A review of some elementary Causal structures in Astrophysics

We will consider how we model Causal structures for three very specific models: a Black hole system, wherein we will consider two examples, a Schwarzschild Black hole and the Nordstrom model. Then, we will consider the Causal structure of models, considering the underlying Singularity theorems that help us to model a "realistic" Cosmological model. Here, we will consider the Raychaudari theorem, the Penrose theorem, and the Hawking Penrose theorem and study how these beautifully show that the origin of a non-static accelerating universe is from a Singularity. We will construct the Penrose diagrams initially, so that we can eventually model the Schwarzschild Black hole and the Nordstrom model, and then talk about Singularity theorems in Cosmology. Then, we will talk about CTCs, or Closed Time-like Curves because the Causal Structure of a universe can also model the possibility of CTCs. An example is the Godel's universe. Throughout, we have only considered the Raychaudari expansion, the Time-like convergence condition and the three Energy Conditions, the weak, the strong and the generic conditions