Gravity with a dynamical preferred frame

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.

9 pages; title changed, references added, relation to prior work of Gasperini discussed, errors in scalar field stress tensor corrected, various minor changes to Introduction; Final version to be published in PRD: relation to prior work of Kostelecky and Samuel spelled out in detail, clarifications and sign errors corrected in section on linearized solutions, references added; Really final version: (u^m \nabla_m u^a)^2 term added to most general Lagrangian eqn.(3.1)

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• Testing alternative theories of gravity with space-based gravitational wave detectors
• Optical Appearance and Shadow of Kalb-Ramond Black Hole: Effects of Plasma and Accretion Models
• Bounds on tidal charges from gravitational-wave ringdown observations
• Black Holes and Thunderbolt Singularities with Lifshitz Scaling Terms
• First-order thermodynamics of scalar-tensor gravity
• The extended Einstein-Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes
• Superluminal Travel Made Possible (in two dimensions)
• Time Orientability and Particle Production from Universal Horizons
• A Keck/HIRES Doppler Search for Planets Orbiting Metal-Poor Dwarfs
• Dynamical obstruction to perpetual motion from Lorentz-violating black holes
• Gravitational Cherenkov losses in MOND theories
• Einstein's quadrupole formula from the kinetic-conformal Horava theory
• Disentangling modified gravity from a dark force with gravitational redshift
• Kerr Black Hole in Einstein--Æther Gravity
• Bumblebee gravity: spherically-symmetric solutions away from the potential minimum
• Aether scalar tensor theory: Hamiltonian Formalism
• A Note on Spontaneously Broken Lorentz Invariance
• Lorentz violation and the speed of gravitational waves in brane-worlds
• Reconstructions of $f(\mathcal{P})$ and $f(\mathcal{Q})$ gravity models from $(m,n)$-type Barrow Holographic Dark Energy: Analysis and Observational Constraints
• Exact black hole solutions in Einstein-Aether Scalar field theory
• Einstein-aether theory in Weyl integrable geometry
• Effective Field Theory of Anisotropic Inflation and Beyond
• Modified Gravitational Equations on Braneworld with Lorentz Invariant Violation
• Anisotropic fluid spheres in Hořava gravity and Einstein-æther theory with a non-static æther
• Testing Lorentz invariance of dark matter with satellite galaxies
• Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking
• Wormholes in Horava gravity with cosmological constant
• Thermodynamics of Einstein-Aether Black Holes
• Thermodynamical study on universal horizons in higher $D$-dimensional spacetime and aether waves
• Towards nonlinear axion-dilaton electrodynamics: How can axionic dark matter mimic dilaton-photon interactions?
• Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
• Consistent first order action functional for gauge theories
• Tests of Relativistic Gravity in Space: Recent Progress and Future Directions
• Gravitational Tunneling in Lorentz Violating Gravity
• Ponderable aether
• Dwarf Galaxies, MOND, and Relativistic Gravitation
• Dispersion relation and surface gravity of universal horizons
• Gravitational plane waves in Einstein-aether theory
• Renormalization in theories with modified dispersion relations: weak gravitational fields
• Kantowski-Sachs Einstein-Aether Scalar Field Cosmological Models: The Sequel
• Relativistic polytropic equations of state in Hořava gravity and Einstein-æther theory
• Collision of particles near a three-dimensional rotating Hořava AdS black hole
• Spontaneous color polarization as a modus originis of the dynamic aether
• Tunneling analysis of null aether black hole theory in the background of Newman-Janis algorithm
• On metric-affine bumblebee model coupled to scalar matter
• Construction of higher-order metric fluctuation terms in spacetime symmetry-breaking effective field theory
• New application of the Killing vector field formalism: Modified periodic potential and two-level profiles of the axionic dark matter distribution
• Effects of coupling constants on chaos of charged particles in the $Einstein-\AE$ ther theory
• Constructing entanglement wedges for Lifshitz spacetimes with Lifshitz gravity
• Space-time thermodynamics in momentum dependent geometries
• UV Dispersive Effects on Hawking Radiation
• Short-range forces due to Lorentz-symmetry violation
• Birefringence induced by pp-wave modes in an electromagnetically active dynamic aether
• Universal horizons and black hole spectroscopy in gravitational theories with broken Lorentz symmetry
• Entropies and The First Laws of Black Hole Thermodynamics in Einstein-aether-Maxwell Theory
• An ecological approach to problems of Dark Energy, Dark Matter, MOND and Neutrinos
• Einstein-aether theory: Dynamics of relativistic particles with spin or polarization in a Gödel-type universe
• Constraints and degrees of freedom in Lorentz-violating field theories
• A note on non singular Einstein-Aether cosmologies
• Redshift-space distortions from vector perturbations II: Anisotropic signal
• Interaction of the axionic dark matter, dynamic aether, spinor and gravity fields as an origin of oscillations of the fermion effective mass
• On the space of solutions of the Horava theory at the kinetic-conformal point
• Is Birkhoff's Theorem Valid in Einstein-Aether Theory?
