Figure 21

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"Exploring New Physics Frontiers Through Numerical Relativity"

Vitor Cardoso and Leonardo Gualtieri and Carlos Herdeiro and Ulrich Sperhake

	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

Figure 21: Left panel: Collision of two shock waves in AdS₅. The energy density $4 ℰ ∕μ$ is represented as a function of an (advanced) time coordinate $v$ and a longitudinal coordinate $z$ . $μ$ defines the amplitude of the waves. Right panel: Evolution of the scalar field in an unstable RN-AdS BH. $z$ is a radial coordinate and the AdS boundary is at $z = 0$ . Due to the instability of the BH, the scalar density grows exponentially for $0 < tTc ≲ 6$ . Then, the scalar density approaches some static function. Images reproduced with permission from (left) [207], copyright by APS and (right) [562], copyright by SISSA.