A Quantum Bound State Description of Black Holes

Black holes are embedded as bound states in a relativistic quantum theory of weakly coupled constituent fields. The constituents are immersed in a non perturbative vacuum structure representing strong collective effects via in medium modifications. The latter are parametrized in terms of condensates. Observables such as the constituent distribution, the constituent number and energy density are constructed, and calculated at the parton level. Remarkably, even at this level, these observables receive only non perturbative contributions. Furthermore, observables associated with the interior of black holes show simple scalings with the total constituent number. Finally, an explicit framework for calculating gauge corrections is presented.

Qualifying the importance of space{time geometry relative to the fundamental status of Hilbert{space geometry gives rise to a prominent cultural clash across physics communities. The favoured perspective seems to prefer quantum mechanics as the sole fundamental framework, while space{time geometry appears to be a derived rather than a basic concept. The combination of quantum mechanics with causal structures, however, requires light{ cones at its foundation. This potential tension is resolved by distinguishing the Minkowski light{cone in accordance with locality principles. Within this framework, general relativity is an e ffective description derived from an underlying quantum theory of the gravitational eld. As such its domain of validity is, a priori, restricted to deformations of the fundamental Minkowski light cone. Beyond this domain, solutions of general relativity are either describing new ground states, thus qualifying the existence of a fundamental light{cone, or, in accordance with a distinguished causal structure, are mere geometrical artefacts void of a Hilbert space connection.

In this article, we follow a more pragmatic approach and show how certain space{times can be, at least complementary, described as quantum bound states. The bound state description is explicitly developed in the case of Schwarzschild black holes. This example is particularly plausible since it admits a distinct spherical surface that is of fundamental signi cance. On the near side of the Schwarzschild surface, the causal structure is granted by light{cones that can be described as weakly deformed cousins of Minkowski light{cones. At the Schwarzschild surface, however, these deformations become strong. Accordingly, the interior of the Schwarzschild sphere might not be represented by a physical geometry, albeit a geometrical solution exists. The relation of this geometrical solution to quantum mechanics is unclear and it is doubtful that one can be established. Therefore, in the present work, it will be quali ed as unphysical. As a consequence, the geometrical de nition of a black hole is valid only on the near side of the Schwarzschild surface. Clearly, this de nition cannot be fundamental.

In summary, the Schwarzschild surface can be considered as a boundary separating the interior of a quantum bound state from an exterior admitting an approximate geometrical description.

Read more : http://arxiv.org/pdf/1403.3224