On the analytic generalization of particle deflection in the weak field regime and shadow size in light of EHT constraints for Schwarzschild-like black hole solutions

Abstract

In this paper, an analytic generalization of the weak field deflection angle (WDA) is derived by utilizing the current non-asymptotically flat generalization of the Gauss-Bonnet theorem. The derived formula is valid for any Schwarzschild-like spacetime, which deviates from the classical Schwarzschild case through some constant parameters. This work provided four examples in the context of bumblebee gravity theory, and one example from a black hole surrounded with soliton dark matter, where some results are new, and some agreed with existing literature. The WDA formula provided a simple calculation, where approximations based on some conditions can be done directly on it, skipping the preliminary steps. For the shadow size analysis, it is shown how it depends solely on the parameter associated with the metric coefficient in the time coordinate. A general formula for the constrained parameter is also derived based on the Event Horizon Collaboration (EHT) observational results. Finally, the work realized further possible generalizations on other black hole models, such as RN-like, dS/AdS-like black hole solutions, and even black hole solutions in higher dimensions.

12 pages. The current version shows major changes and corrections in the paper

References in corpus (42)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Calculating black hole shadows: Review of analytical studies
• Relativistic images of Schwarzschild black hole lensing
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Constraints on black-hole charges with the 2017 EHT observations of M87*
• Progress in Measurements of the Gravitational Bending of Radio Waves Using the VLBA
• A comparison of approximate gravitational lens equations and a proposal for an improved new one
• Distortions of images of Schwarzschild lensing
• Finite-distance gravitational deflection of massive particles by the Kerr-like black hole in the bumblebee gravity model
• Circular orbit of a particle and weak gravitational lensing
• Schwarzschild-like black hole with a topological defect in bumblebee gravity
• Static and spherically symmetric black holes in gravity with a background Kalb-Ramond field
• Cosmological constant corrections to the photon sphere and black hole shadow radii
• Electrically charged black holes in gravity with a background Kalb-Ramond field
• Black hole in quantum wave dark matter
• Probing Schwarzschild-like Black Holes in Metric-Affine Bumblebee Gravity with Accretion Disk, Deflection Angle, Greybody Bounds, and Neutrino Propagation
• An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity
• Quasinormal modes and greybody factor of a Lorentz-violating black hole
• Probing the Lorentz Invariance Violation via Gravitational Lensing and Analytical Eigenmodes of Perturbed Slowly Rotating Bumblebee Black Holes
• Spontaneous Lorentz symmetry-breaking constraints in Kalb-Ramond gravity
• Weak Deflection Angle, Hawking Radiation and Greybody Bound of Reissner-Nordström Black Hole Corrected by Bounce Parameter
• Quasinormal modes of the spherical bumblebee black holes with a global monopole
• Notes on thermodynamics of Schwarzschild-like bumblebee black hole
• Gravitational lensing by a charged spherically symmetric black hole immersed in thin dark matter
• Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data
• Finite-distance gravitational deflection of massive particles by a rotating black hole in loop quantum gravity
• Constraints from Solar System tests on a covariant loop quantum black hole
• Traces of quantum gravitational correction at third-order curvature through the black hole shadow and particle deflection at the weak field limit
• Phantom hairy black holes and wormholes in Einstein-bumblebee gravity
• Violation of Hod's Conjecture and Probing it with Optical properties of a 5-D black hole in Einstein Gauss-Bonnet Bumblebee theory of gravity
• Gravitational Lensing of Spherically Symmetric Black Holes in Dark Matter Halos
• Deflection and Gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit
• Weak gravitational lensing by an ESTGB black hole in the presence of a plasma
• Analyzing the effect of higher dimensions on the black hole silhouette, deflection angles, and PINN approximated quasinormal modes
• Null geodesic structure for the Barriola-Vilenkin spacetime via $k$-essence
• Imprints of a gravitational wave through the weak field deflection of photons

Cited by in corpus (7)

• Analyzing Deflection Angles and Photon Sphere Dynamics of Magnetically Charged Black Holes in Nonlinear Electrodynamic
• Charged black holes in Kalb-Ramond gravity: Weak Deflection Angle, Shadow cast, Quasinormal Modes and Neutrino annihilation
• Multimodal signatures of asymptotic (A)dS Kalb-Ramond black holes: Constraints through the shadow, weak deflection angle, and topological photon spheres
• Curled orbit and epicyclic oscillation of charged particles around the weakly magnetized black hole in the presence of Lorentz violation
• Gravitational Black Hole Shadow Spectroscopy
• Boson Stars in Bumblebee Gravity and Their Gravitational Waveforms from Extreme-Mass-Ratio Inspirals
• Lorentz-violating modifications to particle dynamics, thermodynamics and vacuum energy in bumblebee gravity