Solutions in the generalized Proca theory with the nonminimal coupling to the Einstein tensor

Understand

We investigate the static and spherically symmetric solutions in a class of the generalized Proca theory with the nonminimal coupling to the Einstein tensor.

• First, we show that the solutions in the scalar-tensor theory with the nonminimal derivative coupling to the Einstein tensor can be those in the generalized Proca theory with the vanishing field strength.
• We then show that when the field strength takes the nonzero value the static and spherically symmetric solutions can be found only for the specific value of the nonminimal coupling constant.
• Second, we investigate the first-order slow-rotation corrections to the static and spherically symmetric background.