Velocity and velocity bounds in static spherically symmetric metrics

Arraut, Ivan; Batic, Davide; Nowakowski, M.

doi:10.2478/s11534-010-0147-0

Cited by 10 publications

(7 citation statements)

References 61 publications

(44 reference 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%

Spacetime Symmetry and LemaîTre Class Dark Energy Models

Dymnikova

Dobosz

2019

Symmetry

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We present the regular cosmological models of the Lemaître class with time-dependent and spatially inhomogeneous vacuum dark energy, which describe relaxation of the cosmological constant from its value powering inflation to the final non-zero value responsible for the present acceleration in the frame of one self-consistent theoretical scheme based on the algebraic classification of stress-energy tensors and spacetime symmetry directly related to their structure. Cosmological evolution starts with the nonsingular non-simultaneous de Sitter bang, followed by the Kasner-type anisotropic expansion, and goes towards the present de Sitter state. Spacetime symmetry provides a mechanism of reducing cosmological constant to a certain non-zero value involving the holographic principle which singles out the special class of the Lemaître dark energy models with the global structure of the de Sitter spacetime. For this class cosmological evolution is guided by quantum evaporation of the cosmological horizon whose dynamics entirely determines the final value of the cosmological constant. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale for the inflationary value of cosmological constant, its final value agrees with that given by observations. Anisotropy grows quickly at the postinflationary stage, then remains constant and decreases to A < 10 − 6 when the vacuum density starts to dominate.

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Section: Algebraic Structure Of Tress-energy Tensors For Vacuum Dark mentioning

confidence: 97%

Spacetime Symmetry and LemaîTre Class Dark Energy Models

Dymnikova

Dobosz

2019

Symmetry

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“…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].…”

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confidence: 99%

The Wave-Front Equation of Gravitational Signals in Classical General Relativity

Cremaschini

Tessarotto

2020

Symmetry

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In this paper the dynamical equation for propagating wave-fronts of gravitational signals in classical general relativity (GR) is determined. The work relies on the manifestly-covariant Hamilton and Hamilton–Jacobi theories underlying the Einstein field equations recently discovered (Cremaschini and Tessarotto, 2015–2019). The Hamilton–Jacobi equation obtained in this way yields a wave-front description of gravitational field dynamics. It is shown that on a suitable subset of configuration space the latter equation reduces to a Klein–Gordon type equation associated with a 4-scalar field which identifies the wave-front surface of a gravitational signal. Its physical role and mathematical interpretation are discussed. Radiation-field wave-front solutions are pointed out, proving that according to this description, gravitational wave-fronts propagate in a given background space-time as waves characterized by the invariant speed-of-light c. The outcome is independent of the actual shape of the same wave-fronts and includes the case of gravitational waves which are characterized by an eikonal representation and propagate in a generic curved space-time along a null geodetics. The same waves are shown: (a) to correspond to the geometric-optics limit of the same curved space-time solutions; (b) to propagate in a flat space-time as plane waves with constant amplitude; (c) to display also the corresponding form of the wave-front in curved space-time. The result is consistent with the theory of the linearized Einstein field equations and the existence of gravitational waves achieved in such an asymptotic regime. Consistency with the non-linear Trautman boundary-value theory is also displayed.

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“…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%

On the Black Holes in Alternative Theories of Gravity: The Case of Non-linear Massive Gravity

Arraut

2015

Springer Proceedings in Physics

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I derive general conditions in order to explain the origin of the Vainshtein radius inside dRGT. The set of equations, which I have called "Vainshtein" conditions are extremal conditions of the dynamical metric (g µν ) containing all the degrees of freedom of the theory. The Vainshtein conditions are able to explain the coincidence between the Vainshtein radius in dRGT and the scale r 0 = 3 2 r s r 2 Λ

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Velocity and velocity bounds in static spherically symmetric metrics

Cited by 10 publications

References 61 publications

Spacetime Symmetry and LemaîTre Class Dark Energy Models

Spacetime Symmetry and LemaîTre Class Dark Energy Models

The Wave-Front Equation of Gravitational Signals in Classical General Relativity

On the Black Holes in Alternative Theories of Gravity: The Case of Non-linear Massive Gravity

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