Physics

Gravitation

Spacetime

Gravitational field

Riemann hypothesis

Circular symmetry

Symmetry (geometry)

Mathematics

Mathematical physics

Lorentz transformation

Schwarzschild radius

General relativity

Mathematical analysis

Schwarzschild metric

Geometry

Theoretical physics

Exact solutions in general relativity

Quantum mechanics

Classical mechanics

Physical review. D/Physical review. D.

We obtain an exact vacuum solution from the gravity sector contained in the minimal standard-model extension. The theoretical model assumes a Riemann spacetime coupled to the bumblebee field which is responsible for the spontaneous Lorentz symmetry breaking. The solution achieved in a static and spherically symmetric scenario establishes a Schwarzschild-like black hole. In order to study the effects of the spontaneous Lorentz symmetry breaking we investigate some classic tests, including the advance of perihelion, the bending of light, and Shapiro's time delay. Furthermore, we compute some upper bounds, among which the most stringent associated with existing experimental data provides a sensitivity at the ${10}^{\ensuremath{-}15}$ level and that for future missions at the ${10}^{\ensuremath{-}19}$ level.

Exact Schwarzschild-like solution in a bumblebee gravity model