Gravity with a dynamical preferred frame

David Mattingly; Ted Jacobson

REVIEW

Gravity with a dynamical preferred frame

Ted Jacobson, David Mattingly

General Relativity and Quantum Cosmology · Submitted 14 Jul 2000 · 26 references

Pith's verdict: The founding analysis of the aether action is solid and worth citing, but its headline negative claim — that the aether 'generally' goes singular — is shown only for the Fab=0 subclass and generalized in the abstract and conclusion.

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arXiv IDgr-qc/0007031 (version 4)

Pith IDT6RKVHLC, Pith's permanent record of this paper and its review

CitationDavid Mattingly, Ted Jacobson. "Gravity with a dynamical preferred frame." arXiv:gr-qc/0007031 (2000). https://pith.science/paper/T6RKVHLC

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Editor's note

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Worth your time, and worth citing. This is the paper that takes the unit-timelike-vector action seriously as a gravitational theory and works out what it actually does. The action is not new — Dirac, Gasperini, and Kostelecky–Samuel all got there first, and the authors say so plainly in Section I rather than burying it. What is new is the gravitational analysis, and it is done well. The equivalence to a sector of Einstein–Maxwell-charged dust (Eqs. 3.10–3.16) is derived from the paper's own field equations and cross-checked from the normalization condition, not asserted. The linearized spectrum in Section V is careful about a real subtlety: the trace h does not satisfy a wave equation because of the lambda source, so the usual transverse-traceless gauge has to be modified. That is the kind of detail people get wrong. The static, spherically symmetric case split on lambda is also clean, including the extremal charge-to-mass caveat. No fitted parameters, no data, no circularity. The authors are candid about the pathology and about the cure being speculative — the classifier's 'no stated limitations' is wrong; abstract:s5 and Section VII both state it outright, so credit them for that rather than treating it as a discovery. The soft spot is the genericity claim. Section IV B proves the gradient singularity only for Fab=0, where the aether is the tangent to a hypersurface-orthogonal timelike geodesic congruence and such congruences typically cross. The body hedges correctly ('at least for such solutions'), but abstract:s5 and the discussion promote it to 'generally' and to 'unphysical as an effective theory.' Nothing covers Fab nonzero with lambda nonzero, where the flow lines obey the Lorentz force rather than free fall — and Section IV C's own remark that extremal charged dust can stay static is exactly the regime where the caustic argument might not carry over. A Raychaudhuri-type argument with the acceleration term included would settle it; the paper does not give one. That is a real gap in the negative conclusion, though it does not touch the dust equivalence or the mode count, which are the load-bearing positive results. Minor: the initial value formulation is inferred from the dust equivalence rather than proven, which is fine but worth saying. The terminology hand-wringing over 'spontaneous' in Section I could be a footnote. For anyone working on Lorentz violation, modified gravity, or preferred-frame cosmology, this is required background. Send it out.

Referee report

Significance

The paper's lasting value is the exact equivalence to a sector of Einstein-Maxwell-charged dust, established from the theory's own field equations with an explicit identification of the vector potential (Eq. 3.10) and a matching of the charge-to-mass ratio obtained independently from the Einstein equation, the Maxwell equation, and the unit-norm constraint (Eqs. 3.12–3.16). That is a genuinely useful calculational bridge: it delivers an initial value formulation for free and explains why the model contains all general relativity vacuum solutions. The linearized spectrum in §V is derived cleanly and the mode count is a concrete, checkable prediction. The paper is also candid about its own weak point, naming the gradient singularity and proposing the symmetrized-derivative cure rather than burying it. The observational discussion in §IV C, which reduces the deviation from Schwarzschild to a single 'aether charge' set by cosmological initial conditions, gives the model a falsifiable handle. This is a well-posed and carefully executed first foray, and it is appropriately framed as such.

