Related papers: Two diverse models of embedding class one
We study noncompact and static membrane solutions in Matrix theory. Demanding axial symmetry on a membrane embedded in three spatial dimensions, we obtain a wormhole solution whose shape is the same with the catenoidal solution of…
The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to…
Wormholes are a solution for General Relativity field equations which characterize a passage or a tunnel that connects two different regions of space-time and is filled by some sort of exotic matter, that does not satisfy the energy…
In this thesis, we investigate traversable wormhole spacetimes within the context of a covariant generalization of Einstein's General Relativity, namely the energy-momentum squared gravity, denoted as $f\left(R,T_{ab}T^{ab}\right)$. Here,…
A study of conformally flat but non flat Bianchi type I and cylindrically symmetric static space-times according to proper projective symmetry is given by using some algebraic and direct integration techniques. It is shown that the special…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
We critically examine proposals for the so-called warp-drive spacetimes and classify these models based on their various restrictions within the framework of General Relativity. We then provide a summary of general formalism for each class,…
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an…
The first junction conditions of spherically symmetric bubbles are solved for some cases, and whereby analytic models to the Einstein field equations are constructed. The effects of bubbles on the spacetime structure are studied and it is…
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales. We show that some such results remain valid for metric spaces with non-unique…
This thesis operates within the framework of general relativity without curvature singularities. The motivation for this framework is explored, and several conclusions are drawn with a look towards future research. There are many ways to…
We introduce a class of space-times modeling singular events such as evaporating black holes and topology changes, which we dub as semi-globally hyperbolic space-times. On these space-times we aim to study the existence of reasonable…
The correspondence of stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in…
We determine hidden conformal symmetries behind the evolution equations of black hole perturbations in a vector-tensor theory of gravity. Such hidden symmetries are valid everywhere in the exterior region of a spherically symmetric,…
In this survey-research paper, we first introduce the theory of Smith classes of complexes with fixed-point free, periodic maps on them. These classes, when defined for the deleted product of a simplicial complex $K$, are the same as the…
Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…
Recent developments for the consistent embedding of general 4D static and spherically-symmetric spacetimes in arbitrary single-brane braneworld models in the form of the General Embedding Algorithm (GEA) [Phys.Rev.D 109 (2024) 4, L041501],…
We reconsider the problem of $f(R)$ theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a…
We investigate five dimensional Einstein spaces in warped geometries from the point of view of the four dimensional physically relevant Robertson-Walker-Friedman cosmological metric and the Schwarzschild metric. We show that a…
A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down.…