2011
DOI: 10.2478/s11534-010-0147-0
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Velocity and velocity bounds in static spherically symmetric metrics

Abstract: Abstract:We find simple expressions for velocity of massless particles with dependence on the distance, , in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in… Show more

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Cited by 10 publications
(7 citation statements)
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“…In the Schwarzschild-de Sitter spacetime the similar scale with the background λ appears in the minimum of the metric function g(r) (with M(r) = M = const) for the Kottler-Trefftz geometry [92], and defines the boundary beyond which there are no bound orbits for test particles [93,94]. This scale plays the fundamental role in the non-linear theories of massive gravity.…”
Section: Algebraic Structure Of Tress-energy Tensors For Vacuum Dark mentioning
confidence: 97%
“…In the Schwarzschild-de Sitter spacetime the similar scale with the background λ appears in the minimum of the metric function g(r) (with M(r) = M = const) for the Kottler-Trefftz geometry [92], and defines the boundary beyond which there are no bound orbits for test particles [93,94]. This scale plays the fundamental role in the non-linear theories of massive gravity.…”
Section: Algebraic Structure Of Tress-energy Tensors For Vacuum Dark mentioning
confidence: 97%
“…The canonical map transforms the Lagrangian density L (x, x) ≡ L g, ∇g, g given by Equation (13) in terms of the equation…”
Section: Hamilton and Hamilton-jacobi Representationsmentioning
confidence: 99%
“…As theoretical frameworks for the interpretation of observational features characterizing gravitational waves, with particular reference to the constraints that can be placed on their speed of propagation [13], in turn permitting the implementation of additional confirmations to SF-GR or restriction of the validity of alternative gravity theories [14][15][16][17][18].…”
mentioning
confidence: 99%
“…In [7], Balaguera et al, found that r 0 represents the maximum distance within which we can find bound orbits solutions for a test particle moving around a source. In the same manuscript, the velocity bounds for a test particle inside the S-dS space were obtained, this work was then extended by Arraut et al in [8] in order to incorporate other metric solutions. In [7], the authors also found that there exist a maximum angular momentum L max for the test particle to be inside a bound orbit.…”
Section: Introductionmentioning
confidence: 99%