Major objections (1)

[Abstract (abstract:s5); §IV B; §VII] The headline negative claim is stated more broadly than the derivation supports. Section IV B establishes the gradient singularity only within the F_ab = 0 subclass, where the aether is the unit tangent to a hypersurface-orthogonal timelike geodesic congruence and caustics are generic; the body correctly hedges with 'at least for such solutions, the evolution of ua is generally singular.' The abstract ('the aether generally develops gradient singularities') and §VII ('the aether vector generically develops gradient singularities ... the theory is unphysical as an effective theory') drop that restriction. For F_ab ≠ 0 and λ ≠ 0 the flow lines are charged-dust trajectories obeying the Lorentz-force equation (3.16), not free-falling geodesics, and the free-fall caustic argument does not automatically carry over; §IV C itself notes that for extremal charge-to-mass ratio the dust can remain static under competing gravitational and electric forces. No explicit F_ab ≠ 0 solution with a gradient singularity is exhibited, and no Raychaudhuri-type argument is given showing that the Lorentz-force acceleration term cannot keep the expansion finite. Since the paper's verdict on the model's viability rests on genericity rather than on the existence of one singular subclass, either an argument covering F_ab ≠ 0 should be supplied or the abstract and §VII should be restricted to the demonstrated class. The equivalence result and the linearized mode count are unaffected.

Minor objections (6)

[§VII, final paragraph] The parenthetical remark that the theory 'can be made to agree with observations with an appropriate choice of initial conditions, i.e. by setting Fab to zero' is compressed to the point of ambiguity. Setting F_ab = 0 removes the aether stress tensor from Eq. (3.7) and so decouples the metric evolution from the aether, but by §IV B it does not remove the aether's own gradient singularity. Please state explicitly that the agreement claimed is for the metric sector only.
[§IV C] The statement that for λ ≠ 0 there are no static solutions 'unless the coefficients in the action are such that the charge to mass ratio of the dust is extremal' leaves the exceptional case unanalyzed. Since the charge-to-mass ratio is fixed by b1 rather than by initial data, it would help to say whether the extremal value is attained for some b1 and, if so, whether the unit-norm gauge of Eq. (3.11) can be reached smoothly across the horizon in that case, given the horizon discussion two paragraphs later.
[§VI B, Eq. (6.8)] The index structure of the second and third terms of the energy-momentum tensor is difficult to parse as typeset, particularly the placement of the symmetrization on (a, b) and the contraction with u^m. Please state the symmetrization convention explicitly and confirm that the displayed expression is manifestly symmetric in a and b.
[§IV C, Eq. (4.6)] The gauge shift is written A_μ = A'_μ + α,_μ without specifying that α = βt + γ(r) is the form required to preserve staticity and spherical symmetry; making that explicit, and noting that the two signs in front of the radical correspond to the two time orientations mentioned in footnote 2, would make the construction easier to follow.
[References [2], [3], [4] and [22]] The name is spelled 'Nordtvedt' in the literature but appears as 'Nordvedt' in refs. [2], [3], and [4]; ref. [22] gives 'W.B. Bonner' where 'W.B. Bonnor' is intended. These should be corrected.
[§I and ref. [10]] The attribution of the theory's origin to unpublished work with J.C. Dell (ref. [10]) cannot be checked by the reader. This is not a problem for any result in the paper, but a one-line indication of what that unpublished work contained, or of where the overlap lies, would make the provenance statement more useful.

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The paper

The paper claims

A unit timelike vector field can break local Lorentz invariance while preserving general covariance, and the simplest such theory is exactly a sector of Einstein-Maxwell plus charged dust, though its own gradients diverge.

The reading

The paper asks whether one can give a preferred rest frame at every spacetime point without abandoning general covariance, which a fixed external frame would destroy. The authors' answer is to make the frame dynamical: a unit timelike vector field $u^a$, called the aether, whose norm is enforced by a Lagrange multiplier. They then study the smallest sensible action for it, Einstein-Hilbert plus the square of the antisymmetrized derivative $F_{ab}=2 abla_{[a}u_{b]}$, and show that the resulting equations are exactly those of Einstein-Maxwell theory coupled to a charged dust fluid whose charge-to-mass ratio is fixed by the aether couplings. That equivalence is the paper's engine: it hands the model an initial value formulation, a stock of exact solutions, and a physical picture of what the aether is doing. The sting is in the tail: in the solutions the authors can solve, the aether's integral curves cross and its gradients diverge, which they read as a breakdown of the effective theory rather than a flaw in the metric.

