Dilatonic interpolation between Reissner–Nordström and Bertotti–Robinson spacetimes with physical consequences

Abstract

We give a general class of static, spherically symmetric, non-asymptotically flat and asymptotically non-(anti) de Sitter black hole solutions in Einstein-Maxwell-Dilaton (EMD) theory of gravity in 4-dimensions. In this general study we couple a magnetic Maxwell field with a general dilaton potential, while double Liouville-type potentials are coupled with the gravity. We show that the dilatonic parameters play the key role in switching between the Bertotti-Robinson and Reissner-Nordström spacetimes. We study the stability of such black holes under a linear radial perturbation, and in this sense we find exceptional cases that the EMD black holes are unstable.In continuation we give a detailed study of the spin-weighted harmonics in dilatonic Hawking radiation spectrum and compare our results with the previously known ones. Finally, we investigate the status of resulting naked singularities of our general solution when probed with quantum test particles.We revisit the 4−dimensional Einstein-Maxwell-Dilaton (EMD) theory and show that there are still plenty of rooms available to contribute the subject. Double Liouville potential and general dilaton coupling is considered to obtain more general solutions with extra parameters and diagonal metric in the theory. From the outset we remind that, depending on the relative parameters, the double Liouville potential has the advantage of admitting local extrema and critical points. The Higgs potential also shares such features, whereas single Liouville potential lacks these properties. Double Liouville-type potentials arise also when higher-dimensional theories are compactified to 4−dimensional spacetimes and expectedly bring in further richness. All known solutions to date can be obtained [1-3] as particular limits of our general solution, and it contains new solutions as well. In the most general form our solution covers Reissner-Nordstrom (RN) type black holes and Bertotti-Robinson (BR) spacetimes interpolated within the same metric. Interpolation of two different solutions in general relativity is not a new idea [4]. Particular limits of the dilatonic parameter yield the RN and BR spacetimes. In between the two, the linear dilaton black hole (LDBH) lies for the specific choice of the parameters. It is well-known that the near horizon geometry of the extremal RN black hole yields the BR electromagnetic universe. The latter [5] is important for various reasons: It is a singularity free non-black hole solution which admits maximal symmetry and finds application in conformal field theory correspondence (i.e. AdS/ CFT). Particles in the BR universe move with uniform acceleration in a conformally flat background. These features are mostly valid not only in N = 4 but in higher dimensions (N > 4) as well. The topological structure of the BR spacetime is still AdS 2 × S N −2 in N−dimensions with the radius of S N −2 depending on the dimension of the space. Recently we have extended the Maxwell part of the BR spacetime to cover the Yang-Mills (YM) field and obtained common feature...

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