We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find that Bernoulli, Riccati and confluent hypergeometric equations are possible. These admit solutions in terms of elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Our infinite family of solutions contains specific models found previously. For a particular metric we briefly investigate the physical features, derive the temperature profiles and plot the behaviour of the casual and acasual temperatures.
General Relativity (GR) is shown to be a complete theory with respect to the isochrony of the pendulum. This guarantees that time can be measured with a mechanical clock within the theory itself as a matter of principle. The proper and coordinate oscillation frequencies of a simple pendulum are computed as a function of 3 coordinate parameters: the distance of the fulcrum to the gravity source, its length and the Schwarzschild radius. Novel GR effects appear in the Schwarzschild coordinates as divergences, zeroes and other instabilities of the oscillation frequencies that are absent in Newtoni…
Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a spherically symmetric metric, the Ricci and electric tensors become rank-2, built with a velocity vector field and its acceleration. Their structure dictates the general form of the energy-momentum tensor in the Einstein equations in DW spherical metrics. The anisotropic pressure and the heat current of an imperfect fluid descend from the gradient of the acc…
We investigate the three-dimensional, general relativistic Poynting-Robertson effect in the case of rigidly rotating spherical source which emits radiation radially in the local comoving frame. Such radiation field is meant to approximate the field produced by the surface of a rotating neutron star, or by the central radiating hot corona of accreting black holes; it extends the purely radial radiation field that we considered in a previous study. Its angular momentum is expressed in terms of the rotation frequency and radius of the emitting source. For the background we adopt a Kerr spacetime …
Geodesics on the Torus and other Surfaces of Revolution Clarified Using Undergraduate Physics Tricks with Bonus: Nonrelativistic and Relativistic Kepler Problems
A four-force parallel to the trajectory of a massive particle can always be eliminated by going to an affine parametrization, but the affine parameter is different from the proper time. The main application is to cosmology, in which elements of the cosmic fluid are subject to a pressure gradient parallel to their four-velocities. Natural implementations of parallel four-forces occur when the particle mass changes and in scalar-tensor cosmology.
On the Status of the Geodesic Principle in Newtonian and Relativistic Physics
Bob Geroch和Pong Soo Jang ["广义相对论中的物体运动"]的一个定理。"Journal of数学物理16（1），（1975）]提供了一种意义，其中测地线原理具有广义相对论（GR）中定理的地位。我最近证明了一个类似的定理在几何化的牛顿引力（牛顿-嘉当理论）的背景下也成立。牛顿理论中的物体运动"Journal of数学物理52（3），（2011）]。在这里，我比较这两个定理的解释。我认为，尽管有一些明显的差异之间的定理，在几何化的牛顿引力的测地线原则的地位是，作必要的修改，惊人的相对论性的情况下相似。
Recent observations of the orbits of star clusters around Sgr $A^\star$, imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up with a method to provide all the possible geodesics in an axially symmetric space-time. The Kerr metric is explicitly worked out, recovering the Schwarzschild geodesics in the static limit. We also found the most general Killing tensor and its associated constant of motion for an axisymmetric space-time. The relevance of these results is crucial to understan…
We present a particular solution to the Einstein field equations that could arise as a magnetic monopole in the strong field limit of the Born-Infeld electrodynamics. We solve its geodesics exactly and show that they can mimic the gravitational lensing of a singular isothermal sphere, but with matter and radiation following the same trajectories. This solution has previously been called "cloud of strings" or "string hedgehog," and has appeared as the limit of a global O(3) monopole.
Relativistic Maxwell-Bloch Equations with Applications to Astrophysics
The University of Western Ontario（韦仕敦大学）；Laboratoire Interdisciplinaire des Sciences du Numérique, CNRS（数字科学跨学科实验室，法国国家科学研究中心）；McMaster University（麦克马斯特大学）
Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos
