Bumblebee gravity: spherically-symmetric solutions away from the potential minimum
arXiv:2503.10998 · doi:10.1103/nkbj-vbjf
Abstract
In this work, we study a vector model of spontaneous spacetime-symmetry breaking coupled to gravity: the bumblebee model. The primary focus is on static spherically symmetric solutions. Complementing previous work on black hole solutions, we study the effects on the solutions when the vector field does not lie at the minimum of its potential. We first investigate the flat spacetime limit, which can be viewed as a modified electrostatic model with a nonlinear interaction term. We study the stability of classical solutions generally and in the spherically-symmetric case. We also find that certain potentials, based on hypergeometric functions, yield a Hamiltonian bounded from below for the case of fixed spatial vector magnitude. With gravity, we solve for the spherically-symmetric metric and vector field, for a variety of choices of the potential energy functions, including ones beyond the quadratic potential like the hypergeometric potentials. Special case exact solutions are obtained showing Schwarszchild-Anti de Sitter and Reissner-Nordstrom spacetimes. We employ horizon and asymptotic analytical expansions along with numerical solutions to explore the general case with the vector field away from the potential minimum. We discover interesting features of these solutions including naked singularities, repulsive gravity, and rapidly varying gravitational field near the source. Finally, we discuss observational constraints on these spacetimes using the resulting orbital behavior.
26 pages two-column format, 11 figures, 5 tables, v3: significant corrections added regarding claimed Hamiltonian properties of the hypergeometric potential functions for the vector field including abstract and text wording changes - particularly in subsection IIIA, correcting Table I, and other minor edits throughout the paper. Erratum corrections to be submitted to PRD
References in corpus (81)
- First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
- Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
- Tests of general relativity with GW150914
- Search for New Physics with Atoms and Molecules
- Data Tables for Lorentz and CPT Violation
- Gravity, Lorentz Violation, and the Standard Model
- Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
- Tests of General Relativity with the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1
- Stellar Orbits Around the Galactic Center Black Hole
- Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226
- Tests of General Relativity with GW170817
- Electrodynamics with Lorentz-violating operators of arbitrary dimension
- Signals for Lorentz Violation in Post-Newtonian Gravity
- Tests of Lorentz invariance: a 2013 update
- Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity
- Black holes in scalar-tensor gravity
- Atom Interferometry tests of the isotropy of post-Newtonian gravity
- Fermions with Lorentz-violating operators of arbitrary dimension
- Exact traversable wormhole solution in bumblebee gravity
- An exact Schwarzschild-like solution in a bumblebee gravity model
- Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (I) Inspiral-Merger
- Spontaneous Lorentz and Diffeomorphism Violation, Massive Modes, and Gravity
- Prospects for Large Relativity Violations in Matter-Gravity Couplings
- Testing local Lorentz invariance with gravitational waves
- Lorentz violation with an antisymmetric tensor
- Black holes with a cosmological constant in bumblebee gravity
- Black Holes in Einstein-Aether Theory
- Constraints and Stability in Vector Theories with Spontaneous Lorentz Violation
- Testing the black-hole area law with GW150914
- Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
- Short-range gravity and Lorentz violation
- Astrophysical Black Holes: A Compact Pedagogical Review
- Backgrounds in gravitational effective field theory
- The flight of the bumblebee: vacuum solutions of a gravity model with vector-induced spontaneous Lorentz symmetry breaking
- Tests of local Lorentz invariance violation of gravity in the standard model extension with pulsars
- Black holes in Lorentz-violating gravity theories
- Spontaneous Lorentz Violation and Nonpolynomial Interactions
- Probing Dynamical Gravity with the Polarization of Continuous Gravitational Waves
- Explicit versus Spontaneous Diffeomorphism Breaking in Gravity
- Numerical simulations of gravitational collapse in Einstein-aether theory
- Static spherical vacuum solutions in the bumblebee gravity model
- Instabilities in the Aether
- A positive energy theorem for Einstein-aether and Hořava gravity
- Vacuum solution within a metric-affine bumblebee gravity
- Testing Lorentz symmetry with Lunar Laser Ranging
- Time-delay and Doppler tests of the Lorentz symmetry of gravity
- Polarizations of Gravitational Waves in the Bumblebee Gravity Model
- Testing Lorentz symmetry with planetary orbital dynamics
- Probing Schwarzschild-like Black Holes in Metric-Affine Bumblebee Gravity with Accretion Disk, Deflection Angle, Greybody Bounds, and Neutrino Propagation
- Vector models of gravitational Lorentz symmetry breaking
- Black Hole Thermodynamics and Lorentz Symmetry
- Quantization and stability of bumblebee electrodynamics
- An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity
- Search for Lorentz invariance violation through tests of the gravitational inverse square law at short-ranges
- Bumblebee black holes in light of Event Horizon Telescope observations
- Constraining extra gravitational wave polarizations with Advanced LIGO, Advanced Virgo and KAGRA and upper bounds from GW170817
- Radiative corrections in bumblebee electrodynamics
- Charged spherically symmetric and slowly rotating charged black hole solutions in bumblebee gravity
- Limits on Lorentz violation in gravity from worldwide superconducting gravimeters
- 3+1 Formulation of the Standard-Model Extension Gravity Sector
- Hamiltonian formulation of an effective modified gravity with nondynamical background fields
- Gödel-type universes in bumblebee gravity
- Ricci dark energy in bumblebee gravity model
- Explicit Lorentz violation in a static and spherically-symmetric spacetime
- Dynamic instability analysis for bumblebee black holes: the odd parity
- Explicit spacetime-symmetry breaking and the dynamics of primordial fields
- The bizarre anti-de Sitter spacetime
- Dynamical ambiguities in models with spontaneous Lorentz violation
- Neutron stars in the bumblebee theory of gravity
- Neutron Star Structure in the Minimal Gravitational Standard-Model Extension and the Implication to Continuous Gravitational Waves
- Stars and quark stars in bumblebee gravity
- Spontaneous Lorentz violation and asymptotic flatness
- Spontaneous symmetry breaking in models with second-class constraints
- Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking
- Super-entropy bumblebee AdS black holes
- Classical radiation fields for scalar, electromagnetic, and gravitational waves with spacetime-symmetry breaking
- Short-range forces due to Lorentz-symmetry violation
- Construction of higher-order metric fluctuation terms in spacetime symmetry-breaking effective field theory
- Constraints and degrees of freedom in Lorentz-violating field theories
- Dynamical Lorentz Symmetry Breaking in a Scale-free Theory of Gravity
- Derivative four-fermion model, effective action and bumblebee generation
Cited by in corpus (5)
- Static Spherical Vacuum Solution to Bumblebee Gravity with Time-like VEVs
- Probing a Lorentz-violating parameter from orbital precession of the S2 star around the galactic centre supermassive black hole
- Boson Stars in Bumblebee Gravity and Their Gravitational Waveforms from Extreme-Mass-Ratio Inspirals
- Periodic orbits and gravitational waveforms of black holes in bumblebee gravity
- Non-minimal matter sector couplings in Lorentz-violating gravity: Self-consistent traversable wormholes and quasinormal modes