相关论文: Hyperbolic slicings of spacetime: singularity avoi…
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 two families of characteristic fields can…
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" slicing conditions suggested by…
We study the properties of a modified version of the Bona-Masso family of hyperbolic slicing conditions. This modified slicing condition has two very important features: In the first place, it guarantees that if a spacetime is static or…
We analyze stationary slicings of the Schwarzschild spacetime defined by members of the Bona-Masso family of slicing conditions. Our main focus is on the influence of a non-vanishing offset to the extrinsic curvature, which forbids the…
We consider several families of functions $f(\alpha)$ that appear in the Bona-Masso slicing condition for the lapse function $\alpha$. Focusing on spherically symmetric and time-independent slices we apply these conditions to the…
The family of generalized-harmonic gauge conditions, which is currently used in Numerical Relativity for its singularity-avoidant behavior, is analyzed by looking for pathologies of the corresponding spacetime foliation. The appearance of…
While numerous numerical relativity simulations adopt a 1+log slicing condition, shock-avoiding slicing conditions form a viable and sometimes advantageous alternative. Despite both conditions satisfying similar equations, recent numerical…
The existence of gauge pathologies associated with the Bona-Masso family of generalized harmonic slicing conditions is proven for the case of simple 1+1 relativity. It is shown that these gauge pathologies are true shocks in the sense that…
In numerical relativity, spacetimes involving compact strongly gravitating objects are constructed as numerical solutions of Einstein's equations. Success of such a process strongly depends on the availability of appropriate coordinates,…
A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an…
We examine spacetimes which generalize Lifshitz scaling to allow hyperscaling violation invariance (i.e. a constant conformal transformation) for the types of singularities frequently found in the Lifshitz case. We find that most of these…
We present new many-parameter families of strongly and symmetric hyperbolic formulations of Einstein's equations that include quite general algebraic and live gauge conditions for the lapse. The first system that we present has 30 variables…
We show that the Kidder-Scheel-Teukolsky family of hyperbolic formulations of the 3+1 evolution equations of general relativity remains hyperbolic when coupled to a recently proposed modified version of the Bona-Masso slicing condition.
We study the stability and structure of shock formation in 1D hyperbolic conservation laws. We show that shock formation is stable near shocking simple waves: perturbations form a shock nearby in spacetime. We also characterize the boundary…
It is shown that the initial singularities in spatially compact spacetimes with spherical, plane or hyperbolic symmetry admitting a compact constant mean curvature hypersurface are crushing singularities when the matter content of spacetime…
Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial…
A necessary condition for a globally hyperbolic spacetime ${\mathbb R}\times \Sigma$ to admit a maximal slice is that the Cauchy slice $\Sigma$ admit a metric with nonnegative scalar curvature, $R\ge 0$. In this paper, the two cases…
Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary…
We study the problem of the gravitational collapse of an object as seen by an external observer. We assume that the resultant spacetime is a match of an external Vaidya spacetime with an interior Friedmann-Lema\^itre-Robertson-Walker (FRLW)…
We study static black holes in scalar-Gauss-Bonnet (sGB) gravity with a massive scalar field as an example of higher curvature gravity. The scalar mass introduces an additional scale and leads to a strong suppression of the scalar field…