What carries the argument

The load-bearing object is the dictionary between the aether and a charged dust fluid. The unit-norm constraint $g_{ab}u^a u^b=1$ plays the role of a gauge condition fixing the vector potential to fixed norm, and simultaneously the role of the dust's Lorentz-force equation. Because the same charge-to-mass ratio appears in the Einstein equation, the Maxwell equation, and the dust equation of motion, any aether solution is a charged-dust solution. This is what lets the authors import known results — the initial value formulation, the Reissner-Nordström static solutions in a fixed-norm gauge, and the known fact that non-extremal charged dust cannot hold a static spherical configuration — and it is also what exposes the singularity, since dust world lines in a hypersurface-orthogonal congruence focus.

Extended reading notes

Core claim

The central claim is that the minimal aether action, built from the Ricci scalar $R$ and the square of the antisymmetrized derivative $F_{ab}=2 abla_{[a}u_{b]}$, with $g_{ab}u^a u^b=1$ enforced by a multiplier $ abla$, is equivalent in the absence of matter to a sector of the Einstein-Maxwell-charged dust system. The identification is explicit: the aether is proportional to the vector potential, the field strength $F_{ab}$ becomes the Maxwell field strength, the multiplier becomes twice the dust energy density, and the unit-norm constraint becomes the dust equation of motion with the same charge-to-mass ratio that appears in the Einstein and Maxwell equations. From this the authors draw three corollaries: the equations admit an initial value formulation; every vacuum solution of general relativity is a solution of the model, obtained by taking $F_{ab}=0$ and letting $u^a$ be the tangent field of any hypersurface-orthogonal congruence of timelike geodesics; and the linearized spectrum around flat space contains two massless transverse modes of the metric perturbation and two massless transverse modes of the aether. The negative result is that such geodesic congruences generically cross, so gradients of $u^a$ diverge even where the metric is perfectly regular, which the authors take as a sign that this truncated effective theory is not viable on its own and may need the symmetrized derivative added to the action.

Load-bearing premise

The claim that the aether generally develops gradient singularities is demonstrated only for the special case where the field strength vanishes, and the step to the full solution space is an extrapolation rather than a proof.

Editorial extensions

If this is right

Every vacuum solution of general relativity, including Schwarzschild and Kerr, is a solution of the model, with the aether supplied by the tangent field of a hypersurface-orthogonal timelike geodesic congruence.
The linearized theory around flat space carries four massless modes: two transverse traceless metric modes and two transverse aether modes, plus a time-independent longitudinal sector fixed by an arbitrary $h_{00}$.
Static spherical solutions are the Reissner-Nordström family with an extra aether charge set by initial conditions, so agreement with observation constrains how much aether charge collapsed into a given object.
Homogeneous isotropic cosmology is untouched in the minimal model, because a symmetry-sharing aether has $F_{ab}=0$ and drops out of the field equations entirely.
Couplings to matter of dimension four or less reduce to renormalizable kinetic-term modifications for fermions, gauge bosons, and the Higgs, each shifting that field's propagation speed relative to the aether frame.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The equivalence runs one way only: the aether sector is a proper subset of charged-dust solutions, so any charged-dust configuration whose dust velocity cannot be aligned with the vector potential is automatically excluded from the aether theory.
If the crossing of geodesics is the real failure mode, the natural repair is not to add terms but to ask whether the singular set is a measure-zero caustic that a UV completion could resolve; a count of how generic the caustics are in the full $F_{ab}$ nonzero solution space would settle it.
Because the aether charge is inherited from cosmological initial conditions and is conserved along flow lines, the model predicts a fixed, non-decaying charge-to-mass ratio for collapsed objects, which would show up as a tiny deviation from Schwarzschild far from a black hole.
Adding the symmetrized derivative makes the action sensitive to gradients in a way the antisymmetric-only action is not, which suggests the repaired theory would behave like an elastic medium with a stiffness set by the new couplings rather than like pressureless dust.

