Gravitational Lensing in Spacetimes

This unique monograph provides a rigorous, unified, exposition of gravitational lensing in spacetimes with matter, dark energy, and black holes Can be used as a text for a graduate course or advanced undergraduate seminar Should be of interest to interdisciplinary researchers in mathematics, mathematical physics, astrophysics, cosmology, and general relativity Petters' work has been celebrated in NYTimes and Duke articles

Gravitational lensing occupies a central role in astrophysics and cosmology. It addresses some of the most pressing scientific issues: determining the nature of dark matter, constraining the cosmological constant and evolving dark energy, estimating Hubble's constant, and testing Einstein's general theory of relativity using the Galactic black hole. All these topics are treated in the book. This unique monograph provides a rigorous, unified, exposition of gravitational lensing in spacetimes with matter (ordinary and dark matter), cosmological constant and evolving dark energy, and black holes (includes rotating black holes with accretion disks). Emphasis is placed on the rigorous analytical aspects of the subject, while at the same time introducing general relativity. This work can be used as a text for a graduate level course or advanced undergraduate seminar in General Relativity or Gravitational Lensing. The work is interdisciplinary and should be of interest to researchers in mathematics, mathematical physics, astrophysics, cosmology, and general relativity.

Preface.- General Relativity.- Cosmology.- Gravitational Lensing.- Universal Theorems on Gravitational Lensing.- Matter, Dark Matter, and Dark Energy Lensing.- Schwarzschild Black Hole.- Kerr Black Hole.- Black Hole Lensing.- Appendix A: Tensor Fields.- Appendix B: Lorentzian Geometry.- Index.