## Doctoral defence — Aruna Rajagopal

**When:**Fri, 21/05/2021 – 13:00 to 15:00

**Where:**Askja: Room 132

The defence will be streamed live

**Ph.D. student:** Aruna Rajagopal

**Dissertation title:** Out of equilibrium hydrodynamics with and without boost symmetry

**Opponents:**

Dr. Giuseppe Policastro, Professor at Laboratoire de Physique Théorique, Ecole Normale Superieure, Paris, France

Dr. Koenraad Schalm, Professor at the Instituut Lorentz, Universiteit Leiden, Netherlands

**Advisor:** Dr. Lárus Thorlacius, Professor at the Faculty of Physical Sciences, University of Iceland

**Doctoral committee:**

Dr. Valentina Giangreco M. Puletti, Professor at the Faculty of Physical Sciences, University of Iceland

Dr. Þórður Jónsson, Professor at the Faculty of Physical Sciences, University of Iceland

Dr. Jelle Hartong, Lecturer at the University of Edinburgh, Scotland

**Chair of Ceremony:** Dr. Einar Örn Sveinbjörnsson, Professor and the Head of the Faculty of Physical Sciences, University of Iceland

**Abstract:**

In this thesis, we explore the role of symmetries in hydrodynamics by studying certain properties of relativistic and non-relativistic fluids.

In the first part of the thesis, we examine the theory of relativistic magnetohydrodynamics (Maxwell electromagnetism coupled to hydrodynamics) and its low temperature incarnation, force-free electrodynamics, reformulated in the language of higher-form symmetries and discuss the advantages of such a scheme. Using this framework, we analyse the regime of validity of force-free electrodynamics by evaluating the lifetime of the non-conserved electric field operator via a holographic model sharing the same global symmetries as that of a plasma. We are able to explicitly calculate the lifetime of the electric field, both parallel and perpendicular to the magnetic field, and find that there are indeed no long-lived modes that interfere with a hydrodynamic description of force-free electrodynamics.

In the second part of the thesis, we study the thermodynamic properties of non-relativistic Lifshitz fluids with an arbitrary dynamic exponent z (encoding the anisotropy in the scaling of time and space coordinates). We study energy transport in such fluids far from equilibrium after performing a local quench between two semi-infinite fluid reservoirs. We find that the late time energy flow is universal and accommodated via a steady state occupying an expanding central region between outgoing shock and rarefaction waves (a non-equilibrium steady state), as seen previously for relativistic scale invariant fluids. Armed with an equation of state for a perfect Lifshitz fluid with an arbitrary z and moving with a velocity v, we proceed to study its holographic dual using the well-established Einstein-Maxwell-Dilaton model. We find that the fluid velocity appears as the chemical potential, conjugate to the dual kinetic mass density and the solutions represent a physically distinct class of black branes possessing a linear momentum, different from boosting a static brane.

**About the doctoral candidate:
**Aruna Rajagopal was born in New Delhi, India, where she completed her high school diploma in 2008 and BSc in Physics (Hons) from St. Stephen’s College (University of Delhi) in 2011. She received her MSc degree in Physics from IIT Madras in 2013. She then moved to Canada where she received a master’s degree in theoretical physics from Perimeter Institute in 2014 and completed a one-year research project in theoretical biophysics from the University of Waterloo. After working as a research assistant in the Centre for High Energy Physics in Bangalore in 2016, she moved to Iceland to pursue a PhD degree in November 2016.