Related papers: Race for the Kerr field
We present the first X-ray reflection model for testing the assumption that the metric of astrophysical black holes is described by the Kerr solution. We employ the formalism of the transfer function proposed by Cunningham. The calculations…
A metric representing the Kerr geometry has been obtained by Pretorius and Israel. We make a coordinate transformation on this metric, thereby bringing it into Bondi-Sachs form. In order to validate the metric, we evaluate it numerically on…
Since the full General Theory of Relativity has been unveiled to the scientific community in 1915, many solutions to the vacuum Einstein field equations have been found and studied. This paper aims at documenting exhaustively the derivation…
It is thought that the spacetime metric around astrophysical black holes is well described by the Kerr solution of Einstein's gravity. However, a robust observational evidence of the Kerr nature of these objects is still lacking. Here we…
The Kerr-Newman metric is used to discuss the averagely measured speed of light along the radial direction at the black hole from a weak-gravitation reference frame such as an observer on Earth. The velocity equation of light at the black…
Aguirregabiria et al showed that Einstein, Landau and Lifshitz, Papapetrou, and Weinberg energy-momentum complexes coincide for all Kerr-Schild metric. Bringely used their general expression of the Kerr-Schild class and found energy and…
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…
In the Comment on "Can accretion disk properties observationally distinguish black holes from naked singularities?", by Bertrand Chauvineau, Phys. Rev. D {\bf 98}, 088501 (2018), the author did show that the metric used in Z. Kov\'{a}cs and…
Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry in radial and angular parts. Chakrabarti solved the angular equation and found the corresponding eigenvalues for different Kerr parameters. The…
The equations of motion of massive test particles near Kerr black holes are separable in Boyer-Lindquist coordinates, as established by Carter. This separability, however, is lost when the particles are endowed with classical spin. We show…
Between 1941 and 1962, scalar-tensor theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now…
The Kerr metric is known to present issues when trying to find an interior solution. In this work we continue in our efforts to construct a more realistic exterior metric for astrophysical objects. A new approximate metric representing the…
An active stage of relativistic astrophysics started in 1963 since in this year, quasars were discovered, Kerr solution has been found and the first Texas Symposium on Relativistic Astrophysics was organized in Dallas. Five years later, in…
We are motivated by a problem about running: If a race was completed in an average pace of P minutes per mile, is there necessarily some mile of the race that was run in exactly P minutes? The answer is no. We explain why, and describe the…
In this paper we investigate the shrinking target property for irrational rotations. This was first studied by Kurzweil (1951) and has received considerable interest of late. Using a new approach, we generalize results of Kim (2007) and…
In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily…
Now that English translations of Schwarzschild's original paper exist, that paper has become accessible to more people. Historically, the so-called "standard Schwarzschild solution" was not the original Schwarzschild's work, but it is…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
We analyse the expression for the mass of a stationary axisymmetric configuration in general relativity obtained in our previous work [1]. From the generality of our formula and its incompatibility with the corresponding expression in Kerr…
A very famous ``test'' of the General Theory of Relativity (GTR) is the advance of Mercury's perihelion (and of other planets too). To be more precise, this is not a prediction of General Relativity, since the anomaly was known in the XIXth…