#TITLE_ALTERNATIVE# - AHMAD HIDAYAT (NIM. 10210025); Pembimbing : Prof. Dr. rer. nat Bobby Eka Gunara, ALAM
In this final project we discuss thoroughly the motivation, interpretation, and also preliminary proof of the Penrose inequality in asymptotically flat spacetimes under spherically symmetry assumption.The rest of the proof follows directly from the method carried out by Malec and Murchadha in four dimensional case. In our case, we take for granted the method to show that the inequality also can be established even in higher dimensional spacetimes. To do so, we define a quasilocal mass in higher dimensional spacetimes which matches well with the Hawking mass in ordinary four dimensional spacetimes. Along with Einstein constraint equations, the mass plays crucial role on the proof. We also consider another method using IMCF (inverse mean curvature flow) which will be explained in detail and how it can effectively prove the Penrose inequality in Riemannian case and also restricted in four dimensional spacetimes only. The IMCF method is also used as preliminaries to study the Penrose inequality in asymptotically hyperbolic manifolds, for instance Eintein manifolds, using the modified Hawking mass with an addition of cosmological constant.