Description
Some of the most prominent modern theoretical frameworks of high energy physics and gravity require the existence of spacetimes with dimension greater than four. Time and three space dimensions are the typical ingredients of standard applications of General Relativity to cosmology. In string theory this basic assumption is relaxed. For example, under certain assumptions a flat Minkowski spacetime in string theory requires ten (or eleven) spacetime dimensions. More generally, the concept of spacetime dimension in string theory is emergent and dynamical (spacetime dimension can change dynamically in a process or it can be different in separate regions of spacetime). It may also depend on the degrees of freedom that are used to describe a system --equivalent `dual’ descriptions of a system may require different spacetime dimensions. A prominent example of the latter occurs in the AdS/CFT correspondence: a holographic correspondence between quantum gravity and standard non-gravitational quantum field theories.
The project will survey a key component of these developments: extremal and non-extremal black hole solutions in gravitational theories of higher-dimensional spacetimes. Emphasis will be given to examples that appear in string theory. We will discover that higher-dimensional gravity is already classically a rather complicated framework, which is not constrained by the typical uniqueness theorems in four dimensions. It allows, in particular, black hole solutions with novel exotic horizon topologies. We will study a whole range of classical aspects of such solutions: black strings, black membranes (in general, `black brane') solutions. We will connect their properties to fluid dynamics, string theory dynamics and quantum field theory dynamics via the AdS/CFT (holographic) correspondence.
Literature
`TASI lectures on black holes in string theory’, A.W. Peet, https://cds.cern.ch/record/456069/files/0008241.pdf
`Large N field theories, string theory and gravity’, O. Aharony, S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz , https://arxiv.org/pdf/hep-th/9905111.pdf
`Instabilities of black strings and branes’, T. Harmark, V. Niarchos, N.A. Obers , https://arxiv.org/pdf/hep-th/0701022.pdf
`Phases of higher dimensional black holes’, V. Niarchos , https://arxiv.org/pdf/0808.2776.pdf
`The fluid gravity correspondence’, V.E. Hubeny, S. Minwalla, M. Rangamani, https://arxiv.org/pdf/1107.5780.pdf
`Blackfold approach to higher dimensional black holes’, R. Emparan, T. Harmark, V. Niarchos, N.A. Obers, https://s3.cern.ch/inspire-prod-files-f/f0fb0f54a4c3b5a27026a14de19de6a2
Prerequisites
Mathematical Physics II
Quantum Mechanics III
Corequisite
General Relativity IV
Advanced Quantum Theory IV (not necessary, but would help)