WebJul 9, 2024 · The set of initial conditions which converge towards the photon sphere (which is called the stable manifold) is indicated with a blue line. Photons on this trajectory will … WebMay 14, 2024 · Abstract. We study the ultralight vector dark matter with a mass around 10^ {-23}\,\mathrm {eV}. The vector field oscillating coherently on galactic scales induces oscillations of the spacetime metric with a frequency around nHz, which is detectable by pulsar timing arrays. We find that the pulsar timing signal due to the vector dark matter …
6.3: The Schwarzschild Metric (Part 2) - Physics LibreTexts
WebApr 10, 2012 · However, we will use the inferred value of R h today as one of our boundary conditions. In principle, equation (8) may be integrated either forwards or backwards, ... WebOct 10, 2024 · Geodesic equation: t ¨ + 2 t ˙ r ˙ ( − 2 + r) r = 0. r ¨ + ( − 2 + r) t ˙ 2 r 3 + r ˙ 2 2 r − r 2 + ( 2 − r) ϕ ˙ 2 = 0. ϕ ¨ + 2 r ˙ ϕ ˙ r = 0. Initial Condition: t [ 0] = 1, t ˙ [ 0] = 2. r [ 0] = 1, r ˙ [ … pork in the road
Quasi-geodesics in relativistic gravity SpringerLink
WebNov 8, 2024 · Position determination of photon emitters and associated strong field parallax effects are investigated using relativistic optics when the photon orbits are confined to the equatorial plane of the Schwarzschild spacetime. We assume the emitter is at a fixed space position and the receiver moves along a circular geodesic orbit. This study requires … WebDue to the spherical symmetry of metric, it is convenient to study the photon trajectories on the equatorial plane with the initial condition = ˇ=2 and _ = 0. Combining Eqs. (1) and (6) with the Euler-Lagrange equation, we get the expressions of time, azimuth, and radial components of the four velocities. Since the metric does not explicitly ... WebSep 11, 2015 · In Riemannian geometry, the condition g ( γ ˙, γ ˙) being constant along a geodesic is equivalent to ∇ γ ˙ γ ˙ = 0. This equivalence is false for null curves in Lorentzian geometry. Hence affine parametrization in general pseudo-Riemannian geometry uses the more precise definition ∇ γ ˙ γ ˙ = 0. (For non-affine parametrizations ... porkin\\u0027s monster