The Biggest Ideas in the Universe: Space, Time, and Motion

by Sean Carroll

energy can be transferred back and forth between matter and the curvature of spacetime.

. (8.18) The combination on the left-hand side is the Einstein tensor.

mathematically equivalent: Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics.

General relativity is an example of a field theory, since the metric tensor gµv(t, xi) is a field that has a value at each point in spacetime, rather than a particle that has a location somewhere.

. (9.6) Isn’t it gorgeous? That’s the exact solution to Einstein’s equation in empty space with spherical symmetry. In

r = 2GM. (9.9) This is indeed an important quantity, known as the Schwarzschild radius.

That means that moving to smaller r, inside the event horizon of a Schwarzschild black hole, is moving forward in time.

Reissner–Nordström solution, which was derived soon after the Schwarzschild solution by a number of people. That’s not so surprising; since everything is still spherically symmetric, the solution isn’t all that different from Schwarzschild. At least on the outside. The Reissner–Nordström solution, taken at face value and pushed as far as it can go, describes an infinite series of black holes connecting separate universes, all hidden behind the event horizon.