Reissner-Nordström black holes and mass inflation

The existence and structure of black holes are derived from Einstein’s general theory of relativity. Mass inflation (an increase in mass) is found when the internal structure of black holes is studied. The objective of the present study is two-fold: (i) to obtain an understanding of the nature of Reissner-Nordström black holes and (ii) examine the mass inflation phenomenon. To do so, spherical symmetric solutions to Einstein’s field equations are analyzed.The Schwarzschild solution is analyzed to show the most basic result of general relativity. The analytical (Kruskal) continuation of the Schwarzschild solution and the mechanism of gravitational collapse are also discussed. The Reissner-Nordström metric is then examined in detail analyzing both the general characteristics and the most generic field equations for a body with spherical symmetry. Moreover two important applications are considered: the Vaidya solutions and the Dray-’t Hooft-Redmount (DTR) relation. The mass inflation phenomenon is then formulated by formally integrating Einstein’s field equations considering continuous infalling and outgoing radial fluxes of gravitational radiation. To evaluate the growth rate of the gravitational mass, a formal perturbation expansion in terms of the product of the flux luminosities is developed. Finally, the possibility that the asymmetries occurring during a realistic collapse could change the conclusions obtained for spherical symmetry is considered. The most striking features of the physics behind black holes and the mass inflation phenomenon are shown.