相关论文: Schwarzschild Spacetime without Coordinates

Among the coordinates used to construct a conformal compactification of the Schwarzschild spacetime, none of them simultaneously extend smoothly both through an event horizon and beyond null infinity.To construct such coordinates, instead…

The Kruskal-Szekeres coordinates construction for the Schwarzschild spacetime could be viewed geometrically as a squeezing of the $t$-line associated with the asymptotic observer into a single point, at the event horizon $r=2M$. Starting…

Using new approach to construction of space-times emerging from quantum information theory, we identify the space of quantum states that generates the Schwarzschild space-time. No quantisation procedure is used. The emergent space-time is…

In this paper we construct the Fermi coordinates along any arbitrary line in simple analytical way without use the orthogonal frames and their parallel transport. In this manner we extend the Eddington approach to the construction of the…

Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation…

Starting from the Einstein equations in Schwarzschild-de Sitter (SdS) spacetime and imposing Friedmann-Robertson-Walker coordinates at large distances, we find two coordinate systems with time-dependent metrics that are smooth across both…

In this pedagogical note, the Kruskal - Szekeres completion of the Schwarzschild spacetime is obtained explicitly in a few steps.

A variety of historical coordinates in which the Schwarzschild metric is regular over the whole of the extended spacetime are compared and the hypersurfaces of constant coordinate are graphically presented. While the Kruscal form (one of…

The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global…

We present a discussion of the periodicity in imaginary time of maximally extended black hole spacetimes without reference to Euclidean manifolds. As motivation, we first demonstrate our approach for the Rindler geometry in flat space…

We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition -- in precise sense -- of the Schwarzschild metric with a certain free data set propagating…

We construct semiglobal singular spacetimes for the Einstein equations coupled to a massless scalar field. Consistent with the heuristic analysis of Belinskii, Khalatnikov, Lifshitz or BKL for this system, there are no oscillations due to…

The Schwarzschild-Melvin spacetime is an exact solution of the Einstein electrovacuum equations describing a black hole immersed in a magnetic field which is asymptotically aligned with the z-axis. It plays an important role in our…

An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.

We reconsider space-time singularities in classical Einsteinian general relativity: with the help of several new co-ordinate systems we show that the Schwarzschild solution can be extended beyond the curvature singularity at r=0. The…

We study a non-uniformly rotating universe outside a Schwarzschild black hole by generating a time-dependent manifold of revolution around a straight line. In this simple model where layers of spherical shells of the universe non-uniformly…

The generic null geodesic of the Schwarzschild--Kruskal--Szekeres geometry has a natural complexification, an elliptic curve with a cusp at the singularity. To realize that complexification as a Riemann surface without a cusp, and also to…

After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field…

The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in…

The continuation of the Schwarzschild metric across the event horizon is almost always (in textbooks) carried out using the Kruskal-Szekeres coordinates, in terms of which the areal radius r is defined only implicitly. We argue that from a…