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Multi-black-hole gravitational field
Klimešová, Eliška ; Žofka, Martin (advisor) ; Kubizňák, David (referee)
We study dynamics of an extremally charged black hole on the background of two stationary, mutually orbiting extremally charged black holes, forming thus a seed binary system. We extend the two-body perturbative solution of vacuum Einstein-Maxwell equations, known from literature, to the three body system. Restricting to slow-motion approximation and motion at a large distance, we de- rive the corresponding three-body Lagrangian and investigate limits of evolution of little- and large-mass black hole. Motivated by physical intuition and in order to check our results, we compare the former with solution of geodesic equation of an extremally charged test-body on identical background. Our results mainly consist of interpretation and comparison of characteristic motions. 1
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Properties of multi black-hole spacetimes
Klimešová, Eliška ; Žofka, Martin (advisor) ; Tahamtan, Tayebeh (referee)
In Newtonian physics, a system of extremally charged particles (electric charge equal to gravitational mass in geometrized units) remains in a static equilibrium until an external force is applied. This situation, surprisingly, translates exactly to general relativity in the case of extremely charged black holes, as was inde- pendently shown by Sudhansu Datta Majumdar and Achilles Papapetrou in 1947. Moreover, if the system is perturbed, giving the black holes small initial velocities vi ≪ c, it can be described by a metric first discussed by Robert Craig Ferrell and Douglas Michael Eardley in 1987. We examine whether it is possible to arrive at the perturbed metric in some special cases, such as boosting or spinning up the original static metric. We further study the case of two inter- acting black holes, which is equivalent to a classical mechanics problem with a special Lagrangian. We discuss the critical impact parameter separating cases of coalescing and scattering black holes as they spiral closer together from infinity. We find the critical value as a function of the ratio of the black holes' masses. Finally, we compare the limiting case where one of the holes is much heavier than the other to a trajectory of an extremally charged test particle in extremal Reissner-Nordstr¨om. 1
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