Apparent horizons in simplicial Brill wave initial data

Gentle, Adrian P.; Holz, D. E.; Miller, Warner A.; Wheeler, John Archibald

doi:10.1088/0264-9381/16/6/326

Cited by 15 publications

(37 citation statements)

References 8 publications

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“…Nontrivial results include e.g. Kasner universe, Brill waves, binary black holes, FLRW universe [27,[31][32][33][34]. A key observation in the convergence results is that the deviation of Regge calculus from general relativity is the non-commutativity of rotations in the discrete theory, while the error from the non-commutativity is of higher order in edge lengths [36].…”

Section: Semiclassical Continuum Limitmentioning

confidence: 99%

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Han

2017

Phys. Rev. D

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In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of Einstein equation can be approached by dominant configurations in spinfoam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spinfoam formulation, and how to take advantage of it.

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Section: Semiclassical Continuum Limitmentioning

confidence: 99%

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Han

2017

Phys. Rev. D

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“…[48], we take as initial data a pure gravitational wave data set, based on the axisymmetric ansatz of Brill [49], and later studied by Eppley [45,50,51] and others [52,53]. The metric takes the form…”

Section: Gravitational Wave Spacetimesmentioning

confidence: 99%

Symmetry Without Symmetry: Numerical Simulation of Axisymmetric Systems Using Cartesian Grids

Alcubierre

Brandt

Brügmann

et al. 2001

Int. J. Mod. Phys. D

151

188

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We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3 + 1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x, y, z) coordinate grid which covers (say) the y = 0 plane, but is only one finite-difference-molecule-width thick in the y direction. The field variables in the central y = 0 grid plane can be updated using normal (x, y, z)-coordinate finite differencing, while those in the y = 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3 + 1 numerical general relativity, involving both black holes and collapsing gravitational waves.

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“…It is accepted in the literature that no gravitational wave (GW) (Misner et al, 1973;Thorne, 1980a,b) passes a spacetime region without leaving its fingerprints in this region (Brill and Lindquist, 1963;Eppley, 1977;Tipler, 1980;Urtsever, 1988a,b;Beig and Murchadha, 1991;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). As emphasized in Urtsever (1988a,b) each GW is characterized by its own intrinsic spacetime the geometry of which is imprinted upon the passed region in the sense that its geometry assume the same form as that of the GW.…”

Section: Introductionmentioning

confidence: 99%

“…As emphasized in Urtsever (1988a,b) each GW is characterized by its own intrinsic spacetime the geometry of which is imprinted upon the passed region in the sense that its geometry assume the same form as that of the GW. The imprinted geometry may be either stable for a long time if the relevant GW is strong or transient if it is weak (Eppley, 1977;Beig and Murchadha, 1991;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). This geometry is, theoretically, traced and located in the related trapped surface (Brill and Lindquist, 1963;Eppley, 1977;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981).…”

Section: Introductionmentioning

confidence: 99%

“…The imprinted geometry may be either stable for a long time if the relevant GW is strong or transient if it is weak (Eppley, 1977;Beig and Murchadha, 1991;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). This geometry is, theoretically, traced and located in the related trapped surface (Brill and Lindquist, 1963;Eppley, 1977;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). Among the different kinds of these surfaces one may find either the singular trapped ones (Eppley, 1977;Tipler, 1980;Urtsever, 1988a,b;Abrahams and Evans, 1992) or the nonsingular ones (Beig and Murchadha, 1991) which are related to the regular and asymptotically flat initial data (Misner et al, 1973;Eppley, 1977;Brill, 1959Brill, , 1964Brill and Hartle, 1964;Arnowitt et al, 1962;Nakamura, 1984) in vacuum.…”

Section: Introductionmentioning

confidence: 99%

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