Original abstract

We study a generally covariant model in which local Lorentz invariance is broken "spontaneously" by a dynamical unit timelike vector field $u^a$---the "aether". Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as ``variable speed of light" or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative $\nabla_{[a}u_{b]}$. Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system. The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether generally develops gradient singularities which signal a breakdown of this effective theory. Including the symmetrized derivative in the action for the aether field may cure this problem.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,612 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.32 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We study a generally covariant model in which local Lorentz invariance is broken "spontaneously" by a dynamical unit timelike vector field $u^a$---the "aether". Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as ``variable speed of light" or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative $\nabla_{[a}u_{b]}$. Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system. The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether generally develops gradient singularities which signal a breakdown of this effective theory. Including the symmetrized derivative in the action for the aether field may cure this problem.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study a generally covariant model in which local Lorentz invariance is broken "spontaneously" by a dynamical unit timelike vector field $u^a$---the "aether".	contribution 0.92	0.76	0.06	asserted 0.98
s1	Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as ``variable speed of light" or high frequency dispersion, while preserving a generally covariant metric theory of gravity.	background 0.69	0.17	0.08	hedged possibility 0.72
s2	In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative $\nabla_{[a}u_{b]}$.	method 0.61	0.83	0.04	asserted 0.99
s3	Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system.	result 0.98	0.75	0.11	asserted 1.00
s4	The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions).	result 1.00	0.81	0.21	asserted 1.00
s5	However, the aether generally develops gradient singularities which signal a breakdown of this effective theory.	limitation 0.84	0.80	0.18	asserted 0.92
s6	Including the symmetrized derivative in the action for the aether field may cure this problem.	future work 0.88	0.26	0.16	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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sources read

arXiv listing abstract v4

not examined

full text
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references and citing sentences
relations to other papers

levels run

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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A specific extension of mimetic dark matter, with a tuned coupling between curvature and the scalar field, is free of ghost and gradient instabilities at quadratic order in a cosmological background.
hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System
astro-ph.CO 2016-05 conditional novelty 6.0 of 10

The authors release hi_class, a public CLASS-based Boltzmann solver that computes linear CMB and matter power spectra for any Horndeski scalar-tensor gravity model specified by a background expansion history plus four...
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
gr-qc 2016-04 conditional novelty 6.0 of 10

A Noether-identity-based recipe generates the most general linearly diffeomorphism-invariant quadratic action for cosmological perturbations, yielding complete parameter counts for scalar-tensor, vector-tensor and Ein...
Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
gr-qc 2016-02 accept novelty 6.0 of 10

All quadratic degenerate higher-order scalar-tensor theories fall into three classes that are stable under conformal-disformal metric transformations, with class Ia generated from quartic Horndeski.
Imperfect Dark Matter
gr-qc 2014-12 conditional novelty 6.0 of 10

Mimetic dark matter with a higher-derivative term is an imperfect fluid with vorticity, and a short shift-symmetry-breaking epoch in radiation domination can produce enough charge for it to be the dominant dark matter.
New parametrization for spherically symmetric black holes in metric theories of gravity
gr-qc 2014-07 accept novelty 6.0 of 10

A continued-fraction expansion in a compactified radial coordinate reproduces known spherically symmetric black hole metrics to high accuracy with only a few coefficients, giving a compact template for testing general...
Unifying framework for scalar-tensor theories of gravity
gr-qc 2014-06 conditional novelty 6.0 of 10

A single Lagrangian built from foliation geometry contains Horndeski theory, the EFT of inflation, ghost condensate and Horava gravity as special cases, and admits a new cubic operator that keeps linear perturbations ...
Can environmental effects spoil precision gravitational-wave astrophysics?
gr-qc 2014-04 accept novelty 6.0 of 10

Environmental corrections to black-hole ringdown and binary inspiral waveforms are typically at or below the 10^-3 level relative to detector sensitivity, except for extreme-mass-ratio inspirals in geometrically thin ...
Cosmic Acceleration from Abelian Symmetry Breaking
hep-th 2014-02 conditional novelty 6.0 of 10

