An Analysis on the Membrane Paradigm of Black Holes

Ağca, Çağdaş Ulus
Since the inside of the black hole is not available for an observer outside, one can construct a fake or stretched horizon just outside the true horizon with similar properties. A fiducial observer sees it as a time-like hypersurface, a.k.a a membrane, which has no pathologies in the kinds of the true horizon. The stretched horizon is indeed a D-1 dimensional time-like surface. This surface can be linked through the true horizon by ingoing null congruence as an injection. Since it is not null by nature, it has a non-singular metric on it which brings a healthy approximation to the behaviour of the true horizon. This approach to black hole dynamics was pinned with the name "Membrane Paradigm of Black Holes". The paradigm is known to be valid for static and rotating black holes. We have tested the theory with different conserved charges allowed by the no-hair theorem. Moreover, we test it by using the Johannsen-Psaltis black hole. It is a deviation from the Kerr metric. This metric has no pathology up to higher spin solutions with a set of parameters that clearly indicates linear parametric deviations from the Kerr metric. They have the same metric structure as Kerr in Boyer-Lindquist coordinates such that geodesic tests are also comparable with the Kerr Spacetime.
Citation Formats
Ç. U. Ağca, “An Analysis on the Membrane Paradigm of Black Holes,” M.S. - Master of Science, Middle East Technical University, 2023.