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Open accessJournal ArticleDOI: 10.1088/1361-6382/ABD071

Unit-lapse versions of the Kerr spacetime

04 Mar 2021-Classical and Quantum Gravity (IOP Publishing)-Vol. 38, Iss: 5, pp 055001
Abstract: The Kerr spacetime is perhaps the most astrophysically important of the currently known exact solutions to the Einstein field equations. Whenever spacetimes can be put in unit-lapse form it becomes possible to identify some very straightforward timelike geodesics, (the "rain" geodesics), making the physical interpretation of these spacetimes particularly clean and elegant. The most well-known of these unit-lapse formulations is the Painleve-Gullstrand form of the Schwarzschild spacetime, though there is also a Painleve-Gullstrand form of the Lense-Thirring (slow rotation) spacetime. More radically there are also two known unit-lapse forms of the Kerr spacetime -- the Doran and Natario metrics -- though these are not precisely in Painleve-Gullstrand form. Herein we shall seek to explicate the most general unit-lapse form of the Kerr spacetime. While at one level this is "merely" a choice of coordinates, it is a strategically and tactically useful choice of coordinates, thereby making the technically challenging but astrophysically crucial Kerr spacetime somewhat easier to deal with.

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8 results found

Open access
Roy P. Kerr1, Roy P. Kerr2Institutions (2)
01 Dec 1982-
Topics: Gravitational field (63%)

1,777 Citations

Proceedings ArticleDOI: 10.1142/9789814374552_0165
01 Feb 2012-
Abstract: Regular (non-singular) space-times are given which describe the formation of a (locally defined) black hole from an initial vacuum region, its quiescence as a static region, and its subsequent evaporation to a vacuum region. The static region is Bardeen-like, supported by finite density and pressures, vanishing rapidly at large radius and behaving as a cosmological constant at small radius. The dynamic regions are Vaidya-like, with ingoing radiation of positive energy flux during collapse and negative energy flux during evaporation, the latter balanced by outgoing radiation of positive energy flux and a surface pressure at a pair creation surface. The black hole consists of a compact space-time region of trapped surfaces, with inner and outer boundaries which join circularly as a single smooth trapping horizon.

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Topics: Black hole (57%), Evaporation (52%), Radius (52%) ... read more

8 Citations

Open accessJournal ArticleDOI: 10.1142/S0218271821500711
V. M. Khatsymovsky1Institutions (1)
Abstract: The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordina...

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Topics: Synchronous frame (67%), Reference frame (61%), Kerr metric (59%) ... read more

2 Citations

Open accessPosted Content
Abstract: Recently, the authors have formulated and explored a novel Painleve-Gullstrand variant of the Lense-Thirring spacetime, which has some particularly elegant features -- including unit-lapse, intrinsically flat spatial 3-slices, and some particularly simple geodesics, the "rain" geodesics. Herein, we shall show that this spacetime possesses a nontrivial Killing tensor, implying separability of the Hamilton-Jacobi equation. Furthermore, we shall show that the Klein-Gordon equation is also separable on this spacetime. However, while the Killing tensor has a 2-form square root, we shall see that this 2-form square root of the Killing tensor is not a Killing-Yano tensor. Finally, the Killing-tensor-induced Carter constant is easily extracted, and now, with a fourth constant of motion, the geodesics become (in principle) explicitly integrable.

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Topics: Killing tensor (69%), Tensor (intrinsic definition) (58%), Spacetime (54%) ... read more

1 Citations

Open accessJournal ArticleDOI: 10.1142/S0218271821500711
V. M. Khatsymovsky1Institutions (1)
Abstract: The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a certain way (keeping their interpretation as initial values at large distances), we still have a synchronous frame and the direct analogue of the Lemaitre metric, the singularities of which are exhausted by the physical Kerr singularity (the singularity ring).

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Topics: Kerr metric (63%), Synchronous frame (61%), Reference frame (56%) ... read more

1 Citations


66 results found

Open accessBook
01 Jan 1984-
Topics: Initial value formulation (66%), Hole argument (64%), Geodesics in general relativity (61%) ... read more

8,120 Citations

Open accessBook
01 Jan 1972-
Abstract: Preface. Notation. Copyright Acknowledgements. Part One Preliminaries. Part Two the General Theory of Relativity. Part Three Applications of Feneral Relativity. Part Four Formal Developments. Part Five Cosmology. Appendix. Some Useful Numbers. Index.

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Topics: Theory of relativity (64%), General relativity (56%), Gravitation (53%)

4,049 Citations

Open accessJournal ArticleDOI: 10.12942/LRR-2005-12
13 May 2005-
Abstract: Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity In this review article we will discuss the history, aims, results, and future prospects for the various analogue models We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity)

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947 Citations

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