A ghost-free self-interacting vector with broken Abelian symmetry admits a de Sitter cosmological solution whose scale is set by a small, technically natural mass.
Constraints on Einstein-\AE ther theory and Horava gravity from binary pulsar observations
gr-qc 2013-11 accept novelty 6.0 of 10

Binary pulsar orbital decay, combined with the first numerical neutron-star sensitivities in Einstein-Aether and khronometric gravity, excludes coupling constants above roughly a part in a thousand.
Strong Binary Pulsar Constraints on Lorentz Violation in Gravity
gr-qc 2013-07 conditional novelty 6.0 of 10

Binary pulsar timing of PSR J1141-6545, J0348+0432 and J0737-3039 squeezes the Lorentz-violating couplings of Einstein-Aether and khronometric gravity into a region far smaller than stability, Cherenkov or big bang nu...
Compact binary systems in scalar-tensor gravity: Equations of motion to 2.5 post-Newtonian order
gr-qc 2013-01 conditional novelty 6.0 of 10

Two-body equations of motion in scalar-tensor gravity are derived through 2.5 post-Newtonian order, showing binary black holes mimic general relativity while mixed black-hole neutron-star binaries deviate through a si...
Non-relativistic holography from Horava gravity
hep-th 2012-10 conditional novelty 6.0 of 10

Horava gravity coupled to non-relativistic electromagnetic fields is proposed as the holographic dual of any non-relativistic field theory with time-dependent spatial diffeomorphisms and a conserved particle number.
Mechanics of universal horizons
hep-th 2012-02 conditional novelty 6.0 of 10

A Smarr formula and a first law of black hole mechanics hold for universal horizons in Einstein-æther theory, with a modified surface gravity that includes the extrinsic curvature of the preferred foliation.
Black holes in Einstein-aether and Horava-Lifshitz gravity
gr-qc 2011-04 conditional novelty 6.0 of 10

Regular, asymptotically flat spherical black holes exist throughout the experimentally allowed parameter space of Einstein-aether and IR Horava-Lifshitz gravity, and each contains a universal horizon that traps even i...
Models of non-relativistic quantum gravity: the good, the bad and the healthy
hep-th 2010-07 accept novelty 6.0 of 10

Of three non-relativistic gravity models, only the non-projectable Horava extension has a stable, weakly coupled scalar mode, and its predicted preferred-frame PPN parameters satisfy existing solar-system limits.
Imprints of a Primordial Preferred Direction on the Microwave Background
astro-ph 2007-01 accept novelty 6.0 of 10

A small preferred direction during inflation imprints a specific, calculable pattern of off-diagonal correlations in the CMB, parameterized by one amplitude and one direction on the sky.
Interacting Vector-like Dark Energy, the First and Second Cosmological Coincidence Problems
astro-ph 2006-03 conditional novelty 6.0 of 10

Interacting vector-like dark energy has stable late-time attractors with comparable dark energy and matter densities and with wA < -1, offered as a simultaneous alleviation of two cosmological coincidence problems.
Quasinormal Modes, Partial Transmission Probabilities, and Hod's Conjecture of Charged Black Holes in Perfect Fluid Dark Matter within Kalb-Ramond Gravity
gr-qc 2026-08 conditional novelty 5.0 of 10

For a charged black hole in Kalb-Ramond gravity with perfect fluid dark matter, the authors find that the Lorentz-violating parameter shifts quasinormal frequencies and transmission spectra more than the dark matter o...
Alternative LISA-TAIJI networks: polarization separation of the stochastic gravitational wave background
gr-qc 2026-08 conditional novelty 5.0 of 10

For stochastic gravitational wave backgrounds containing simultaneous tensor, vector, and scalar modes, the more inclined LISA-TAIJIm network separates polarization components substantially better than LISA-TAIJIp, al...
Reference Frames and Gravitational-Wave Polarizations: Symmetry Classification and Preferred-Frame Phenomenology
gr-qc 2026-07 unverdicted novelty 5.0 of 10

