, and Rindler-AdS.

hep-th↗

arXiv2017

Induced density correlations in a sonic black hole condensate

Analog black/white hole pairs, consisting of a region of supersonic flow, have been achieved in a recent experiment by J. Steinhauer using an elongated Bose-Einstein condensate. A growing standing density wave, and a checkerboard feature in the density-density correlation function, were observed in the supersonic region. We model the density-density correlation function, taking into account both quantum fluctuations and the shot-to-shot variation of atom number normally present in ultracold-atom experiments. We find that quantum fluctuations alone produce some, but not all, of the features of the correlation function, whereas atom-number fluctuation alone can produce all the observed features, and agreement is best when both are included. In both cases, the density-density correlation is not intrinsic to the fluctuations, but rather is induced by modulation of the standing wave caused by the fluctuations.

cond-mat.quant-gas↗

arXiv2017

Mechanism of stimulated Hawking radiation in a laboratory Bose-Einstein condensate

We model a sonic black hole analog in a quasi one-dimensional Bose-Einstein condensate, using a Gross-Pitaevskii equation matching the configuration of a recent experiment by Steinhauer [Nat. Phys. 10, 864 (2014)]. The model agrees well with important features of the experimental observations, demonstrating their hydrodynamic nature. We find that a zero-frequency bow wave is generated at the inner (white hole) horizon, which grows in proportion to the square of the background condensate density. The relative motion of the black and white hole horizons produces a Doppler shift of the bow wave at the black hole, where it stimulates the emission of monochromatic Hawking radiation. The mechanism is confirmed using temporal and spatial windowed Fourier spectra of the condensate. Mean field behavior similar to that in the experiment can thus be fully explained without the presence of self-amplifying Hawking radiation.

cond-mat.quant-gas↗

arXiv2017

Membrane paradigm for Einstein-Gauss-Bonnet gravity

We construct the membrane paradigm for black objects in Einstein-Gauss-Bonnet gravity in spacetime dimensions $ \ge 5$. As in the case of general relativity, the horizon can be modeled as a membrane endowed with fluidlike properties. We derive the stress tensor for this membrane fluid and study the perturbation around static backgrounds with constant curvature horizon cross section, for which the stress tensor can be regularized with the usual redshift factor, and expressed in the form of a Newtonian viscous fluid with pressure, shear viscosity and bulk viscosity. We evaluate the transport coefficients for black holes with constant curvature horizons and negative or zero cosmological constant. For the black brane geometry our result for the ratio of shear viscosity to entropy density agrees with that obtained previously in different frameworks.

gr-qc↗

arXiv2016

Spin on a 4D Feynman Checkerboard

We discretize the Weyl equation for a massless, spin-1/2 particle on a time-diagonal, hypercubic spacetime lattice with null faces. The amplitude for a step of right-handed chirality is proportional to the spin projection operator in the step direction, while for left-handed it is the orthogonal projector. Iteration yields a path integral for the retarded propagator, with matrix path amplitude proportional to the product of projection operators. This assigns the amplitude $i^{\pm T}\, {3}^{-B/2}\,2^{-N}$ to a path with $N$ steps, $B$ bends, and $T$ right-handed minus left-handed bends, where the sign corresponds to the chirality. Fermion doubling does not occur in this discrete scheme. A Dirac mass $m$ introduces the amplitude $iεm$ to flip chirality in any given time step $ε$, and a Majorana mass similarly introduces a charge conjugation amplitude.

quant-ph↗

arXiv2016

Entanglement Equilibrium and the Einstein Equation

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.

gr-qc↗

arXiv2015

Black hole entropy and Lorentz-diffeomorphism Noether charge

We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.

gr-qc↗

arXiv2015

Variations on an aethereal theme

We consider a class of Lorentz-violating theories of gravity involving a timelike unit vector field (the aether) coupled to a metric, two examples being Einstein-aether theory and Hořava gravity. The action always includes the Ricci scalar of the metric and the invariants quadratic in covariant derivatives of the aether, but the theories differ in how the aether is constructed from other fields, and whether those fields are varied in the action. Fields that are not varied define background structures breaking diffeomorphsim invariance, including threadings, folations, and clocks, which generally produce novel degrees of freedom arising from the violation of what would otherwise be initial value constraints. The principal aims of this paper are to survey the nature of the theories that arise, and to understand the consequences of breaking diffeomorphism invariance in this setting. In a companion paper [arXiv:1504.03305], we address some of the phenomenology of the "ponderable aether" case in which the presence of a background clock endows the aether with a variable internal energy density that behaves in some respects like dark matter.

gr-qc↗

arXiv2015

Nonaxisymmetric Poynting Jets

The relativistic plasma jets from a misaligned black hole-accretion disk system will not be axially symmetric. Here we analyze nonaxisymmetric, stationary, translation invariant jets in the force-free approximation where the field energy dominates the particle energy. We derive a stream equation for these configurations involving the flux function $ψ$ for the transverse magnetic field, the linear velocity $v(ψ)$ of field lines along the jet, and the longitudinal magnetic field $B_z(ψ)$. The equations can be completely solved when $|v|=1$, and when $|v|<1$ the problem can be reduced to the pure magnetic case $v=0$ by a "field line dependent boost". We also find a large class of nonaxisymmetric solutions with arbitrary dependence on the longitudinal retarded time. A subclass of these constitutes a novel type of jet that has vanishing electromagnetic pressure $\tfrac{1}{2}(B^2-E^2)$ and requires no external pressure for confinement. We prove that such self-confinement is impossible when $B^2>E^2$. Finally, we write down specific solutions approximating numerical results for the nonaxisymmetric jet produced by a spinning black hole in an external, misaligned magnetic field.

astro-ph.HE↗