The Carter constant and Petrov classification of the Vaidya–Einstein–Kerr spacetime

Ramachandra, B.

doi:10.1007/s10714-009-0805-y

Cited by 5 publications

(3 citation statements)

References 10 publications

(14 reference statements)

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“…We would like to emphasise that only form of the metric is important for this formalism, it does not depend on the nature of the source or asymptotic conditions. Because it is possible to have Carter-like constant for SASS which are not asymptotical flat [17]. More formally, the L 2 can be defined using Killing tensor and its projection onto a space orthogonal to the space formed by the ZAMO and radial vector.…”

Section: Discussionmentioning

confidence: 99%

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Butterfly diversity in Kolkata, India: An appraisal for conservation management

Mukherjee

Banerjee

Saha

et al. 2015

Journal of Asia-Pacific Biodiversity

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We investigate the Carter-like constant in the case of a particle moving in a nonrelativistic dipolar potential. This special case is a missing link between Carter constant in stationary axially symmetric spacetimes such as Kerr solution and its possible Newtonian counterpart. We use this system to carry over the definition of angular momentum from the Newtonian mechanics to the relativistic stationary axially symmetric spacetimes.

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Section: Discussionmentioning

confidence: 99%

“…In the past, there have been attempts to define angular momentum through the Floyd tensor [16,17]. However, we take a simpler approach, by defining the quantities L z and L 2 .…”

Section: Stationary Axially Symmetric Spacetimesmentioning

confidence: 99%

Butterfly diversity in Kolkata, India: An appraisal for conservation management

Mukherjee

Banerjee

Saha

et al. 2015

Journal of Asia-Pacific Biodiversity

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“…Following the coordinates introduced by Finkelstein [3], the metric in (1.1) can be construed as ds 2 = − 1 − 2m(u) r du 2 − 4 m(u) r dudr + 1 + 2m(u) r dr 2 + r 2 (dθ 2 + sin 2 θ dφ 2 ). (1.2) Various studies relating to the Vaidiya metric has been done, for e.g., the 'nature of naked singularities' [4], the 'Carter constant and Petrov classification' [5] and references therein which include aspects of the nature of the Killing tensors and well known notion of the 'isometries' of the metric which are the diffeomorphisms of the manifold onto itself which preserve the metric tensor [7]. In this paper, we consider a novel approach to the 'invariance' studies associated with the metric in (1.1) and (1.2).…”

Section: Introductionmentioning

confidence: 99%

The Noether Conservation Laws of Some Vaidiya Metrics

Narain

Kara

2009

Int J Theor Phys

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In this paper, we show that a large amount information can be extracted from a knowledge of the vector fields that leave the action integral invariant, viz., Noether symmetries. In addition to a larger class of conservation laws than those given by the isometries or Killing vectors, we may conclude what the isometries are and that these form a Lie subalgebra of the Noether symmetry algebra. We perform our analysis on versions of the Vaidiya metric yielding some previously unknown information regarding the corresponding manifold. Lastly, with particular reference to this metric, we show that the only variations on m(u) that occur are m = 0, m = constant, m = u and m = m(u).

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Invariance analysis and conservation laws of the wave equation on Vaidya manifolds

Narain

Kara

2011

Pramana - J Phys

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In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds.

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The Carter constant and Petrov classification of the Vaidya–Einstein–Kerr spacetime

Cited by 5 publications

References 10 publications

Butterfly diversity in Kolkata, India: An appraisal for conservation management

Butterfly diversity in Kolkata, India: An appraisal for conservation management

The Noether Conservation Laws of Some Vaidiya Metrics

Invariance analysis and conservation laws of the wave equation on Vaidya manifolds

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