# Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks

@article{Alcubierre2002HyperbolicSO, title={Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks}, author={Miguel Alcubierre}, journal={Classical and Quantum Gravity}, year={2002}, volume={20}, pages={607-623} }

I study the Bona–Masso family of hyperbolic slicing conditions, considering in particular its properties when approaching two different types of singularities: focusing singularities and gauge shocks. For focusing singularities, I extend the original analysis of Bona et al and show that both marginal and strong singularity avoidance can be obtained for certain types of behaviour of the slicing condition as the lapse approaches zero. For the case of gauge shocks, I rederive a condition found…

## 42 Citations

Stationary hyperboloidal slicings with evolved gauge conditions

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We analyze stationary slicings of the Schwarzschild spacetime defined by members of the Bona–Massó family of slicing conditions. Our main focus is on the influence of a non-vanishing offset to the…

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We study how different types of blowups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be…

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We present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift…

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While the 1+log slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop “gauge-shocks” in some examples. Alternative “shock-avoiding”…

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- 2011

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## References

SHOWING 1-10 OF 26 REFERENCES

Appearance of coordinate shocks in hyperbolic formalisms of general relativity

- Physics
- 1997

I consider the appearance of shocks in hyperbolic formalisms of General Relativity. I study the particular case of the Bona-Masso formalism with zero shift vector and show how shocks associated with…

NUMERICAL RELATIVITY: EVOLVING SPACETIME

- Physics
- 1993

The construction of numerical solutions of Einstein's General Relativity equations is formulated as an initial-value problem. The space-plus-time (3 + 1) decomposition of the spacetime metric tensor…

Horizon boundary condition for black hole spacetimes.

- PhysicsPhysical review. D, Particles and fields
- 1995

The details of the implementation of a horizon boundary condition scheme based on using a horizon locking coordinate which locks the coordinate system to the geometry, and a finite differencing scheme which respects the causal structure of the spacetime are reported.

Kinematical conditions in the construction of spacetime

- Physics
- 1978

We adopt the point of view that a solution of Einstein's equations is an evolution of given initial Cauchy data. Implementing the evolution equations necessarily requires a determination, not…

Towards a singularity-proof scheme in numerical relativity.

- PhysicsPhysical review letters
- 1992

A scheme which excises a region inside an apparent horizon containing the singularity through the use of a horizon-locking coordinate and a finite differencing which respects the causal structure of the spacetime.

Coordinates and boundary conditions for the general relativistic initial data problem

- Physics
- 1987

Using York's method, the author discusses techniques for numerically constructing GR initial data on a Cauchy surface representing spacetimes containing arbitrary numbers of black holes, each with…

New formalism for numerical relativity.

- Mathematics, PhysicsPhysical review letters
- 1995

A new formulation of the Einstein equations is presented that casts them in an explicitly first order, flux-conservative, hyperbolic form, which permits the application to the Einstein equation of advanced numerical methods developed to solve the fluid dynamic equations, for the first time.

Fixing Einstein's equations

- Mathematics
- 1999

Einstein's equations for general relativity, when viewed as a dynamical system for evolving initial data, have a serious flaw: they cannot be proven to be well-posed (except in special coordinates).…

Three-dimensional numerical relativity: The evolution of black holes.

- PhysicsPhysical review. D, Particles and fields
- 1995

It is shown how special treatment of the conformal factor can lead to more accurate evolution, and techniques to handle black hole spacetimes in the absence of symmetries are discussed, which can prevent the development of large gradients in the metric functions that result from singularity avoiding time slicings.

Black Hole Excision for Dynamic Black Holes

- Physics
- 2001

We extend the previous work on 3D black hole excision to the case of distorted black holes, with a variety of dynamic gauge conditions that respond naturally to the spacetime dynamics. We show that…