Artificial gravity field

Using computer algebra to run Einstein’s equations “backward”, from field to source rather than from source to field, we design an artificial gravity field for a space station or spaceship. Everywhere inside astronauts experience normal Earth gravity, while outside they float freely. The stress-energy that generates the field contains exotic matter of negative energy density but also relies importantly on pressures and shears, which we describe. The same techniques can be readily used to design other interesting spacetimes and thereby elucidate the connection between the source and field in general relativity.