3+1 Formalism in General Relativity

Gourgoulhon, Éric

doi:10.1007/978-3-642-24525-1

Cited by 522 publications

(670 citation statements)

References 10 publications

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“…19 In our case, such Eulerian worldlines are in fact geodesics with affine parameter β. Indeed, the acceleration of such worldlines is given by [22]:…”

Section: Ricci-flat Asymptoticsmentioning

confidence: 99%

“…Moreover, we found that it is possible to move past such order and reconstruct the bulk metric near the surface up to very high order 20 from the knowledge of the normalizable mode g (d) . On each 19 See also section 3.3 of [22] for further details. 20 The obstacle to the reconstruction up to all orders is associated to the Fefferman-Graham coordinates (3.13) on the surface.…”

Section: Outlinementioning

confidence: 99%

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Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Costa

2012

J. High Energ. Phys.

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In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the family of CFTs and show how the asymptotics is mapped to and reconstructed from conformal field theory data. In even dimensions, the holographic Weyl anomalies identify the bulk time coordinate with the spectrum of central charges with characteristic length the bulk Planck length. Consistency with locality in the bulk time direction requires a notion of locality in this spectrum.

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“…19 In our case, such Eulerian worldlines are in fact geodesics with affine parameter β. Indeed, the acceleration of such worldlines is given by [22]:…”

Section: Ricci-flat Asymptoticsmentioning

confidence: 99%

Section: Outlinementioning

confidence: 99%

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Costa

2012

J. High Energ. Phys.

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“…the spatial metric (see, e.g., [17,22,23] for textbook introductions). In terms of the lapse and the shift, the normal vector n a on each spatial slice can be written as…”

Section: A Reference-metric Formulation Of the Bssn Equationsmentioning

confidence: 99%

“…In these coordinates, the black-hole horizon is located at a coordinate distance r hor = 0.779M away from the black hole's center. We evolve these data with the non-advective 1+log slicing (17) and Gamma driver condition (20), using the analytical values for the lapse and shift as initial data. Analytically, the resulting evolution should result in all metric components remaining time-independent; any evolution away from the initial data is therefore caused by numerical error.…”

Section: Off-centered Schwarzschild Black Holesmentioning

confidence: 99%

“…We set up the initial data as a relativistic poly- , while the isotropic radius is r = 0.700 = 4.46M . We evolve this star with nonadvective 1+log slicing (17) and zero shift, so that, analytically, the star should remain static. Any deviation from the initial data is therefore a measure of the numerical error.…”

Section: Off-centered Tolman-oppenheimer-volkoff Starsmentioning

confidence: 99%

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Numerical relativity in spherical polar coordinates: Off-center simulations

Baumgarte¹,

Montero

Müller

2015

Phys. Rev. D

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We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system. 04.25.dg, 95.30.Lz, 97.60.Lf

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Canonical formulation of spin in general relativity

Steinhoff

2011

Annalen der Physik

143

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The present thesis aims at an extension of the canonical formalism of Arnowitt, Deser, and Misner from self-gravitating point-masses to objects with spin. This would allow interesting applications, e.g., within the post-Newtonian (PN) approximation. The extension succeeded via an action approach to linear order in the single spins of the objects without restriction to any further approximation. An orderby-order construction within the PN approximation is possible and performed to the formal 3.5PN order as a verification. In principle both approaches are applicable to higher orders in spin. The PN next-toleading order spin(1)-spin(1) level was tackled, modeling the spin-induced quadrupole deformation by a single parameter. All spin-dependent Hamiltonians for rapidly rotating bodies up to and including 3PN are calculated.

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3+1 Formalism in General Relativity

Cited by 522 publications

References 10 publications

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Numerical relativity in spherical polar coordinates: Off-center simulations

Canonical formulation of spin in general relativity

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