The Initial Value Formulation of Dynamical Chern-Simons Gravity
arXiv:1407.6727 · doi:10.1103/PhysRevD.91.024027
Abstract
We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but the full field equations are in no sense hyperbolic. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.
16 pages; matches published version
References in corpus (15)
- The Confrontation between General Relativity and Experiment
- A Massive Pulsar in a Compact Relativistic Binary
- LIGO: The Laser Interferometer Gravitational-Wave Observatory
- Dynamical Chern-Simons Modified Gravity I: Spinning Black Holes in the Slow-Rotation Approximation
- Non-Spinning Black Holes in Alternative Theories of Gravity
- The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
- Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity
- How do Black Holes Spin in Chern-Simons Modified Gravity?
- Interaction of the Barbero--Immirzi Field with Matter and Pseudo-Scalar Perturbations
- Testing Chern-Simons Modified Gravity with Gravitational-Wave Detections of Extreme-Mass-Ratio Binaries
- Perturbations of Schwarzschild Black Holes in Chern-Simons Modified Gravity
- Causal Structures in Gauss-Bonnet gravity
- Rapidly rotating black holes in dynamical Chern-Simons gravity: Decoupling limit solutions and breakdown
- Scalar field excited around a rapidly rotating black hole in Chern-Simons modified gravity
- Anti de Sitter black holes and branes in dynamical Chern-Simons gravity: perturbations, stability and the hydrodynamic modes