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In a nutshell
In a nutshell
Relativity is full of surprises. Well-established theories such as thermodynamics, hydrodynamics, kinetic theory, statistical mechanics, and quantum mechanics can undergo dramatic conceptual changes when embedded in a Lorentzian spacetime manifold. I specialize in formulating mathematically well-posed theories of matter that are consistent with the four-dimensional geometric nature of our world. I am particularly interested in studying the implementation of the principle of relativistic causality (see Fig. 1 below) in theories of matter, and in understanding the extreme consequences of relativity of simultaneity (see Fig. 2 below).
Relativity is full of surprises. Well-established theories such as thermodynamics, hydrodynamics, kinetic theory, statistical mechanics, and quantum mechanics can undergo dramatic conceptual changes when embedded in a Lorentzian spacetime manifold. I specialize in formulating mathematically well-posed theories of matter that are consistent with the four-dimensional geometric nature of our world. I am particularly interested in studying the implementation of the principle of relativistic causality (see Fig. 1 below) in theories of matter, and in understanding the extreme consequences of relativity of simultaneity (see Fig. 2 below).
My research finds applications in relativistic astrophysics (neutron stars, accretion disks near black holes, and cosmology) and high-energy physics (especially the quark-gluon plasma).
My research finds applications in relativistic astrophysics (neutron stars, accretion disks near black holes, and cosmology) and high-energy physics (especially the quark-gluon plasma).
Fig.1: Illustration of the principle of causality in relativity
A matter field (such as the energy density) at a spacetime point x can only receive information from within the past lightcone of x, marked in red in the figure. The surface of the past lightcone is defined as the set of all points y which can emit a photon that reaches x traveling along a null geodesic.
Fig.2: Consequences of relativity of simultaneity, a gedankenexperiment
In the reference frame of Alice (A), a neutron is in a quantum superposition, with 1/2 probability of being in the left box and 1/2 probability of being in the right box. After some time T, it beta-decays. Bob (B) moves with velocity −v with respect to Alice. His line of contemporary events (dashed line) is oblique by relativity of simultaneity, and intersects the two boxes at two different Alice's times. Thus, in Bob’s frame, there is 1/2 probability of having a neutron in the right box, and 1/2 probability of having a proton, an electron, and an antineutrino in the left box. The Lorentz boost has entangled the "decayed-ness" operator with the position of center of mass of the system. This has surprising implications for the relativistic theory of unstable particles, see this article.
Main research areas
Main research areas
Relativistic Hydrodynamics
Relativistic Hydrodynamics
Relativistic hydrodynamics studies the large-scale motion of fluids in spacetime. A "fluid" is a substance that does not exhibit a response in shear stress when subjected to infinitely slow shear deformation. Liquids, gases, and plasmas are examples of fluids. Similarly to Newtonian hydrodynamics, relativistic hydrodynamics relies on partial differential equations to determine the evolution of matter.
The study of relativistic fluids has received a boost in recent years, with the production of the quark-gluon plasma at RHIC and LHC, the detection of gravitational waves from neutron star mergers by LIGO and Virgo, and the photographic imaging of the accretion disk of a black hole by the EHT. These are three notable examples of experimental manifestations of physical processes in which relativistic matter is believed to exist in a fluid state. The physical interpretation of the experimental data relies on numerical simulations, which solve the differential equations of relativistic hydrodynamics (often coupled with gravity).
I mostly work on the theoretical development of the hydrodynamic equations. This includes the following research activities:
Deriving the equations from a more fundamental description (like kinetic theory, see e.g. this paper);
Testing the physical predictions of the equations in analytically solvable scenarios, see e.g. this paper and this paper;
Verifying the mathematical consistency of the equations (e.g. determining if the initial value problem is well-posed, see e.g. this paper);
Comparing the predictions of alternative theories, see e.g. this paper and this paper;
Interpreting the results of simulations, see e.g. this paper and this paper.
Relativistic Kinetic Theory
Relativistic Kinetic Theory
Most of the Baryonic matter in our universe exists in a plasma or gaseous state. Substances of this kind can usually be modeled, at the microscopic level, through kinetic theory, which tracks the number of particles in a given phase-space cell (i.e. in a given location and with a given momentum). The master equation governing the evolution of these systems is the celebrated Boltzmann transport equation.
For large-scale processes, with slowly varying fields, kinetic theory is known to reduce to Navier-Stokes hydrodynamics, with some corrections. I am interested in understanding the impact of these corrections, especially in a relativistic context. I study kinetic effects in high-energy gases and plasmas that escape conventional hydrodynamics, and try to understand whether hydrodynamics can be expanded to account for these effects. See this paper and this paper for a couple of examples.
Relativistic Thermodynamics
Relativistic Thermodynamics
The maximum entropy principle states that, when an isolated system is in thermodynamic equilibrium, its entropy is maximal. This fundamental postulate lays the foundations of statistical mechanics, and it can be used to derive well-known thermodynamic inequalities (e.g. the specific heat of extensive systems is non-negative).
In a sequence of papers (see e.g. this, this, and this paper), I and some collaborators have shown that, when we apply the maximum entropy principle to relativistic matter, and require it to hold simultaneously in all reference frames, novel thermodynamic inequalities emerge. As it turns out, one such inequality is the requirement that the speed of sound cannot exceed the speed of light. These findings have set the foundations of a new research area in high-energy physics, which studies how the principle of Lorentz invariance affects the mathematical structure of thermodynamic laws.
Relativistic Quantum Mechanics
Relativistic Quantum Mechanics
Relativity and quantum mechanics, taken individually, are renowned for giving rise to all sorts of apparent paradoxes and counterintuitive phenomena, most of which are now well-understood. However, when we try to combine relativity and quantum mechanics together, the resulting paradoxes become much more difficult to resolve, and some of them (like the black hole information paradox) are still open. I have been working on the following selected problems:
Relativistic quantum theory of unstable particles: According to Special Relativity, an unstable particle that travels close to the speed of light takes a longer time to decay, due to relativistic time dilation. However, it is perhaps less known that formulating a rigorous quantum theory of high-energy unstable particles is quite challenging. Most calculations (also based on quantum field theory) do not seem to recover the time dilation formula exactly. In this article, we have explained the origin of the discrepancy, by proving that decay probabilities can never be exactly Lorentz invariant in a relativistic quantum theory.
Quantum mechanics on Closed Timelike Curves: A spacetime with closed timelike curves is a spacetime that admits time travel to the past. Time travel is often assumed to lead to possible self-contradictory histories, as exemplified by the grandfather paradox. In this article, we prove that, in a quantum theory, all self-contradictory theories are forbidden.
Speed of quantum tunneling in relativity: Some claims have been made that quantum tunneling (when modeled using the Dirac equation) might be a superluminal process. In this article , we demonstrate that, for all practical purposes, no superluminal effect is physically detectable.
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