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The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are…
We consider a universe formed in a black hole in the Einstein--Cartan theory of gravity. The interior of a Schwarzschild black hole can be represented by the Kantowski--Sachs metric that describes a closed anisotropic universe. We use this…
We give a comparative description of different types of regular static, spherically symmetric black holes (BHs) and discuss in more detail their particular type, which we suggest to call black universes. The latter have a Schwarzschild-like…
We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with lambda>=0) in a Euclidean space E^N. Assume that the immersion is proper, that is, the preimage of every compact set in E^N is also…
The issue of defining the volume of black holes has significant implications for quantum gravity. Drawing on concepts from quantum theory and general relativity, several motivations for introducing discreteness in geometry can be proposed.…
The Universal Extra Dimension (UED) paradigm is particularly attractive as it not only includes a natural candidate for the Dark Matter particle but also addresses several issues related to particle physics. Non-observations at the Large…
We study black hole solutions in the Einstein gravity with Gauss-Bonnet term, the dilaton and a positive "cosmological constant" in various dimensions. Physically meaningful black holes with a positive cosmological term are obtained only…
Euclid is a European Space Agency medium class mission selected for launch in 2020 within the Cosmic Vision 2015 2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will…
Using black-hole arguments with widely accepted premises, we show that it is extremely improbable that space is Euclidean, and that it is unspeakably improbable that space is hyperbolic. Independently, using an argument which makes no…
The nucleation and evolution of bubbles are investigated in the model of an $O(3)$-symmetric scalar field coupled to gravity in the high temperature limit. It is shown that, in addition to the well-known bubble of which the inside region is…
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive…
Several different approaches to quantum gravity suggest the effective dimension of spacetime reduces from four to two near the Planck scale. In light of such evidence, this letter re-examines the thermodynamics of primordial black holes…
We present the geodesical completion of the Schwarzschild black hole in four dimensions which covers the entire space in (u,v) Kruskal-Szekeres coordinates, including the spacetime behind the black and white hole singularities. The…
Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple…
I give a brief informal introduction to the idea and tests of large extra dimensions, focusing on the case in which the space-time manifold has a direct product structure. I then describe some attractive implementations in which the…
One of the simplest way to extend 4D cosmological models is to add another spatial dimension to make them 5D. In particular, it has been shown that the simplest of such 5D models, i.e., one in which the right hand side of the Einstein…
We construct a static solution for 4+1 dimensional bulk such that the 3+1 dimensional world has a linear warp factor and describes the Schwarzschild-dS_{4} black hole. For m=0 this four dimensional universe and Friedmann Robertson Walker…
Given a bulk scalar field with sufficient self-interactions in a higher dimensional spacetime, it is shown that the continuous symmetries in four dimensions, induced by the topological structure of the compact manifold, naturally lead to…
The concept of Euclidean time is proposed which is dual to the usual Minkowski time. The De Sitter solution is shown to be dual to the anti-De Sitter solution under the dual transformation in which Euclidean time and Minkowski time are…
We reconsider entropy arguments which have been previously argued to support the idea that the dark matter constituents are primordial black holes with many solar masses. It has recently been shown that QCD axions which solve the strong CP…