Related papers: Reinstating Schwarzschild's original manifold and …
In a recent paper Liu considered the complete Schwarzschild interior and exterior solution in harmonic coordinates. There he argued about the necessity to keep an integration constant, in contrast with previous treatments. The purpose of…
We construct a complete embedded minimal surface with arbitrary genus in the doubled Schwarzschild 3-manifold. A classical desingularization method is used for the construction.
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
The double Schwarzschild solution in the equal mass case is studied in bispherical coordinates. An explicit conformal transformation from cylindrical Weyl coordinates to bispherical coordinates is given in terms of elliptic functions. A…
We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. The metric perturbation induced by a particle can be divided into two parts, the direct part (or…
The brachistochrone problem can be solved either by variational calculus or by a skillful application of the Snellius' law of refraction. This suggests the question whether also other variational problems can be solved by an analogue of the…
We consider inverse curvature flows in warped product manifolds, which are constrained subject to local terms of lower order, namely the radial coordinate and the generalized support function. Under various assumptions we prove longtime…
The purpose of this work is to show a possible reconciliation between Mach's principle and the Schwarzschild solution, using a description of this solution in terms of a new radial cooordinate related to the behaviour of Unruh detectors.
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…
We resume former discussions of the conformally invariant wave equation on a Schwarzschild background, with a particular focus on the behaviour of solutions near the 'cylinder', i.e. Friedrich's representation of spacelike infinity. This…
In this note the Schwarzschild and Kerr solutions are constructed for 3 space and $N$ time dimensions. Solutions, by construction, possesses symmetry with respect to rotations in time volume.
We investigate static spherically symmetric solutions within the framework of the local limit of nonlocal gravity. This theory departs from Einstein's general relativity (GR) through the introduction of a scalar gravitational susceptibility…
Though popular presentations give the Schwarzschild singularity as a point it is known that it is spacelike and not timelike. Thus it has a "length" and is not a "point". In fact, its length must necessarily be infinite. It has been proved…
Some solutions of the Einstein equations for the eight-dimensional Riemann extension of the classical four-dimensional Schwarzschild metric are considered.
The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse…
We compute the first-order correction in the quartic coupling $\alpha$ to the entanglement entropy of a massive, non-minimally coupled scalar across the horizon of a four-dimensional Schwarzschild black hole, treating the non-minimal…
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…
C.T.C. Wall and the first author discovered an extension of Arnold's strange duality embracing on one hand series of bimodal hypersurface singularities and on the other, isolated complete intersection singularities. In this paper, we derive…
We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…
This paper is an expansion of my lecture for David Epstein's birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3-manifolds. This `logical…