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Zielinski, Sophia (2016): Spacetime geometry from graviton condensation: a new perspective on black holes. Dissertation, LMU München: Faculty of Physics



In this thesis we introduce a novel approach viewing spacetime geometry as an emergent phenomenon based on the condensation of a large number of quanta on a distinguished flat background. We advertise this idea with regard to investigations of spacetime singularities within a quantum field theoretical framework and semiclassical considerations of black holes. Given that in any physical theory apart from General Relativity the metric background is determined in advance, singularities are only associated with observables and can either be removed by renormalization techniques or are otherwise regarded as unphysical. The appearance of singularities in the spacetime structure itself, however, is pathological. The prediction of said singularities in the sense of geodesic incompleteness culminated in the famous singularity theorems established by Hawking and Penrose. Though these theorems are based on rather general assumptions we argue their physical relevance. Using the example of a black hole we show that any classical detector theory breaks down far before geodesic incompleteness can set in. Apart from that, we point out that the employment of point particles as diagnostic tools for spacetime anomalies is an oversimplification that is no longer valid in high curvature regimes. In view of these results the question arises to what extent quantum objects are affected by spacetime singularities. Based on the definition of geodesic incompleteness customized for quantum mechanical test particles we collect ideas for completeness concepts in dynamical spacetimes. As it turns out, a further development of these ideas has shown that Schwarzschild black holes, in particular, allow for a evolution of quantum probes that is well-defined all over. This fact, however, must not distract from such semiclassical considerations being accompanied by many so far unresolved paradoxes. We are therefore compelled to take steps towards a full quantum resolution of geometrical backgrounds. First steps towards such a microscopic description are made by means of a non-relativistic scalar toy model mimicking properties of General Relativity. In particular, we model black holes as quantum bound states of a large number N of soft quanta subject to a strong collective potential. Operating at the verge of a quantum phase transition perturbation theory naturally breaks down and a numerical analysis of the model becomes inevitable. Though indicating 1/N corrections as advertised in the underlying so-called Quantum-N portrait relevant for a possible purification of Hawking radiation and henceforth a resolution of the long-standing information paradox we recognize that such a non-relativistic model is simply not capable of capturing all relevant requirements of a proper black hole treatment. We therefore seek a relativistic framework mapping spacetime geometry to large-N quantum bound states. Given a non-trivial vacuum structure supporting graviton condensation this is achieved via in-medium modifications that can be linked to a collective binding potential. Viewing Minkowski spacetime as fundamental, the classical notion of any other spacetime geometry is recovered in the limit of an infinite constituent number of the corresponding bound state living on Minkowski. This construction works in analogy to the description of hadrons in quantum chromodynamics and, in particular, also uses non-perturbative methods like the auxiliary current description and the operator product expansion. Concentrating on black holes we develop a bound state description in accordance with the isometries of Schwarzschild spacetime. Subsequently, expressions for the constituent number density and the energy density are reviewed. With their help, it can be concluded that the mass of a black hole at parton level is proportional to its constituent number. Going beyond this level we then consider the scattering of a massless scalar particle off a black hole. Using previous results we can explicitly show that the constituent distribution represents an observable and therefore might ultimately be measured in experiments to confirm our approach. We furthermore suggest how the formation of black holes or Hawking radiation can be understood within this framework. After all, the gained insights, capable of depriving their mysteries, highlights the dubiety of treating black holes by means of classical tools. Since our setup allows to view other, non-black-hole geometries, as bound states as well, we point out that our formalism could also shed light on the cosmological constant problem by computing the vacuum energy in a de Sitter state. In addition, we point our that even quantum chromodynamics, and, in fact, any theory comprising bound states, can profit from our formalism. Apart from this, we discuss an alternative proposal describing classical solutions in terms of coherent states in the limit of an infinite occupation number of so-called corpuscles. Here, we will focus on the coherent state description of Anti-de Sitter spacetime. Since most parts of this thesis are directed to find a constituent description of black holes we will exclude this corpuscular description from the main part and introduce it in the appendix.