Richard Feynman, one of the great physicists of the twentieth century, gave a series of lectures for the general public in 1964 that delved deeply into the nature of the laws that control our universe. He wrote up his lectures in one of my favorite books of all time, The Character of Physical Law (Feynman 1965). For a more detailed, more up-to-date, and much longer book on the same topic, see The Fabric of the Cosmos: Space, Time, and the Texture of Reality (Greene 2004). Easier going, perhaps more fun, and equally deep is The Grand Design (Hawking and Mlodinow 2010).
Chapter 4. Warped Time and Space, and Tidal GravityFor historical details on Einstein’s concepts of warped time and space, their connection to tidal gravity, and his relativistic laws built on these concepts, see Chapters 1 and 2 of Black Holes & Time Warps: Einstein’s Outrageous Legacy (Thorne 1994); and for a plethora of experiments that show Einstein was right, see Was Einstein Right? Putting General Relativity to the Test (Will 1993). “Subtle Is the Lord…”: The Science and the Life of Albert Einstein (Pais 1982) is a biography of Einstein that focuses in depth on all of Einstein’s contributions to science; it’s much tougher going and much more scholarly than Thorne or Will. There are other, more comprehensive biographies of Einstein—I especially like Einstein: His Life and Universe (Isaacson 2007)—but no other biography treats Einstein’s science with anything approaching the accuracy and detail of Pais.
Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity (Schutz 2003) is an in-depth discussion of gravity and its roles in our universe (both Newtonian gravity and Einstein’s warped spacetime), written for the general reader. For the same material at the level of an advanced undergraduate physics or engineering student, I like the textbooks by James Hartle, Gravity: An Introduction to Einstein’s General Relativity (Hartle 2003), and by Bernard Schutz, A First Course in General Relativity (Schutz 2009).
Chapter 5. Black HolesFor greater detail on black holes and how we came to know the things we think we know about them, I suggest Gravity’s Fatal Attraction: Black Holes in the Universe (Begelman and Rees 2009), Black Holes & Time Warps (Thorne 1994), and a lecture that I gave in 2012 at Stephen Hawking’s seventieth birthday party: http://www.ctc.cam.ac.uk/hawking70/multimedia_kt.html. Andrea Ghez describes her team’s wonderful discoveries about the black hole at the center of our Milky Way Galaxy in a Ted talk at http://www.ted.com/speakers/andrea_ghez and on her team’s website, http://www.galacticcenter.astro.ucla.edu.
Chapter 6. Gargantua’s AnatomyFor properties of black holes that are featured in this chapter, see Chapter 7 of Black Holes & Time Warps (Thorne 1994), especially pp. 272–295; and at a more technical level, with equations, Gravity: An Introduction to Einstein’s General Relativity (Hartle 2003). Also see the appendix Some Technical Notes in this book. For the shell of fire and the orbits of photons temporarily trapped in it, see Edward Teo’s technical paper (Teo 2003).
Chapter 7. Gravitational SlingshotsFor a discussion of gravitational slingshots at a modestly more technical level than mine, I recommend the Wikipedia article http://en.wikipedia.org/wiki/Gravity_assist. But don’t believe what it says about slingshots around black holes. Its statement (as of July 4, 2014) that “if a spacecraft gets close to the Schwarzschild radius [horizon] of a black hole, space becomes so curved that slingshot orbits require more energy to escape than the energy that could be added by the black hole’s motion” is just plain wrong. Indeed, you should always read Wikipedia with some cautious skepticism. In my experience, in areas where I am an expert, roughly 10 percent of Wikipedia’s statements are wrong or misleading.