• On optical appearance of Einstein-Maxwell-Æther black holes surrounded by various accretions
• Macroscopic theory of dark sector
• From Analogue Models to Gravitating Vacuum
• A covariant approach to parameterised cosmological perturbations
• Gravitational Lorentz Violation and Superluminality via AdS/CFT Duality
• A generalization of the Lorentz ether to gravity with general-relativistic limit
• Theory-agnostic searches for non-gravitational modes in black hole ringdown
• Moment of Inertia for Axisymmetric Neutron Stars in the Standard-Model Extension
• Photon velocity, power spectrum in Unruh effect with modified dispersion relation
• On the constraint equations in Einstein-aether theories and the weak gravitational field limit
• A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection
• Photon and photino as Nambu-Goldstone zero modes in an emergent SUSY QED
• Galaxy rotation curves and preferred reference frame effects
• Unruh's detector in the presence of Lorentz symmetry breaking
• Revisiting linear stability of black hole odd-parity perturbations in Einstein-Aether gravity
• Solar system relativity tests, formulas for light deflection by a central mass, and modification of the lens equation, for a Weyl scaling invariant dark energy
• Observational Constraints on Local Lorentz Invariance
• A discrete, unitary, causal theory of quantum gravity
• I-Love-Q in Hořava-Lifshitz Gravity
• Modified Hawking temperatures of black holes in Lorentz violation theory
• Minimal Einstein-Aether Theory
• Constraining primordial vector mode from B-mode polarization
• Comment on "Scalar Einstein-Aether theory"
• Modified propagation of gravitational waves from the early radiation era
• Ether and Relativity
• On the Resilience of Black Hole Evaporation: Gravitational Tunneling through Universal Horizons
• Propagator of a scalar field on a stationary slowly varying gravitational background
• Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time
• Einstein-Yang-Mills-aether theory with nonlinear axion field: Decay of color aether and the axionic dark matter production
• Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in Hořava Gravity
• Static Cylindrical Symmetric Solutions in the Einstein-Aether Theory
• n-DBI gravity, maximal slicing and the Kerr geometry
• Gauge Fields as Goldstone Bosons Triggered by Spontaneously Broken Supersymmetry
• Buchdahl bound, photon ring, ISCO and radial acceleration in Einstein-æther theory
• Reconstructions of Einstein-Aether Gravity from Barrow Agegraphic and New Barrow Agegraphic Dark Energy models: Examinations and Observational Limits
• On continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
• New Asymptotically Lifshitz Black Holes in Horava gravity
• Parameterised free functions and saddle stresses in modified gravity
• Strange Horizons: Understanding Causal Barriers Beyond General Relativity
• Angular Momentum Loss for a Binary System in Einstein-Æther Theory
• Isotropic cosmological model with aetherically active axionic dark matter
• Deep Learning solutions to singular ordinary differential equations: from special functions to spherical accretion
• Einstein-aether models III: conformally static metrics, perfect fluid and scalar fields
• Can MONDian vector theories explain the cosmic speed up ?
• Impact of Lorentz Violation on Cosmology
• Motion of Rotating Black Holes in Homogeneous Scalar Fields: A General Case
• Rescuing the Unruh Effect in Lorentz Violating Gravity
• Constraints on cosmological parameters and CMB first acoustic peak in conformal Killing gravity
• Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric
• Gravitational Waves in Scalar-Tensor-Vector Gravity Theory
• K-essence Explains a Lorentz Violation Experiment
• Aether SUSY breaking: Can aether be alternative to F-term SUSY breaking?
• Testing for gravitational preferred directions with galaxy and lensing surveys
• Holography and $Ad{S}_2$ gravity with a dynamical aether
• Black hole horizons at the extremal limit in Lorentz-violating gravity
• Exploring black hole mechanics in cotangent bundle geometries
• Are inertial vacua equivalent in Lorentz-violating theories? Does it matter?
