General relativity in (1 + 1) dimensions

General relativity in (1 + 1) dimensions

We describe a theory of gravity in (1 + 1) dimensions that can be thought of as a toy model of general relativity. The theory should be a useful pedagogical tool, because it is mathematically much simpler than general relativity but shares much of the same conceptual structure; in particular, it gives a simple illustration of how gravity arises from spacetime curvature. We derive the theory fro...

Numerical Relativity in 3+1 Dimensions

Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest are briefly reviewed: binary black hole mergers, the evolution of strong gravitational waves, and shift conditions for neutron star binaries.

Relativity Principles in 1+1 Dimensions and Differential Aging Reversal

We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient β, special relativity being recovered for β = 0. The effect of differential aging is studied for the different values of β. Below the cr...

3 + 1 General Relativity In Hyperbolic Form

Hydrodynamic simulations in 3¿1 general relativity

We solve Einstein’s field equations coupled to relativistic hydrodynamics in full 311 general relativity to evolve astrophysical systems characterized by strong gravitational fields. We model rotating, collapsing and binary stars by idealized polytropic equations of state, with neutron stars as the main application. Our scheme is based on the Baumgarte-Shapiro-Shibata-Nakamura formulation of th...