To search for anything in astrophysics as well as any topic in science you can use the scholar google.
As specialized in astrophysics I recommend the abstract service.
For achieving the hottest news you need to read the Archive everyday.
Note: You can use the search capability of the abstract service also for making search in the archive by including “the archive” in “databases to query” in your searches within “the abstract service.”
If you are new to a research topic, a review paper can be good place to start.
A useful resource is the Living Reviews in Relativity.
I strongly recommend the website the net advance of physics.
Need to learn General Relativity? Start
from here.
Some links to reviews on some interesting topics in astrophysics are listed below. Note that many of the pages are under construction at the moment.
Compact Objects in general
Black holes (BH)
Neutron Stars (NS) and SuperNovae (SN)
White Dwarfs (WD)
Gamma Ray Burts (GRBs)
Gravitational Waves (GW)