Abstract
Bopp–Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekenstein’s method. It is shown that the solutions split up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp–Podolsky black holes, the non-homogeneous solutions are found to be Maxwell’s solutions leading to a Reissner–Nordström black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell one. Thus, in the light of the energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp–Podolsky fields in spherically symmetric space-times.
Highlights
The decades of 1960 and 1970 witnessed a boom of interest in this area
In 1963, Kerr [5] presented his solution for a spinning mass, a result that was generalized by Newman 2 years later with the introduction of electric charge to the rotating body [6,7]
A few years later, important developments related to the interaction between matter and gravitational fields were achieved. In this line of research, a relevant contribution was given by Israel [8] in 1967, when he proposed the first version of the no-hair theorem/conjecture for the spherically symmetric black holes
Summary
The decades of 1960 and 1970 witnessed a boom of interest in this area. In 1963, Kerr [5] presented his solution for a spinning mass, a result that was generalized by Newman 2 years later with the introduction of electric charge to the rotating body [6,7]. A few years later, important developments related to the interaction between matter and gravitational fields were achieved In this line of research, a relevant contribution was given by Israel [8] in 1967, when he proposed the first version of the no-hair theorem/conjecture for the spherically symmetric black holes. This result was soon extended to include rotating and charged BHs [9,10] and a final version of this theorem states that an exterior solution of a BH is completely characterized by its mass, electric charge and angular momentum. The real Proca field is a interesting case, studied by Bekenstein in [11] He analyzed BHs in the presence of a massive vector field ( called Proca black holes). Bekenstein built an ingenious argument to show that the massive field cannot propagate outside the event horizon
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
