相关论文: Embedding spacetime via a geodesically equivalent …
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an…
A duality between spacetime manifolds, the geodesic duality, is introduced. Two manifolds are geodesic dual, if the transformation between their metrics is also the transformation between their geodesics. That is, the transformation that…
Under certain conditions, a $(1+1)$-dimensional slice $\hat{g}$ of a spherically symmetric black hole spacetime can be equivariantly embedded in $(2+1)$-dimensional Minkowski space. The embedding depends on a real parameter that corresponds…
We study the approach to gravity in which our curved spacetime is considered as a surface in a flat ambient space of higher dimension (the embedding theory). The dynamical variable in this theory is not a metric but an embedding function.…
A simple algebraic global isometric embedding is presented for the nonrotating BTZ black hole and its counterpart of Euclidean signature. The image of the embedding, in Minkowski space of two extra dimensions, is the interection of two…
Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for…
We prove that the isometric embedding of any metric of differentiability class C1 in E3 exists. We use simplified notation for the given metric, namely geodesic parameters, and level parameters for the embedded surface in E3. Central to our…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be…
The idea of an oscillating Universe has remained a topic of interest even after the discovery of dark energy. This paper confirms this idea by means of another well-established theory in general relativity, the embedding of curved…
This is one of a number of papers in which the metric for space-time is defined on the subatomic level by means of the interchange of photons, and constrained to be consistent with radar. It is shown that the discrete nature of particle…
This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…
Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by reducing the problem to the motion of a test particle in an effective potential. In absence of magnetic field comparison is established with Schwarzschild's geometry.…
It is proved in the manuscript that as long as the proper coordinate transformation is introduced,, the equations of geodetic lines described in curved space-time can be transformed into the dynamic equations in flat space-time, that is to…
We introduce a class of metrics on $\mathbb{R}^n$ generalizing the classical Grushin plane. These are length metrics defined by the line element $ds = d_E(\cdot,Y)^{-\beta}ds_E$ for a closed nonempty subset $Y \subset \mathbb{R}^n$ and…
We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric.…
The rotational metric provides an exact solution to Einstein's clock-rate problem in curved spacetime, specifically, whether time flows more slowly at the equator of a compact object such as a neutron star than at its poles. It features a…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
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…
In recent papers on spacetimes with a signature-changing metric, the concept of a Lorentzian-Euclidean black hole and new elements for Lorentzian-Riemannian signature change have been introduced. A Lorentzian-Euclidean black hole is a…