Einstein-Gauss-Bonnet gravity coupled to bumblebee field in four dimensional spacetime

Understand

We study Einstein-Gauss-Bonnet gravity coupled to a bumblebee field which leads to a spontaneous Lorentz symmetry breaking in the gravitational sector.

• We obtain an exact black hole solution and a cosmological solution in four dimensional spacetime by a regularization scheme.
• We also obtain a Schwarzschild-like bumblebee black hole solution in $D$-dimensional spacetime.
• We find that the bumblebee field doesn't affect the locations of the black hole horizon, but only affects the gravitational potential.