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Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…
While General Relativity ranks undoubtedly among the best physics theories ever developed, it is also among those with the most striking implications. In particular, General Relativity admits solutions which allow faster than light motion…
Space and matter may both be manifestations of a single fundamental quantum dynamics, as it may become evident during black-hole evaporation. Inspired by the fact that quantum electrodynamics underlies the classical theory of elasticity,…
A conventional space-time diagram is $r-ct$ one, which satisfies the Minkowski geometry. This geometry conflict the intuition from the Euclid geometry. In this work an Euclid space-time diagram is proposed to describe relativistic world…
We present a dynamical toy model for an expanding universe inside a black hole. The model is built by matching a spherically symmetric collapsing matter cloud to an expanding Friedmann-Robertson-Walker universe through a phase transition…
Most approaches to quantum gravity suggest that relativistic spacetime is not fundamental, but instead emerges from some non-spatiotemporal structure. This paper investigates the implications of this suggestion for the possibility of time…
A generic spacetime topology contains timelike boundaries. Making use of two such boundaries, we formulate a microscopic holographic dual that captures cosmological spacetime beyond the cosmic horizon patch, including the future wedge. We…
These lecture notes are an elementary and pedagogical introduction to the black hole evaporation, based on a lecture given by the author at the Ninth Modave Summer School in Mathematical Physics and are intended for PhD students. First,…
The first comprehensive analyses of Planck data reveal that the cosmological model with dark energy and cold dark matter can satisfactorily explain the essential physical features of the expanding Universe. However, the inability to…
Camanho, Edelstein, Maldacena and Zhiboedov have shown that gravitons can experience a negative Shapiro time delay, i.e. a time advance, in Einstein-Gauss-Bonnet theory. They studied gravitons propagating in singular "shock-wave"…
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…
We study traversable wormholes by considering the duality between BTZ black holes and two-dimensional conformal field theory on the thermofield double state. The BTZ black holes can be rendered traversable by a negative energy shock wave.…
If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological…
It is commonly believed that Alcubierre's warp drive works by contracting space in front of the warp bubble and expanding space behind it. We show that this expansion/contraction is but a marginal consequence of the choice made by…
In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat.…
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman's path integral for superposition…
2+1 dimensional anti-de Sitter space has been the subject of much recent investigation. Studies of the behaviour of point particles in this space have given us a greater understanding of the BTZ black hole solutions produced by topological…
We discuss the macroscopic quantum tunneling from the black hole to the white hole of the same mass. Previous calculations in Ref.[1] demonstrated that the probability of the tunneling is $p \propto \exp(-2S_\text{BH})$, where $S_\text{BH}$…
Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often…