This
book concludes our exploration of the most profound theory of science,
Einstein’s General Theory of Relativity.
All of modern astrophysics and cosmology stands on
the foundation of General Relativity that is best expressed in tensors.
This book, and its prequel General Relativity 3, present the
clearest, most comprehensible, and most complete introduction to the
tensor calculus of differential topology, which Einstein used to
explain the cosmos. Derivations that are difficult to find elsewhere,
are all collected here and explained in detail.
This book explores:

photon
orbits around black holes

the
black hole mirror effect

framedragging
near rotating black holes

Riemann
normal coordinates and Riemann symmetries

the
Bianchi Identity

how
energy and momentum conservation are tied to the geometry of spacetime

the
tensors of relativistic electromagnetism

the
structure of relativistic stars, including neutron stars

and
the FRW expansion equation of the universe
All this using the tensor calculus of General
Relativity.
Example

In the image above, the dotted circle represents
a black
hole’s event horizon and the black dot represents its singularity.
Consider the fate of a photon emitted just outside a black hole’s event
horizon. If its initial trajectory points directly toward the
singularity, the photon will plummet into oblivion; if it points in
exactly the opposite direction, the photon will escape. Where is the
dividing line separating oblivion from escape?


