Geodesic motion in a charged 2D stringy black hole spacetime

We study the time-like geodesics and geodesic deviation for a two-dimensional (2D) stringy black hole (BH) spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of BH parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector. The results are also compared with an another 2D stringy BH spacetime.

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Tidal forces in Kottler spacetimes

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09427-8 ◽

2021 ◽

Vol 81 (7) ◽

Author(s):

V. P. Vandeev ◽

A. N. Semenova

Keyword(s):

Black Hole ◽

Cosmological Constant ◽

Radial Component ◽

Tidal Force ◽

De Sitter ◽

Geodesic Deviation ◽

Tidal Forces ◽

Sitter Spacetime ◽

Deviation Equation ◽

Deviation Vector

AbstractThe article considers tidal forces in the vicinity of the Kottler black hole. We find a solution of the geodesic deviation equation for radially falling bodies, which is determined by elliptic integrals. And also the asymptotic behavior of all spatial geodesic deviation vector components were found. We demonstrate that the radial component of the tidal force changes sign outside the single event horizon for any negative values of the cosmological constant, in contrast to the Schwarzschild black hole, where all the components of the tidal force are sign-constant. We also find the similarity between the Kottler black hole and the Reissner–Nordström black hole, because we indicate the value of the cosmological constant, which ensures the existence of two horizons of the black hole, between which the angular components of the tidal force change sign. It was possible to detect non-analytical behavior of geodesic deviation vector components in anti-de Sitter spacetime and to describe it locally.

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Tidal effects in 4D Einstein–Gauss–Bonnet black hole spacetime

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09400-5 ◽

2021 ◽

Vol 81 (7) ◽

Author(s):

Jing Li ◽

Songbai Chen ◽

Jiliang Jing

Keyword(s):

Black Hole ◽

Initial Conditions ◽

Tidal Force ◽

Coupling Constant ◽

Tidal Effects ◽

Schwarzschild Spacetime ◽

Geodesic Deviation ◽

Tidal Forces ◽

Black Hole Spacetime ◽

Deviation Vector

AbstractWe have investigated tidal forces and geodesic deviation motion in the 4D-Einstein–Gauss–Bonnet spacetime. Our results show that tidal force and geodesic deviation motion depend sharply on the sign of Gauss–Bonnet coupling constant. Comparing with Schwarzschild spacetime, the strength of tidal force becomes stronger for the negative Gauss–Bonnet coupling constant, but is weaker for the positive one. Moreover, tidal force behaves like those in the Schwarzschild spacetime as the coupling constant is negative, and like those in Reissner–Nordström black hole as the constant is positive. We also present the change of geodesic deviation vector with Gauss–Bonnet coupling constant under two kinds of initial conditions.

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Tidal forces in the charged Hayward black hole spacetime

International Journal of Modern Physics D ◽

10.1142/s021827182041014x ◽

2020 ◽

Vol 29 (11) ◽

pp. 2041014

Author(s):

Haroldo C. D. Lima ◽

Luís C. B. Crispino

Keyword(s):

Black Hole ◽

Initial Conditions ◽

Radial Coordinate ◽

Geodesic Deviation ◽

Regular Black Hole ◽

Tidal Forces ◽

Deviation Equation ◽

Spacetime Curvature ◽

Black Hole Spacetime ◽

Electrically Charged

Tidal forces produced by black holes are an important result of General Relativity related to the spacetime curvature tensor. Among the astrophysical implications of tidal forces, the tidal disruption events stand out. We analyze the tidal forces in the spacetime of an electrically charged Hayward regular black hole, obtaining the components of the tidal tensor and the geodesic deviation equation. We find that the radial and angular tidal forces may vanish and change sign unlike in the Schwarzschild spacetime. We note that tidal forces are finite at the origin of the radial coordinate in this regular black hole spacetime. We obtain the geodesic deviation vector for a body constituted of dust infalling towards the black hole with two different initial conditions.

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A scalar geodesic deviation equation and a phase theorem

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171283000678 ◽

1983 ◽

Vol 6 (4) ◽

pp. 795-802 ◽

Cited By ~ 1

Author(s):

P. Choudhury ◽

P. Dolan ◽

N. S. Swaminarayan

Keyword(s):

Gravitational Field ◽

Phase Shift ◽

Relative Motion ◽

Plane Waves ◽

Relative Energy ◽

Positive Definite ◽

Geodesic Deviation ◽

Deviation Equation ◽

Test Particles ◽

Geodesic Deviation Equation

A scalar equation is derived forη, the distance between two structureless test particles falling freely in a gravitational field:η¨+(K−Ω2)η=0. An amplitude, frequency and a phase are defined for the relative motion. The phases are classed as elliptic, hyperbolic and parabolic according asK−Ω2>0,<0,=0.In elliptic phases we deduce a positive definite relative energyEand a phase-shift theorem. The relevance of the phase-shift theorem to gravitational plane waves is discussed.

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A “constant of the motion” for the geodesic deviation equation

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000002526 ◽

1980 ◽

Vol 22 (1) ◽

pp. 28-33 ◽

Cited By ~ 3

Author(s):

P. Dolan ◽

P. Choudhury ◽

J. L. Safko

Keyword(s):

Relative Motion ◽

Short Paper ◽

Linear Superposition ◽

Geodesic Deviation ◽

Deviation Equation ◽

Test Particles ◽

Geodesic Deviation Equation ◽

Kinetic And Potential Energies

AbstractIn this short paper, it is shown that the geodesic deviation equation admits a “constant of the motion” and so can be solved exactly. We also derive an expression for the energy E of relative motion between two freely falling test particles. We can infer that, in general, E will not be a linear superposition of kinetic and potential energies.

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Generalized Mattig’s relation in Brans–Dicke–Rastall gravity

International Journal of Modern Physics D ◽

10.1142/s0218271816500760 ◽

2016 ◽

Vol 25 (07) ◽

pp. 1650076 ◽

Cited By ~ 15

Author(s):

Ines G. Salako ◽

M. J. S. Houndjo ◽

Abdul Jawad

Keyword(s):

Null Vector ◽

Geodesic Deviation ◽

Deviation Equation ◽

Geodesic Deviation Equation ◽

Vector Formula ◽

Deviation Vector ◽

Distance Formula

The geodesic deviation equation (GDE) is being studied in Brans–Dicke–Rastall (BDR) gravity. We briefly discuss the BDR gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the BDR gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector [Formula: see text] and observer area distance [Formula: see text] and compare the results with [Formula: see text]CDM model.

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