Abstract
We consider a class of Einstein–Maxwell–dilaton theories in general dimensions and construct both static and dynamic charged black holes. We adopt the reverse engineering procedure and make a specific ansatz for the scalar field and then derive the necessary scalar potential and the non-minimal coupling function between the scalar and the Maxwell field. The resulting static black holes contain mass and electric charge as integration constants. We find that some of the static solutions can be promoted to become dynamical ones in the Eddington–Finkelstein-like coordinates. The collapse solutions describe the evolution from a smaller charged black hole to a larger black hole state, driven by the scalar field.
Highlights
We find that a subset of the static solutions can be promoted to become exact dynamic ones in this process
It is important to note that the parameter q that appears in the metric does not appear in the potential V, and q can be viewed as an integration constant of the solution
Fixing k = 1 or k = −1, the parameter q appears in the scalar potential and cannot be viewed as an integration constant of the solution any longer
Summary
We consider a class of EMD theories in general dimensions D. As we shall see later, the parameter q turns out to be an integration constant and can be viewed as the scalar hair parameter or the scalar “charge” We will reversely engineer the relevant scalar potential V (φ) and the coupling function Z (φ) and construct static black holes with dilaton φ and the metric function σ given by (9) and (11) respectively. Using the remaining equations of motion, we can straightforwardly determine the scalar potential V , as a function of r. It is important to note that the parameter q that appears in the metric does not appear in the potential V , and q can be viewed as an integration constant of the solution. We have chosen the gauge such that the electric potential vanishes at asymptotic infinity
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
