Figure 18

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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 18: Trajectories of BHs immersed in a scalar field bubble of different amplitudes. The BH binary consists of initially non-spinning, equal-mass BHs in quasi-circular orbit, initially separated by $11M$ , where $M$ is the mass of the binary system. The scalar field bubble surrounding the binary has a radius $r0 = 120M$ and thickness $σ = 8M$ . Panels $A, B, C$ correspond to $φ0 = 0(GR ),1∕80,1 ∕40$ and a zero potential amplitude $λ$ . Panel $D$ corresponds to $3 2 φ0 = 1∕80, 4πλ = 10 M$ . Image reproduced with permission from [410], copyright by IOP. All rights reserved.