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"Exploring New Physics Frontiers Through Numerical Relativity"
Vitor Cardoso and Leonardo Gualtieri and Carlos Herdeiro and Ulrich Sperhake
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Abstract
Acronyms
Notation and conventions
1
Prologue
2
Milestones
3
Strong Need for Strong Gravity
3.1
Astrophysics
3.2
Fundamental and mathematical issues
3.3
High-energy physics
4
Exact Analytic and Numerical Stationary Solutions
4.1
Exact solutions
4.2
Numerical stationary solutions
5
Approximation Schemes
5.1
Post-Newtonian schemes
5.2
Spacetime perturbation approach
5.3
The zero-frequency limit
5.4
Shock wave collisions
6
Numerical Relativity
6.1
Formulations of the Einstein equations
6.2
Higher-dimensional NR in effective “3 + 1” form
6.3
Initial data
6.4
Gauge conditions
6.5
Discretization of the equations
6.6
Boundary conditions
6.7
Diagnostics
7
Applications of Numerical Relativity
7.1
Critical collapse
7.2
Cosmic censorship
7.3
Hoop conjecture
7.4
Spacetime stability
7.5
Superradiance and fundamental massive fields
7.6
High-energy collisions
7.7
Alternative theories
7.8
Holography
7.9
Applications in cosmological settings
8
Conclusions
Acknowledgements
References
Footnotes
Figures
![R¯ = (D − 4)(¯∇ ∂ ψ − ∂ ψ ∂ ψ ) − Λ ¯g , (86 ) 2¯μψ¯ν[ ¯μ ν¯ ¯μ ¯μ¯μ ¯ν ] ¯μ¯ν e (D − 4 )∂ ψ∂μ¯ψ + ¯∇ ∂¯μψ − Λ = (D − 5). (87 )](article709x.gif)