Numerical Relativity

This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.

Contents:

• Preliminaries for Numerical Relativity

• Methodology:

  • Formulation for Initial-Value Problems of General Relativity
  • Numerical Methods for a Solution of Einstein's Evolution Equation
  • Matter Equations in General Relativity
  • Formulations for Initial Data, Equilibrium, and Quasi-Equilibrium
  • Extracting Gravitational Waves
  • Finding Black Holes

• Applications:

  • Coalescence of Binary Compact Objects
  • Gravitational Collapse to a Black Hole
  • Non-Radial Instability and Magnetohydrodynamics Instability
  • Higher-Dimensional Simulations
  • Conclusion

• Appendices:

  • Killing Vector and Frobenius' Theorem
  • Numerical Relativity in Spherical Symmetry
  • Decomposition by Spherical Harmonics
  • Lagrangian and Hamiltonian Formulations of General Relativity
  • Solutions of Riemann Problems in Special Relativistic Hydrodynamics
  • Landau–Lifshitz Pseudo Tensor
  • Laws of Black Hole and Apparent Horizon
  • Post–Newtonian Results for Coalescing Compact Binaries

Readership: This book is suitable for advanced ungraduate students, postgraduate students and researchers who are interested in numerical relativity.