• NAT Black Holes
• Universal Horizons without Hypersurface Orthogonality
• Dark aspects of massive spinor electrodynamics
• On the viability of minimal Hořava gravity
• Modified gravity one-loop partition function
• On the Lorentz symmetry in conformally reduced Quantum Gravity
• Search for exotic gravitational wave signals beyond general relativity using deep learning
• Reply to ``Comment on Model-dependence of Shapiro time delay and the `speed of gravity/speed of light' controversy''
• Lorentz Violation with Gravitational Waves: Constraints from NANOGrav and IPTA Data
• Interaction of the Cosmic Dark Fluid with Dynamic Aether: Parametric Mechanism of Axion Generation in the Early Universe
• Energy-entropy relation for asymptotically Lifshitz spacetimes with universal horizons
• Mimetic Tensor-Vector-Scalar Cosmology: Incorporating Dark Matter, Dark Energy and Stiff Matter
• Hubble Diagrams in the Jordan and Einstein Frames
• Gravitational baryogenesis beyond the spectator approximation
• Velocity-dependent deformations of the energy spectrum of a quantum cavity from Lorentz symmetry violations
• Superluminal Travel, UV/IR Mixing and Turbulence in the Lineland
• Neural Post-Einsteinian Test of General Relativity with the Third Gravitational-Wave Transient Catalog
• Perturbation Theory in the Minimally Extended Varying Speed of Light (meVSL) Model
• Lorentz symmetry violation and the tunneling radiation of fermions with spin $1/2$ for Kerr Anti-de-Sitter black hole
• Conserved charges and asymptotic symmetries of BTZ-like black holes in Einstein-bumblebee gravity
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor
• Non-relativistic entanglement entropy from Horava gravity
• About a "nonlocal" local model considered by L. Vervoort, and the necessity to distinguish locality from Einstein locality
• The Eternal Sunshine of the Spotless Mind
• Tests of Modified Gravity Theories in the Solar System
• Notes on f(R) Theories of Gravity
• Eikonal gravitational-wave lensing in Einstein-aether theory
• An Improvement for Quantum Tunneling Radiation of Fermions in a Stationary Kerr-Newman Black Hole Spacetime
• SU(N) - symmetric dynamic aether: General formalism and a hypothesis on spontaneous color polarization
• Around MOND: Lagrangians, Hubble Equations, Perturbations and External Field Effect
• Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
• Phenomenologically viable gravitational theory based on a preferred foliation without extra modes
• Gravitational waves in metric-affine bumblebee gravity
• Extended thermodynamics and $P-v$ Criticality of Kalb-Ramond black hole coupled with nonlinear electrodynamics
• Generalized Chern-Pontryagin models
• Cosmological Asymptotics in Higher-Order Gravity Theories
• Complete Classification of Analytical Models in Einstein-Aether Cosmology
• Qualitative analysis of Einstein-aether models with perfect fluid and scalar fields
• Curvature vs degrees of freedom: The case of the critical 2+1 Horava theory
• Exact analytic solutions in 2+1 Hořava gravity with cosmological constant
• The radial metric function does not identify null surfaces
• Lorentz-violating modifications to particle dynamics, thermodynamics and vacuum energy in bumblebee gravity
• Gravity with a Dynamical Spinning Aether
• Effects of bumblebee gravity on neutrino motion
• Introduction of the generalized Lorenz gauge condition into the vector-tensor theory
• The Entropic Dynamics of Relativistic Quantum Fields in Curved Space-time
• Constraints on Energy Conditions in $f(R,L_m)$ Gravity
• Energy conditions and gravitational baryogenesis in $f(R,\mathcal{R})$ gravity
• Extension of the Einstein-Dirac-axion-aether theory based on an effective metric with a spinor kernel
• Non-metricity effects on electron scattering in bumblebee gravity
• Black hole solutions with a linear equation of state in Hořava gravity and Einstein--æther theory
• Superluminal modes in a quantum field simulator for cosmology from analog trans-Planckian physics
• Einstein-Aether Theory With and Without Einstein
• A physicist's view of the universe: a philosophical approach
• Effect of bulk Lorentz violation on anisotropic brane cosmologies
• Electromagnetic Origin for Planck Mass and Dark Energy
• A realisation of Lorentz algebra in Lorentz violating theory
• Solution to the problem of time
• The Preferred System of Reference Reloaded