Solar system tests in constraining parameters of dyon black holes

Abstract

In the present paper we examine the possibility of constraining dyon black holes based on the available observational data at the scale of the Solar system. For this we consider the classical tests of general relativity, viz., the perihelion precession of the planet Mercury and the deflection of light by the Sun. In connection to mathematical analysis we are considering static and spherically symmetric dyon black hole which carries both the electric and magnetic charge simultaneously, which are encoded it by the parameters λ 0 and β 0 . We constrain these two parameters using the Solar system tests and obtain the permissible range from theoretical analysis based on our model and later on compare them with the available observational data.

Scattering and absorption of a scalar field impinging on a charged black hole in the Einstein-Maxwell-dilaton theory

“…where is the Laplace-Beltrami operator on curved spacetime M = R × Σ 3 and g is the metric determinant. It is convenient to mention that the solutions of (20) have associated an inner Klein-Gordon product defined by [2], [3]…”

“…its components include the number density of the field, J t , along with the current densities, J i . The general solution to equation (20) for the spherically symmetric dilatonic charged balck hole background can be found using the separation of variables method, that is, we propose the following ansatz…”

“…The spacetime variables cover the exterior of black hole, namely, 2M < r < ∞, 0 < t < ∞, 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π. Substituting (23) in (20) we obtain the master equation for the radial solution (24) where the prime stands for derivatived w.r.t. the radial coordinate.…”

“…We also check that the general shape of the potential does not change as M e increases, at least for large x/M , but V eff becomes negative near the horizon provided the electric contribution seems to dominate over the gravitational terms [cf. (20)]. In order to solve the Regge-Wheeler equation ( 66) we must add some boundary conditions for the radial modes at the end of the interval.…”