abstract

Gravitational waves were predicted by Einstein in 1916 as wave solutions of the Einstein–Hilbert equations of General Relativity. Indirect experimental evidence of their existence was only obtained in the past 40 years, most famously through observations of the binary pulsar PSR 1913+16. Direct detection of gravitational waves is anticipated later this decade. It will be enabled by interferometric detectors Virgo and LIGO. We begin with a brief theoretical description and the historical background of the search for gravitational waves. We describe techniques used in interferometric detectors. We introduce the likely sources of gravitational waves and the foundations of data analysis. We briefly summarize key results to date and conclude with perspectives on future scientific payoffs.

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In these lectures we describe how a quantum geometry of space arises from the composition of angular momenta providing a realization of Penrose’s spin-geometry.

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We review the state-of-the-art of the numerical modeling of black-hole spacetimes in the framework of General Relativity in four and more spacetime dimensions. The latest developments of the applications of these techniques to study black holes in the context of astrophysics, gravitational wave physics and high-energy physics are summarized.

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In this paper we review our present understanding of the fractal structure of two-dimensional Euclidean quantum gravity coupled to matter.

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The model of Causal Dynamical Triangulations is a nonperturbative and background independent approach to quantum theory of gravity. In this paper, we give introduction to the four dimensional framework of Causal Dynamical Triangulations and present recent results. We describe the phase structure of the model and show how a macroscopic four dimensional de Sitter universe emerges dynamically from the full gravitational path integral. We advocate that the effective action describing scale factor fluctuations reconstructed from Monte Carlo data agrees with the minisuperspace model.

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We explain how to compute the conductivity of strongly interacting quantum field theories which have a dual holographic description in terms of gravitational physics in anti-de Sitter space-time.

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This is an extended version of my lecture at the LIII Cracow School of Theoretical Physics in Zakopane in which I presented the results of joint work with P. Bizoń (Phys. Rev. Lett. 111, 041102 (2013)) concerning (in)stability of the three-dimensional anti-de Sitter spacetime.

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After a brief introduction to classical relativity, we describe how to solve the Cauchy problem in general relativity. In particular, we introduce the notion of gauge source functions and explain how they can be used in order to reduce the problem to that of solving a system of hyperbolic partial differential equations. We then go on to explain how the initial value problem is formulated for the so-called Einstein–Vlasov system and describe a recent future global non-linear stability result in this setting. In particular, this result applies to models of the universe which are consistent with observations.

abstract

We present a brief overview of tools and methods of noncommutative geometry and its applications to theoretical physics. Starting with some mathematical background and basic foundations of NCG, we describe the new notion of geometry and demonstrate that changing the paradigm of geometry allows to interpret the physical reality of fundamental interactions from a completely new angle. We present some easy do-it-yourself toy models, which help to understand the principles and results hidden behind the interpretation of the Standard Model in the language of noncommutative geometry.