We have considered the bumblebee gravity model where lorentz-violating (LV) scenario gets involved through a bumblebee field vector field $$B_\mu $$ B μ . A spontaneous symmetry breaking allows the field to acquires a vacuum expectation value that generates LV into the system. A Kerr–Sen-like solution has been found out starting from the generalized form of a radiating stationery axially symmetric black hole metric. We compute the effective potential offered by the null geodesics in the bumblebee rotating black hole spacetime. The shadow has been sketched for different variations of the parameters involved in the system. A careful investigation has been carried out to study how the shadow gets affected when Lorentz violation enters into the picture. The emission rate of radiation has also been studied and how it varies with the LV parameter $$\ell $$ ℓ is studied scrupulously.

A metric with a Lorentz violating parameter is associated with the bumblebee gravity model. We study the motion of a particle in this bumblebee background where the dynamical variables satisfy non-canonical Snyder algebra along with some critical survey on the classical observations in the bumblebee background to see how these would likely differ from Schwarzschild background. It has been found that the perihelion shift acquires a generalized expression with two independent parameters. One of these two is connected with the Lorentz violating factor and the other is involved in the Snyder algebraic formulation. We also observe that the time period of revolution, in general, acquires a Lorentz violating factor in the bumblebee background, however, for the circular orbit, it remains unchanged even in the presence of the Lorentz violating factor in the bumblebee background. The parameters used here can be constrained with the same type of conjecture used earlier.

A Kerr-Sen-like black hole solution appears in the Einstein-bumblebee theory of gravity. The solution contains contains a Lorentz violating parameter in an explicit manner. We study the null geodesics in the background of this Kerr-Sen-like black hole surrounded by a dispersive medium like plasma. We investigate the effect of the charge of the black hole, the Lorentz violation parameter, and the plasma parameter on the photon orbits with the evaluation of the effective potential in the presence of both the Lorentz violation parameter and the plasma parameter. We also study the influence of the Lorentz violation parameter and plasma parameter on the emission of energy from the black hole due to thermal radiation. Besides, we compute the angle of deflection of massless particles with weak-field approximation in this generalized situation and examine how it varies with the Lorentz violation parameter in presence of plasma. Constraining the parameters of this Lorentz violating Kerr-Sen-like black hole is also attempted here with the result obtained from the observations of the Event Horizon Telescope (EHT) collaboration.

Thomas–Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first reformulate the Thomas–Fermi model for the non-relativistic case. We have shown that it can also be reformulated for taking into account the relativistic effect. We study the dialectic screening for both the non-relativistic and relativistic cases and find out the Fermi length for both the cases explicitly.

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