How Penrose Diagrams are used part1(Topology +Cosmology)
- Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole system(arXiv)
Author : Susovan Maity, Md Arif Shaikh, Pratik Tarafdar, Tapas K. Das
Abstract : or general relativistic, inviscid, axisymmetric flow around Kerr black hole one may choose different flow thickness. The stationary flow equations can be solved using methods of dynamical system to get transonic accretion flows , i.e, flow infalling in the blackhole that turns supersonic from subsonic with decreasing radial distance, or vice versa. This transonic flows are obtained by choosing the particular flow passing through critical points of phase portrait. For certain flow thickness like the one maintaining conical shape, the sonic point coincide with the critical point. But there are certain flows maintaining hydrostatic equilibrium, such as the one described by Novikov-Thorne, where the sonic point is not same as the critical point. We perturb the flow for both kind of flow and study the behaviour of linear perturbation which behaves like massless scalar field in some curved spacetime, known as, analogue space time. We draw the compactified causal structure, i.e, Penrose Carter diagram for both kind of analogue metric and prove that for both cases critical points are the acoustic horizons, whereas in the case where sonic points do not coincide with critical points, the sonic points are not the acoustic horizon, as one may expect from the definition of sound speed.
2. Algorithms for the explicit computation of Penrose diagrams(arXiv)
Author : J C Schindler, A Aguirre
Abstract : An algorithm is given for explicitly computing Penrose diagrams for spacetimes of the form ds2=−f(r)dt2+f(r)−1dr2+r2dΩ2. The resulting diagram coordinates are shown to extend the metric continuously and nondegenerately across an arbitrary number of horizons. The method is extended to include piecewise approximations to dynamically evolving spacetimes using a standard hypersurface junction procedure. Examples generated by an implementation of the algorithm are shown for standard and new cases. In the appendix, this algorithm is compared to existing methods.
