Multipole moments of isolated horizons

Ashtekar, Abhay; Engle, Jonathan; Pawłowski, Tomasz; Broeck, C. Van Den

doi:10.1088/0264-9381/21/11/003

Cited by 157 publications

(287 citation statements)

References 32 publications

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“…As this paper was being completed, an analysis appeared on the gr-qc archive by Ashtekar et al [35] of the multipole moments of isolated horizons [36]. Although we have not investigated this in any depth, it may be beneficial to pursue a connection between the bumpiness of a black hole and the multipole moments expressed in the language of Ref.…”

Section: Discussionmentioning

confidence: 98%

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

2004

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Astronomical observations have established that extremely compact, massive objects are common in the universe. It is generally accepted that these objects are, in all likelihood, black holes. As observational technology has improved, it has become possible to test this hypothesis in ever greater detail. In particular, it is or will be possible to measure the properties of orbits deep in the strong field of a black hole candidate (using x-ray timing or future gravitational-wave measurements) and to test whether they have the characteristics of black hole orbits in general relativity. Past work has shown that, in principle, such measurements can be used to map the spacetime of a massive compact object, testing in particular whether the object's multipolar structure satisfies the rather strict constraints imposed by the black hole hypothesis. Performing such a test in practice requires that we be able to compare against objects with the "wrong" multipole structure. In this paper, we present tools for constructing the spacetimes of bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. In this first analysis, we focus on objects with no angular momentum. Generalization to bumpy Kerr black holes should be straightforward, albeit labor intensive. Our construction has two particularly desirable properties. First, the spacetimes which we present are good deep into the strong field of the object -we do not use a "large r" expansion (except to make contact with weak field intuition). Second, our spacetimes reduce to the exact black hole spacetimes of general relativity in a natural way, by dialing the "bumpiness" of the black hole to zero. We propose that bumpy black holes can be used as the foundation for a null experiment: if black hole candidates are indeed the black holes of general relativity, their bumpiness should be zero. By comparing the properties of orbits in a bumpy spacetime with those measured by an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are in fact the black holes of general relativity.

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Section: Discussionmentioning

confidence: 98%

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

2004

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“…The IH multipole moments are defined in an invariant coordinate system [41] which requires the knowledge of the axial KVF on the horizon. Our approach does not explicitly require the KVF to extract the IH multipole moments and circumvents the invariant coordinates by using the surface averages µ n ( 2R ), µ n (ImΨ 2 ) which can be easily computed in any coordinate system.…”

Section: Solving the 2d Killing Equation Numericallymentioning

confidence: 99%

“…Ashtekar et al [41] exploit the axisymmetry to define an invariant coordinate system (χ, φ) for which the 2-metric has the form (3.1), ∂ φ is the KVF and the (zonal) harmonics…”

Section: Invariants Of Axisymmetric Isolated Horizonsmentioning

confidence: 99%

“…In analogy to electro dynamics dimensionfull factors can be added to attribute a physical interpretation to theÎ l ,L l , see [41]. To obtain the spin we need 10 Here the indices I , L in l 11 Formally the solutions of the algebraic systems depend on n max .…”

Section: A the Invariants µ N On Axisymmetric Isolated Horizonsmentioning

confidence: 99%

“…[34,42,43]. The dipole term reads 2) where A is the horizon area, (χ, φ) an invariant coordinate system [41] 'tied' to the axisymmetry, such that J 1 and J[Φ j ] are identical, and Y 10 (χ) is the spherical harmonic l = 1, m = 0. We circumvent the use of invariant coordinates/KVFs and instead use the surface averages µ n 1 of the scalar 2-curvature 2 R and ImΨ 2 to obtain J 1 and higher multipole moments 3) which are well defined, even if the axisymmetry is perturbed and that allow us to benefit from exact numerical integration in order to reduce grid size and numerical error significantly.…”

Section: Introductionmentioning

confidence: 99%

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A new method for computing quasi-local spin and other invariants on marginally trapped surfaces

Jasiulek¹

2009

Class. Quantum Grav.

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We accurately compute the scalar 2-curvature, the Weyl scalars, associated quasi-local spin, mass and higher multipole moments on marginally trapped surfaces in numerical 3+1 simulations. To determine the quasi-local quantities we introduce a new method which requires a set of invariant surface integrals, allowing for surface grids of a few hundred points only. The new technique circumvents solving the Killing equation and is also an alternative to approximate Killing vector fields. We apply the method to a perturbed non-axisymmetric black hole ringing down to Kerr and compare the quasi-local spin with other methods that use Killing vector fields, coordinate vector fields, quasinormal ringing and properties of the Kerr metric on the surface. Interesting is the agreement with the spin of approximate Killing vector fields during the phase of perturbed axisymmetry. Additionally, we introduce a new coordinate transformation, adapting spherical coordinates to any two points on the sphere like the two minima of the scalar 2-curvature on axisymmetric trapped surfaces.

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Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

Bombelli¹,

Corichi²,

Winkler

2005

Ann. Phys.

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This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum scales" and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a "semiclassical" state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity.

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Multipole moments of isolated horizons

Cited by 157 publications

References 32 publications

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

A new method for computing quasi-local spin and other invariants on marginally trapped surfaces

Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

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