Scalar quasibound states in Einstein-Maxwell-Bumblebee black holes with non-minimal Maxwell-Bumblebee coupling

We investigate the dynamics of a relativistic scalar field in a static spherically symmetric Einstein-Maxwell-Bumblebee black hole spacetime in ( 3 + 1 ) dimensions, incorporating non-minimal Maxwell-Bumblebee coupling. The covariant Klein-Gordon equation is constructed component by component, and, using a separation of variables ansatz, the polar and radial parts are successfully decoupled. The exact solution of the polar equation is expressed in terms of spherical harmonics, while the radial solution is obtained via the confluent Heun function. Quasibound state quantization is achieved by imposing the polynomial condition on the confluent Heun function, resulting in complex-valued energy levels for a massive scalar field. The real part of the energy corresponds to the relativistic particle energy, whereas the imaginary part characterizes the stability of the configuration. We find that light neutral scalar fields are unable to trigger a black hole bomb in this spacetime. Additionally, we study Hawking radiation from the outer horizon of the spherically symmetric Einstein-Maxwell-Bumblebee black hole using the Damour-Ruffini method, employing the exact scalar wave functions. The Hawking temperature is slightly reduced compared to the Schwarzschild due to the combined influence of Lorentz violation and electromagnetism, highlighting subtle deviations from general relativity can affect the thermal properties of black holes.