Optical and Thermodynamic Signatures of Lorentz Symmetry Breaking in Bumblebee AdS Black Holes

Abstract

We investigate the impact of spontaneous Lorentz symmetry breaking on scalar wave propagation, null geodesics, and thermodynamic behavior of four-dimensional asymptotically AdS black holes in bumblebee gravity. The static, spherically symmetric solutions are characterized by a dimensionless parameter $\ell >-1$ arising from the vacuum expectation value of the bumblebee vector field, which globally rescales the radial geometry. Massless scalar fields are analyzed via the radial Klein--Gordon equation cast into a generalized Helmholtz form, yielding an effective frequency-dependent refractive index that identifies oscillatory and evanescent regions, classical turning points, and confinement induced by curvature and Lorentz violation. In the high-frequency limit, wave propagation coincides with null geodesics, with $\ell$ controlling radial scaling and governing the geometric-optics limit. The AdS boundary reflects waves, while the horizon acts as a one-way absorber. Thermodynamic analysis in non-extended and extended phase spaces confirms the first law and Smarr relation, with $\ell$ influencing heat capacity, free energy, and stability. \textcolor{black}{Modeling these black holes as heat engines, we construct explicit cycles and show that efficiency increases with $\ell$, leading to an upper bound imposed by $\eta \le 1$. Our results provide a framework connecting Lorentz violation, wave propagation, geometric optics, and AdS black hole thermodynamics in bumblebee gravity.

References in corpus (37)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Confrontation between General Relativity and Experiment
• Spontaneous Lorentz and Diffeomorphism Violation, Massive Modes, and Gravity
• Black holes with a cosmological constant in bumblebee gravity
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Bumblebee gravity with a Kerr-Sen-like solution and its Shadow
• Lorentz-CPT violation, radiative corrections and finite temperature
• Analogue simulations of quantum gravity with fluids
• Compton Scattering in the Presence of Lorentz and CPT Violation
• Greybody Radiation and Quasinormal Modes of Kerr-like Black Hole in Bumblebee Gravity Model
• Cosmological implications of Bumblebee vector models
• An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity
• Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field
• Constraint on parameters of a rotating black hole in Einstein-bumblebee theory by quasi-periodic oscillations
• Some Observable Physical Properties of the Higher Dimensional dS/AdS Black Holes in Einstein-Bumblebee Gravity Theory
• Heat engine in the three-dimensional spacetime
• How does non-metricity affect particle creation and evaporation in bumblebee gravity?
• Gravitational traces of bumblebee gravity in metric-affine formalism
• Superradiance in the BTZ black hole with Robin boundary conditions
• Testing EGB gravity coupled to bumblebee field and black hole parameter estimation with EHT observations
• Reply to "Comment on 'Greybody radiation and quasinormal modes of Kerr-like black hole in Bumblebee gravity model' "
• Black holes and gravitational waves in three-dimensional f(R) gravity
• Probing bumblebee gravity with black hole X-ray data
• Phantom RN-AdS black holes in noncommutative space
• Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect
• Kasner cosmology in bumblebee gravity
• Scalar field instabilities in charged BTZ black holes
• Scalar tidal response of a rotating BTZ black hole
• On the self-consistency of compact objects in Lorentz-violating gravity theories
• Bulk reconstruction in rotating BTZ black hole
• Ray geodesics and wave propagation on the Beltrami surface: Optics of an optical wormhole
• Full Classification of Static Spherical Vacuum Solutions to Bumblebee Gravity with General VEVs
• On heat properties of charged AdS black holes in Gauss-Bonnet gravity coupled with nonlinear electrodynamics
• The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution
• Anisotropic cosmology in Bumblebee gravity theory
• Optics in spiral dislocation spacetime: Torsion as a geometric waveguide and frequency-filtering mechanism
• Accretion of matter of a new bumblebee black hole