General Relativity 4: Astrophysics & Cosmology e-book

General Relativity 4:
& Cosmology

Robert L. Piccioni, Ph.D.

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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
  • frame-dragging 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.


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?

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