Dynamics of test particles in the general five-dimensional Myers-Perry spacetime

Diemer, Valeria; Kunz, Jutta; Lämmerzahl, Cláus; Reimers, Stephan

doi:10.1103/physrevd.89.124026

Cited by 31 publications

(36 citation statements)

References 96 publications

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“…In General Relativity (GR), the curvature and geometry of the space-time play crucial role as space-time is curved with the presence of matter fields [26,27,28,29]. A number of studies related to the geodesic motion in the background of various spacetimes has been performed time and again due to its astrophysical importance [30,31,32,33,34,35]. In general, the effects of the curvature in a given space-time is studied through the Geodesic Deviation Equations (GDE) [36,37,38], the equations which describe the relative acceleration of two neighbouring geodesics in diversified scenario [28,29,39,40,41,42].…”

Section: Introductionmentioning

confidence: 99%

Geodesic motion in Schwarzschild spacetime surrounded by quintessence

et al. 2015

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We study the time-like geodesic congruences, in the space-time geometry of a Schwarzschild black hole surrounded by quintessence. The nature of effective potential along with the structure of the possible orbits for test particles in view of the different values of quintessence parameter are analysed in detail. An increase in quintessence parameter is seen to set the particles from further distance into motion around black hole. The effect of quintessence parameter is investigated analytically wherever possible otherwise we perform the numerical analysis to probe the structure of possible orbits. It is observed that there exist a number of different possible orbits for a test particle in case of non-radial geodesics, such as circular (stable as well as unstable) bound orbits, radially plunge and fly-by orbits, whereas no bound orbits exist in case of radial geodesics.

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Section: Introductionmentioning

confidence: 99%

Geodesic motion in Schwarzschild spacetime surrounded by quintessence

et al. 2015

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“…It follows that the corresponding Jacobi system is also integrable and in principle can be solved by the same steps described in this section. Let us, however, stress that in higher dimensions, the generic geodesic is given only in terms of complicated integrals [38], see also [46][47][48] for special cases, and the solution of the Jacobi system thus becomes far from explicit.…”

Section: Integrability Of Jacobi Equation In Rotating Black Hole Smentioning

confidence: 99%

On integrability of the geodesic deviation equation

et al. 2018

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The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics. Namely, by linearizing the geodesic equation and its conserved charges, we arrive at the invariant Wronskians for the Jacobi system that are linear in the 'deviation momenta' and thus yield a system of first-order differential equations that can be integrated. The procedure is illustrated on an example of a rotating black hole spacetime described by the Kerr geometry and its higher-dimensional generalizations. A number of related topics, including the phase space formulation of the theory and the derivation of the covariant Hamiltonian for the Jacobi system are also discussed.1 The convention we use in this work for the commutation of covariant derivatives, when acting for example on a vector V a , is

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“…The study of geodesics alongwith their deformations in the background of a given spacetime is an elegant way to describe the underlying geometry of that particular spacetime [1][2][3]5,6,13,30]. A number of studies related to the geodesic motion in the background of various BH spacetimes have been performed time and again mainly in view of their astrophysical importance [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Geodesic flows in a charged black hole spacetime with quintessence

Nandan

Uniyal

2017

Eur. Phys. J. C

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We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded by quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focussing of timelike geodesic congruences. The effect of the normalisation constant (α) and the equation of state parameter (ε) on the evolution of the expansion scalar is discussed, for the congruences with and without an initial shear and rotation. It is observed that there always exists a critical value of the initial expansion below which we have focussing with smaller values of the normalisation constant and the equation of state parameter. As the corresponding values of both of these parameters are increased, no geodesic focussing is observed. The results obtained are then compared with those of the Reissner Nordström and Schwarzschild black hole spacetimes as well as their de Sitter black hole analogues accordingly.

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Dynamics of test particles in the general five-dimensional Myers-Perry spacetime

Cited by 31 publications

References 96 publications

Geodesic motion in Schwarzschild spacetime surrounded by quintessence

Geodesic motion in Schwarzschild spacetime surrounded by quintessence

On integrability of the geodesic deviation equation

Geodesic flows in a charged black hole spacetime with quintessence

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