Almost-Killing conserved currents: A general mass function

Ruiz, Milton; Palenzuela, Carlos; Bona, Carles

doi:10.1103/physrevd.89.025011

Cited by 12 publications

(14 citation statements)

References 18 publications

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“…Fitting formula for the spindown have also been recently established depending on compactnesses and rotation speed by Carrasco et al (2018). Ruiz et al (2014) computed a full solution from the MHD stellar interior into the force-free external magnetosphere for several compactnesses. The spindown luminosities found are very similar.…”

Section: Force-free Dipolementioning

confidence: 99%

The illusion of neutron star magnetic field estimates

Pétri

2019

Monthly Notices of the Royal Astronomical Society

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Neutron stars radiate in a broad band spectrum from radio wavelengths up to very high energies. They have been sorted into several classes depending on their respective place in the P − P diagram and depending on spectral/temporal properties. Fundamental physical parameters such as their characteristic age and magnetic field strength are deduced from these primary observables. However this deduction relies mostly on interpretations based on simple vacuum or force-free rotating dipole models that are unrealistic. In this paper, we show that the computation of the stellar surface magnetic field is poorly estimated or even erroneous if multipolar components and particle loading are neglected. We show how quadrupolar magnetic field and monopolar winds alter field estimates and characteristic ages in the P − P diagram. Corrections brought by general relativity are also discussed. We derive some important parameters of pulsar physics such as the wind Lorentz factor (γ) times the pair multiplicity (κ) to be around γ κ ≈ 10 8 − 10 10 . Therefore, the standard magnetodipole radiation losses formula must be used with caution to reckon neutron star surface magnetic fields and related secular evolution parameters. Depending on models we found that all field strengths, both for magnetars and for pulsars lie below the quantum critical value of B c ≈ 4,4 · 10 9 T.

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Section: Force-free Dipolementioning

confidence: 99%

The illusion of neutron star magnetic field estimates

Pétri

2019

Monthly Notices of the Royal Astronomical Society

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“…Explicit solutions to the AKE have been constructed for some spacetimes-see the examples in [10]. In [11], a solution to the µ = 2 AKE was constructed for a Vaidya spacetime describing the emission of a spherical pulse of radiation from a star; this solution has the property that it approximately satisfies the Killing condition everywhere away from the pulse.…”

Section: Ake and Gauss Lawmentioning

confidence: 99%

“…Since then, there have been several attempts to construct approximate notions of Killing vectors, for instance the Eigenvector approach of Matzner [5], the symmetry-seeking coordinates of Garfinkle and Gundlach [6], the affine collineation approach of Harte [7], and the almost-Killing equation (AKE) [8,9], the properties of which will form the main focus of this article. The study of Komar currents constructed from solutions of the AKE was examined in [10] and [11], and we explore further the properties of Komar currents constructed from solutions of the AKE.…”

Section: Introductionmentioning

confidence: 99%

Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law

Feng¹,

Gasperin²,

Williams³

2019

Phys. Rev. D

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We examine the Hamiltonian formulation and hyperbolicity of the almost-Killing equation (AKE). We find that for all but one parameter choice, the Hamiltonian is unbounded and in some cases, the AKE has ghost degrees of freedom. We also show the AKE is only strongly hyperbolic for one parameter choice, which corresponds to a case in which the AKE has ghosts. Fortunately, one finds that the AKE reduces to the homogeneous Maxwell equation in a vacuum, so that with the addition of the divergence-free constraint (a "Lorenz gauge") one can still obtain a well-posed problem that is stable in the sense that the corresponding Hamiltonian is positive definite. An analysis of the resulting Komar currents reveals an exact Gauss law for a system of black holes in vacuum spacetimes, and suggests a possible measure of matter content in asymptotically flat spacetimes.

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“…However, Komar currents may be of limited use in certain circumstances. As discussed earlier, any globally conserved charge constructed from the Komar Fortunately, one can construct globally conserved currents that do not correspond to a Komar current-the conserved current of Ruiz et al is one example [15] (note, however, that it also vanishes in a vacuum spacetime). There is a more general class of conserved currents (containing the Komar current) defined as those formed from divergences of superpotentials; the discussion of this approach is beyond the scope of this article, and I refer the reader to [5,21,22] and references contained therein.…”

Section: Globally Conserved Non-komar Currents From Scalar Test Fimentioning

confidence: 99%

Some globally conserved currents from generalized Killing vectors and scalar test fields

Feng

2018

Phys. Rev. D

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In this article, I discuss the construction of some globally conserved currents that one can construct in the absence of a Killing vector. One is based on the Komar current, which is constructed from an arbitrary vector field and has an identically vanishing divergence. I obtain some expressions for Komar currents constructed from some generalizations of Killing vectors which may in principle be constructed in a generic spacetime. I then present an explicit example for an outgoing Vaidya spacetime which demonstrates that the resulting Komar currents can yield conserved quantities that behave in a manner expected for the energy contained in the outgoing radiation. Finally, I describe a method for constructing another class of (non-Komar) globally conserved currents using a scalar test field that satisfies an inhomogeneous wave equation, and discuss two examples; the first example may provide a useful framework for examining the arrow of time and its relationship to energy conditions, and the second yields (with appropriate initial conditions) a globally conserved energy-and momentumlike quantity that measures the degree to which a given spacetime deviates from symmetry. I. THE KOMAR CURRENTIn a 1959 article [1], Arthur Komar presented a globally conserved current (the Komar current) for general relativistic spacetimes, which is constructed from an arbitrary vector field U µ (which serves as the generator for diffeomorphisms). The Komar current is of the form: 1(1)The Komar current has theoretical appeal because it can be derived from the action in the context of Noether's theorem-in [2][3][4], it was shown that the Komar current is in fact the conserved current corresponding to the diffeomorphism invariance of the Einstein-Hilbert Lagrangian coupled to matter. 2 Using the Ricci identity [∇ µ , ∇ ν ]T αβ = R α σµν T σβ + R β σµν T ασ for the Levi-Civita connection ∇ µ , it is straightforward to show that the divergence of J µ K identically vanishes:The above result is an identity for any quantity of the form given in Eq. (1); it only depends on the Ricci identity for rank-2 tensors. Note also that Eq. (2) permits a shift freedom in J µ K ; any divergence-free vector added to J µ K preserves the divergence-free property Eq. (2). One potentially useful example is a vector field of the form 1 Note that there is a gauge freedom in this definition; for a torsionfree connection ∇µ, J µ K is invariant under the transformation U µ → U µ + ∇ µ σ (σ being a scalar field). 2 I also refer the reader to [5] and related work which extend the analysis to more general theories of gravity [6][7][8].∇ µ φ, which is divergence free if the scalar field satisfies the wave equation φ = 0. From the Komar current J µ K , I may construct the 3form:By Stokes' theorem, the integral of the above over some constant-time hypersurface Σ t becomes:where dΣ µ and dS µν are the respective surface elements 3 for Σ t and ∂Σ t . Equation (4) may be used to construct quasilocal expressions for quantities associated with a Komar current. Note in a close...

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Almost-Killing conserved currents: A general mass function

Cited by 12 publications

References 18 publications

The illusion of neutron star magnetic field estimates

The illusion of neutron star magnetic field estimates

Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law

Some globally conserved currents from generalized Killing vectors and scalar test fields

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