Derives boost transformations for GW polarizations, proposes symmetry classification without preferred frames, and analyzes preferred-frame effects in Bumblebee gravity including novel polarization conversion.
Black hole solutions with a linear equation of state in Ho\v{r}ava gravity and Einstein--{\ae}ther theory
gr-qc 2025-12 conditional novelty 5.0 of 10

Three families of static spherically symmetric black-hole solutions in Hořava/Einstein-æther theory are generated from chosen linear equations of state, yielding RN-like, extremal degenerate-horizon, and repulsive-pot...
Neural Post-Einsteinian Test of General Relativity with the Third Gravitational-Wave Transient Catalog
gr-qc 2025-10 unverdicted novelty 5.0 of 10

Neural post-Einsteinian analysis of GWTC-3 finds no GR violation and sets constraints covering both post-Newtonian and beyond-post-Newtonian deviations in a single theory-agnostic setup.
Dynamics of the $N$-body system in energy-momentum squared gravity: II. Existence of a Self-Acceleration
gr-qc 2025-09 unverdicted novelty 5.0 of 10

In quadratic-EMSG the self-acceleration of self-gravitating bodies vanishes at 1PN order and total linear momentum is conserved, consistent with binary-pulsar bounds.
Kalb-Ramond Black Holes Sourced by ModMax Electrodynamics: Some Perturbative Properties in the Phantom Sector
gr-qc 2025-07 reject novelty 5.0 of 10

A new analytical black hole solution in Kalb-Ramond gravity with ModMax electrodynamics is presented, and its perturbative properties (QNMs, greybody factors, Hawking sparsity) are computed in both ordinary and phanto...
Hodge Dual Gauge Symmetry in Minimal Einstein-Aether Theory
gr-qc 2025-04 conditional novelty 5.0 of 10

The minimal Einstein-aether vector field is the Hodge dual of a 3-form gauge field, making the two theories equivalent and showing that divergence-free aether fields are physically trivial.
Standard sirens with a running Planck mass
astro-ph.CO 2019-01 conditional novelty 5.0 of 10

A running Planck mass shifts gravitational-wave amplitudes, so standard sirens constrain H0 and the modified-gravity parameter c_M jointly; GW170817 gives c_M = -9 (+21/-28), and 100 A+ events could reach sigma(c_M) ~ 0.5.
Parameterized Post-Einsteinian Gravitational Waveforms in Various Modified Theories of Gravity
gr-qc 2018-09 accept novelty 5.0 of 10

The authors derive parameterized corrections to gravitational-wave amplitude and phase in six modified gravity theories and in varying-G theories, extending prior work that focused on phase corrections only.
Direct detection of gravitational waves can measure the time variation of the Planck mass
astro-ph.CO 2017-12 conditional novelty 5.0 of 10

The ratio of gravitational-wave to electromagnetic luminosity distance for the same source measures the running of the Planck mass, and LISA could constrain it to 3-13% at z around 1.5.
The fate of large-scale structure in modified gravity after GW170817 and GRB170817A
astro-ph.CO 2017-11 conditional novelty 5.0 of 10

The light-speed bound on gravitational waves leaves only conformally coupled scalar-tensor models able to produce gravitational slip, and in all surviving models dark matter must cluster at least as fast as in general...
Theoretical Physics Implications of Gravitational Wave Observation with Future Detectors
gr-qc 2017-04 conditional novelty 5.0 of 10

Projected Fisher forecasts show that future space- and ground-based gravitational wave detectors will constrain negative post-Newtonian deviations from General Relativity up to twelve orders of magnitude better than a...
Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226
gr-qc 2016-03 accept novelty 5.0 of 10

The first two LIGO black-hole mergers bound scalar hair, extra dimensions, a varying Newton constant, a massive graviton, and Lorentz violation, but the authors show most of these limits are weaker than existing tests...
Anisotropic stress as signature of non-standard propagation of gravitational waves
astro-ph.CO 2014-06 conditional novelty 5.0 of 10

