Related papers: A Physics-First Approach to the Schwarzschild Metr…
The gravitaional force produced by a point particle, like the sun, in the background of the static Einstein universe is studied. Both the approximate solution in the weak field limit and exact solution are obtained. The main properties of…
With Einstein's inertial motion (free-falling and non-rotating relative to gyroscopes), geodesics for non-relativistic particles can intersect repeatedly, allowing one to compute the space-time curvature $R^{\hat{0} \hat{0}}$ exactly.…
Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
It was suggested that observations of the solar system exclude massive gravity, in the sense that the graviton mass must be rigorously zero. This is because there is a discontinuity in the linearized gravity theory at graviton mass equal to…
We derive a relativistic field equation for the trace of the metric perturbation beyond the weak field approximation to the Einstein field equations. The dynamics is governed by a massive Klein-Gordon equation on curved space-time, where…
Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. L\"u, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett. 114 (2015), 171601]…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
Starting from the revelation of the nature of inertial forces, this article discusses the subdivision of the basic physical concept of space-time and raises questions about the metric of standard cosmology. A new form of particle dynamics…
The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…
Using only a thought experiment and Einstein's correspondence principal, a model is derived that correctly predicts the Schwarzschild time dilation expression in limiting cases. The method requires almost no prerequisite knowledge from the…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic…
GR and other metric theories of gravity are formulated with an arbitrary auxiliary curved background in a Lagrangian formalism. A new sketch of how to include spinor fields is included. Conserved quantities are obtained using Noether's…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
We analyze the quantum mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. We consider the static Schwarzschild metric in spherical and isotropic coordinates, the stationary Eddington-Finkelstein…
We illustrate a simple derivation of the Schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of Einstein's special theory of relativity. We do this by extending the wave equation for…