Related papers: Massive particle surfaces and black hole shadows f…

The generalization of photon spheres by considering the trajectories of massive particles leads to the definition of Massive Particle Surfaces (MPS). These surfaces are built with the trajectories of massive particles, and have a partial…

Finsler geometry is just riemannian geometry without the quadratic restriction[1]. In this paper, we study the motion of massive(non-zero rest mass) and massless particles for schwarzschild metric in finsler spacetime in the case of two…

The Kerr-Newman metric is the unique vacuum solution of the General Relativistic field equations, in which any singularities or spacetime pathologies are hidden behind horizons. They are believed to describe the spacetimes of massive…

We review the extraordinary fertility and proliferation in mathematics and physics of the concept of a surface with constant and negative Gaussian curvature. In his outstanding 1868 paper Beltrami discussed how non-Euclidean geometry is…

In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There…

Black hole spacetimes contain several geometrically distinguished hypersurfaces, including event and Cauchy horizons, stationary-limit surfaces, curvature singularities, and asymptotic infinity. These structures are usually identified by…

We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…

Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…

An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove…

We develop a perturbation theory for surfaces confining photons and massive particles in static spherically symmetric spacetimes in terms of two parameters: the mass-to-energy ratio and the deviation of metric functions from a given form,…

We establish a one-to-one correspondence between static spacetimes and Riemannian manifolds that maps causal geodesics to geodesics, as suggested by L. C. Epstein. We then explore constant curvature spacetimes - such as the de Sitter and…

We construct a static spherically symmetric regular black hole with a Minkowski core, and a degenerate inner horizon with vanishing surface gravity. The spacetime contains a non-extremal outer horizon and exhibits two notable features.…

The Gaussian curvature of a two-dimensional Riemannian manifold is uniquely determined by the choice of the metric. The formulas for computing the curvature in terms of components of the metric, in isothermal coordinates, involve the…

It is shown that the free motion of massive particles moving in static spacetimes are given by the geodesics of an energy-dependent Riemannian metric on the spatial sections analogous to Jacobi's metric in classical dynamics. In the…

We combine notions of a maximal curvature scale in nature with that of a minimal curvature scale to construct a non-singular Schwarzschild-de Sitter black hole. We present an exact solution within the context of two-dimensional dilaton…

The curvature scalar invariants of the Riemann tensor are important in General Relativity because they allow a manifestly coordinate invariant characterisation of certain geometrical properties of spacetimes such as, among others, curvature…

It is a common belief that a theory of quantum gravity should ultimately cure curvature singularities which are inevitable within General Relativity, and plague for instance the Schwarzschild and Kerr metrics, usually considered as…

It is widely believed that the curvature singularities are an artifact of general relativity and may not exist in the Universe, and likely to be defined by the quantum gravity. In the absence of successful quantum gravity, significant…

We revisit the notion of massive particle hypersurfaces and place it within a unified framework alongside photon hypersurfaces in stationary spacetimes. More precisely, for Killing-invariant timelike hypersurfaces $T=\mathbb{R}\times S_0$,…

Using a second law of complexity, we prove a black hole singularity theorem. By introducing the notion of trapped extremal surfaces, we show that their existence implies null geodesic incompleteness inside globally hyperbolic black holes.…