On quadratic first integrals of the geodesic equations for type {22} spacetimes

We derive constraints on the form of the renormalized stress tensor for states on Kerr space-time based on general physical principles: symmetry, the conservation equations, the trace anomaly and regularity on (sections of) the event horizon. This is then applied to the physical vacua of interest. We introduce the concept of past and future Boulware vacua and discuss the non-existence of a state empty at both I − and I + . By calculating the stress tensor for the Unruh vacuum at the event horizon and at infinity, we are able to check our earlier conditions. We also discuss the difficulties of defining a state equivalent to the Hartle-Hawking vacuum and comment on the properties of two candidates for this state.

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“…The Kerr geometry also possesses a Killing-Yano tensor [11], which is a skew-symmetric tensor f µν satisfying…”

Section: The Killing-yano Tensormentioning

confidence: 99%

Renormalized stress tensor in Kerr space-time: General results

2000

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“…The Kerr metric [4] is probably the most well known and interesting example of a spacetime admitting an irreducible KT [5], [6]. KTs are admitted by other Petrov type D spacetimes [6] - [8].…”

Section: Introductionmentioning

confidence: 99%

Killing tensors in pp-wave spacetimes

Keane¹,

Tupper²

2010

Class. Quantum Grav.

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Abstract. The formal solution of the second order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.

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“…As will be shown below, this Killing tensor is reducible in the terminology of [6] because it can be constructed from the Killing vectors corresponding to SO(2, 1) × U(1) isometry group.…”

Section: Background Geometrymentioning

confidence: 99%

Particle dynamics near extreme Kerr throat and supersymmetry

Galajinsky

2010

J. High Energ. Phys.

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The extreme Kerr throat solution is believed to be non-supersymmetric. However, its isometry group SO(2, 1) × U (1) matches precisely the bosonic subgroup of N = 2 superconformal group in one dimension. In this paper we construct N = 2 supersymmetric extension of a massive particle moving near the horizon of the extreme Kerr black hole. Bosonic conserved charges are related to Killing vectors in a conventional way. Geometric interpretation of supersymmetry charges remains a challenge.

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On quadratic first integrals of the geodesic equations for type {22} spacetimes

Cited by 526 publications

References 12 publications

Renormalized stress tensor in Kerr space-time: General results

Renormalized stress tensor in Kerr space-time: General results

Killing tensors in pp-wave spacetimes

Particle dynamics near extreme Kerr throat and supersymmetry

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