Linearised conformal Einstein field equations

Feng, Justin C.; Gasperin, Edgar

doi:10.1088/1361-6382/ace606

Cited by 3 publications

(2 citation statements)

References 55 publications

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“…The hyperboloidal approach allows numerical simulations to reach future null infinity from first principles and without complicated constructions. While it needs to be further understood and developed, progress in the non-linear regime is taking place along several fronts [81,98,99] and will also benefit from work in the linear one, e.g., [100]. The focus in the present study has been on spherically symmetric hyperboloidal trumpet initial data for puncture-type evolutions of BHs.…”

Section: Discussionmentioning

confidence: 99%

Spherically symmetric black hole spacetimes on hyperboloidal slices

Vañó-Viñuales

2023

Front. Appl. Math. Stat.

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Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity (ℐ+). This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are extracted for gravitational wave modeling purposes. One promising method to include future null infinity in the numerical domain is the evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity. The main challenge in this approach is the treatment of the compactified asymptotic region at ℐ+. Evolution on a hyperboloidal slice of a spacetime including a black hole entails an extra layer of difficulty in part due to the finite coordinate distance between the black hole and future null infinity. Spherical symmetry is considered here as the simplest setup still encompassing the full complication of the treatment along the radial coordinate. First, the construction of constant-mean-curvature hyperboloidal trumpet slices for Schwarzschild and Reissner-Nordström black hole spacetimes is reviewed from the point of view of the puncture approach. Then, the framework is set for solving hyperboloidal-adapted hyperbolic gauge conditions for stationary trumpet initial data, providing solutions for two specific sets of parameters. Finally, results of testing these initial data in evolution are presented.

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Section: Discussionmentioning

confidence: 99%

Spherically symmetric black hole spacetimes on hyperboloidal slices

Vañó-Viñuales

2023

Front. Appl. Math. Stat.

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“…In the weak field limit-which is analogous to electromagnetism in the context of Maxwell's equations-the Lagrange density for the gravitational field (Given g µν = η µν + h µν and h µν 1, we consider only first order terms in the fields. This process is known as the linearization of Einstein field equations [25,26]-the source is far away from a singularity.) is,…”

Section: Fractional Gravitational Wavesmentioning

confidence: 99%

Free Fractional Gauge Fields: An Elementary Model Based on the Standard Model (SM)

Eastmond

2024

Preprint

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We study the Lagrangian density for freely propagating gauge fields on the basis of the Stan- dard Model (SM); namely its fractional counterpart. From this, we attain some free fractional Klein- Gordon equations, associated with the electromagnetic, weak, and strong forces. In addition to that, we verify that the Lagrange density is gauge invariant by virtue of the fractional Hessian condition. Also, using the fractional energy density we establish the fractional continuity equation for the freely propa- gating gauge bosons. And finally, a fractional analog of the Riemann-Silberstein vector and its equation is presented. Hence, we formulate fractional analogs of the Riemann-Silberstein and gravitoelectro- magnetic equations, which are compared to the fractional Maxwell’s equations.

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Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime

Gasperin

Pinto

2023

Journal of Mathematical Physics

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Newman–Penrose (NP) constants of massless spin-0 fields propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich’s i0-cylinder. Assuming a certain regularity condition on the initial data ensuring that the field extends analytically to critical sets, it is shown that the NP constants at future I+ and past null infinity I− are independent of each other. In other words, the classical NP constants at I± stem from different parts of the initial data given on a Cauchy hypersurface. In contrast, it is shown that, using a slight generalization of the classical NP constants, the associated quantities (i0-cylinder NP constants) do not require the regularity condition being satisfied and give rise to conserved quantities at I± that are determined by the same piece of initial data, which, in turn, correspond to the terms controlling the regularity of the field. Additionally, it is shown how the conservation laws associated with the NP constants can be exploited to construct, in flat space, heuristic asymptotic-system expansions, which are sensitive to the logarithmic terms at the critical sets.

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Linearised conformal Einstein field equations

Cited by 3 publications

References 55 publications

Spherically symmetric black hole spacetimes on hyperboloidal slices

Spherically symmetric black hole spacetimes on hyperboloidal slices

Free Fractional Gauge Fields: An Elementary Model Based on the Standard Model (SM)

Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime

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