scholarly journals Influence of geometry variations on the gravitational focusing of timelike geodesic congruences

2015 ◽  
Vol 92 (8) ◽  
Author(s):  
Masafumi Seriu
Keyword(s):  
Timelike Geodesic

scholarly journals Every timelike geodesic in Anti-de Sitter spacetime is a circle of the same radius

2016 ◽  
Vol 25 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Leszek M. Sokołowski ◽  
Zdzisław A. Golda
Keyword(s):  
Flat Space ◽  
De Sitter Space ◽  
Ambient Space ◽  
Alternative Proof ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Timelike Geodesic ◽  
Sitter Spacetime

In this paper, we refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti-de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by [Formula: see text], lying on a Euclidean two-plane. Then, we outline an alternative proof for [Formula: see text]. We also make a comment on the shape of timelike geodesics in de Sitter space.

scholarly journals Geodesics in Margulis spacetimes

2011 ◽  
Vol 32 (2) ◽  
pp. 643-651 ◽  
Author(s):  
WILLIAM M. GOLDMAN ◽  
FRANÇOIS LABOURIE
Keyword(s):  
Compact Convex ◽  
Hyperbolic Surface ◽  
Orbit Equivalence ◽  
Closed Geodesics ◽  
Timelike Geodesic ◽  
Convex Core

AbstractLet M3 be a Margulis spacetime whose associated complete hyperbolic surface Σ2 has a compact convex core. Generalizing the correspondence between closed geodesics on M3 and closed geodesics on Σ2, we establish an orbit equivalence between recurrent spacelike geodesics on M3 and recurrent geodesics on Σ2. In contrast, no timelike geodesic recurs in either forward or backward time.

scholarly journals TIMELIKE GEODESIC MOTION IN HORAVA–LIFSHITZ SPACE–TIME

2010 ◽  
Vol 25 (07) ◽  
pp. 1439-1448 ◽  
Author(s):  
JUHUA CHEN ◽  
YONGJIU WANG
Keyword(s):  
Initial Conditions ◽  
Detailed Balance ◽  
Critical Value ◽  
Space Time ◽  
Three Dimensions ◽  
Geodesic Motion ◽  
Timelike Geodesic ◽  
Particle Orbit ◽  
Renormalizable Theory ◽  
Finite Distance

Recently a nonrelativistic renormalizable theory of gravitation has been proposed by P. Horava. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory is expected to flow to the relativistic value λ = 1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. In this paper under allowing the lapse function to depend on the spatial coordinates xi as well as t, we obtain the spherically symmetric solutions. And then by analyzing the behavior of the effective potential for the particle, we investigate the timelike geodesic motion of particle in the Horava–Lifshitz space–time. We find that the nonradial particle falls from a finite distance to the center along the timelike geodesics when its energy is in an appropriate range. However, we find that it is complexity for radial particle along the timelike geodesics. There are three different cases due to the energy of radial particle: (i) when the energy of radial particle is higher than a critical value EC, the particle will fall directly from infinity to the singularity; (ii) when the energy of radial particle equals to the critical value EC, the particle orbit at r = rC is unstable, i.e. the particle will escape from r = rC to the infinity or to the singularity, depending on the initial conditions of the particle; (iii) when the energy of radial particle is in a proper range, the particle will rebound to the infinity or plunge to the singularity from a infinite distance, depending on the initial conditions of the particle.

Geodesic structure of magnetically charged regular black hole

2017 ◽  
Vol 14 (09) ◽  
pp. 1750120 ◽  
Author(s):  
Muhammad Azam ◽  
Ghulam Abbas ◽  
Syeda Sumera ◽  
Abdul Rauf Nizami
Keyword(s):  
Black Hole ◽  
Effective Potential ◽  
Proper Time ◽  
Massive Particle ◽  
Circular Motion ◽  
Geodesic Path ◽  
Timelike Geodesic ◽  
Null Geodesics ◽  
Regular Black Hole ◽  
Geodesic Structure

The purpose of this paper is to study the geodesic structure of magnetically charged regular black hole (MCRBH). The behavior of timelike and null geodesics of MCRBH is investigated. The graphs have been plotted to show the relation between distance versus time and proper time for photon-like and massive particle. For radial and circular motion, the effective potential has been plotted with different parameters of BH. We conclude that massive particles move around the BH in timelike geodesic path.

Closed geodesies on compact Lorentzian manifolds of splitting type

1998 ◽  
Vol 128 (3) ◽  
pp. 447-462 ◽  
Author(s):  
Flavia Antonacci ◽  
Rosell Sampalmieri
Keyword(s):  
Variational Methods ◽  
Category Theory ◽  
Closed Geodesic ◽  
Compact Manifold ◽  
Topological Properties ◽  
Timelike Geodesic ◽  
Lorentzian Manifolds ◽  
Time Coordinate ◽  
Splitting Type ◽  
Relative Category

In this paper, we consider the problem of the existence of a spacelike closed geodesic on compact Lorentzian manifolds. Tipler and Galloway proved that, under suitable topological properties of the manifold, there exists a closed timelike geodesic. In their proofs, they use the hypothesis that the time coordinate of one timelike geodesic has derivative always different from zero. This clearly fails for spacelike geodesies. Using variational methods and applying the relative category theory, we prove the existence of a closed spacelike geodesic on a compact manifold of splitting type. Observe that, thanks to the previous results, the existence of at least two geometrically distinct closed geodesies on follows.

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