In Horndeski scalar-tensor, Einstein-Aether, and bimetric massive gravity, the coefficients that produce apparent anisotropic stress from perfect fluids are the same ones that modify gravitational-wave propagation, so...
Horava gravity vs. thermodynamics: the black hole case
hep-th 2011-10 conditional novelty 5.0 of 10

Aspherical perturbations are argued to turn the universal horizon of Horava-gravity black holes into a finite-area singularity, potentially resolving a conflict with black hole thermodynamics.
On horizon structure of bimetric spacetimes
gr-qc 2011-07 accept novelty 5.0 of 10

Two regular diagonal metrics sharing a Killing vector must share its Killing horizon, and if one horizon's bifurcation surface lies inside the other spacetime, the surface gravities must match.
Extended Horava gravity and Einstein-aether theory
hep-th 2010-01 accept novelty 5.0 of 10

Restricting Einstein-aether theory's vector field to be hypersurface orthogonal reproduces the IR limit of extended Horava gravity exactly, so existing aether solutions transfer.

See all 77 Pith citations

How the literature uses it

238 arXiv papers cite this in 350 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 143 sentences without a confident label

Builds on it 4 papers

Subsequently, in Ref. [ref] , the authors of this paper extended this analysis to Einstein-Æther (EÆ) gravity [ref] , a manifestly local Lorentz-violating scalar-vector-tensor theory.

Gravitational Memory in Generalized Proca Gravity · Introduction · 0.92
In what follows, we will separately consider $1+1$ and $2+1$ Hořava–Lifshitz gravity, we will construct the full actions and discuss their dynamics, utilizing (and extending to lower dimensions) also the equivalence [ref] between Einstein-aether theory [ref] and the low energy limit of Hořava–Lifshitz gravity.

Lower-dimensional Horava-Lifshitz gravity · Introduction · 0.95
We generalize the gravitational effects of the vector fields in four dimensions [ref] to include five dimensional braneworld gravity.

Modified Gravitational Equations on Braneworld with Lorentz Invariant Violation · Introduction · 0.99

Compares with it 11 papers

The pathologies are essentially the MONDian equivalent of those found in the Einstein-Aether theory studied in [ref] .

Constraining Relativistic Generalizations of Modified Newtonian Dynamics with Gravitational Waves · Generalized Einstein-Aether Theories · 0.85
The equations ([ref]), ([ref]) - although in slightly different form - had been obtained and investigated by Jacobson in his 2006 paper [ref] .

Einstein-Aether Theory With and Without Einstein · Introduction · 0.89
This distinguishing feature sets meVSL apart from traditional VSL models, which often assume or necessitate an explicit mechanism driving the evolution of the speed of light [ref] .

Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lema\^itre-Robertson-Walker Metric · Introduction · 0.83

Cites it as support 1 paper

It actually contains viable theories of gravity [ref] [ref] as well as proposals for high energy physics beyond the standard model [ref] and is clearly important for discussions of realistic or causal interpretations of quantum theory and the violations of Bell's inequalities.]

About a "nonlocal" local model considered by L. Vervoort, and the necessity to distinguish locality from Einstein locality · Introduction · 0.97

Cites it as background 156 papers

The action ([ref]) is closely related [ref] to the action of the Einstein-aether theory [ref] (see [ref] for a review).

Models of non-relativistic quantum gravity: the good, the bad and the healthy · Stability and absence of strong coupling · 0.82
Specifically, we shall focus on the Einstein-aether (EA) theory proposed by Jacobson and Mattingly [ref] , in which a fixed norm vector field with a Lorentz-violating vacuum expectation value takes part in the gravitational interaction.

The Music of the Aetherwave - B-mode Polarization in Einstein-Aether Theory · Introduction · 0.94
Einstein-Æther (EÆ) gravity [ref] is defined as the most general metric theory up to two powers of derivative operators, that includes an additional vector field $A$ that explicitly breaks local Lorentz symmetry in the gravity sector through a constraint on its norm.

Constraining superluminal Einstein-\AE{}ther gravity through gravitational memory · Action and Equations of Motion · 0.95

Discussion

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