Research

Research overview

In our everyday life mass and energy are naturally positive and gravity is attractive. These properties of classical matter were exactly what allowed Roger Penrose, who was awarded the 2020 Nobel prize in Physics, to show the inevitability of singularities; points of infinite density at the center of black holes. Positive energy also does not allow for so called "exotic" spacetimes, those with spacetime bridges known as wormholes and time machines. 

Meanwhile, quantum matter surprisingly allows for negative energy, a fact that has been measured in the lab. However, this negative energy is not without restrictions. It has been shown that within quantum mechanics we can have a large amount of negative energy for a short time, or a small amount for a long time. Such restrictions are called quantum energy inequalities. Using quantum energy inequalities we can prove the existence of singularities for quantum matter and rule out causality violating spacetimes.   

My research focuses on the semiclassical regime where quantum fields live on a classical curved spacetime described by the general theory of relativity. This is the intersection of gravity and field theory, and brings together different approaches such as mathematical relativity, algebraic quantum field theory and black hole thermodynamics. 

I have co-authored a topical review on "Energy conditions in general relativity and quantum field theory" invited by Classical and Quantum Gravity [1] with Dr. Ko Sanders from Dublin City University. This is the first review to combine classical and quantum results in the field and summarize the applications of energy conditions.

Null quantum energy inequalities: Important relativity theorems have in their hypotheses the null energy condition whose natural generalization to semiclassical gravity is a null smeared quantum energy inequality. Lower bounds for quantum energy inequalities smeared on null segments are known to diverge. One idea is to introduce a UV cutoff for the quantum field theory which prevents the divergence of the lower bound. Using this quantum inequality, known as the smeared null energy condition, my collaborators and I proved a Penrose-type singularity theorem as well as a generalization of the Hawking area theorem in semiclassical gravity. A better null quantum energy inequality that does not use the UV cutoff but instead averages over both null directions is the double smeared null energy condition that we recently derived for free scalar fields in Minkowski. The bound can be generalized to spacetimes with curvature.  (Relevant publications: [1], [2], [3], [4], [5])

Singularity theorems from worldvolume inequalities: The absence of a lower bound on the renormalized null energy on finite geodesic segments but the existence of such a bound on area or volume integrals motivates the research for classical relativity theorems with wolrdvolume integrated quantum energy inequalities. We derived such a theorem for the Hawking-type singularity theorem using techniques from Riemannian mathematical relativity. In an ongoing project we examine the null incompleteness case. (Relevant publications: [1], [2])

The QuEST project:  The "Quantum Energy Conditions and Singularity Theorems" project received funding by EU Horizon 2020 programme. The project that I developed and worked on under the supervision of Prof. Christopher J. Fewster at the University of York explored an important topic in mathematical physics today: the occurrence of singularities in spacetime - places where the usual understanding of physics breaks down. For example, singularities may exist at the center of black holes, or may have occurred at the beginning of the universe. Singularity theorems, developed over the past 50 years following pioneering work of Penrose and Hawking, are mathematically rigorous results that imply that singularities are inevitable provided the matter content of the universe obeys a suitable energy conditions. Although forms of matter described by quantum field theory can violate the original energy conditions, they can obey quantum energy inequalities. During the project we rigorously showed that singularity theorems for quantized matter fields are possible. Such a theorem was proven in the timelike incompleteness case and the required initial contraction was estimated. Additionally, a new method of proving singularity theorems (of both types) with weakened energy conditions was developed. (Relevant publications: [1], [2], [3], [4] , [5])

Energy conditions and eternal inflation: Eternal inflation requires upward fluctuations of the energy in a Hubble volume, which appear to violate the energy conditions. In a project with my collaborator Prof. Ken D. Olum we investigated the violation of energy conditions during eternal inflation and showed how eternal inflation is possible when energy conditions (even the null energy condition) are obeyed. The critical point is that energy conditions restrict the evolution of any single quantum state, while the process of eternal inflation involves repeatedly selecting a subsector of the previous state, so there is no single state where the conditions are violated. (Relevant publications: [1], [2])

ANEC: My PhD work focused on the averaged null energy condition or ANEC. ANEC requires the non-negativity of the null-contracted stress-energy tensor averaged over an entire null geodesic. It is of special interest since it is sufficient to rule out exotic spacetimes such as those with wormholes, closed timelike curves and superluminal travel. In series of publications, my advisor Ken D. Olum and Iproved that a minimally coupled quantum scalar field in a classical curved background has to obey ANEC, thus ruling our the existence of exotic phenomena in this kind of spacetimes. (Relevant publications: [1], [2], [3], [4], [thesis]) 

Research with undergraduate students

During my time at Bard College and the College of the Holy Cross I engaged in research with undergraduate students during the academic year, supervising senior projects and leading summer research under the Bard summer research institute and the Holy Cross research associates program. One of the projects that I have worked on with undegraduate students is exoplanetary microlensing. 

Exoplanetary microlensing: Gravitational lensing is the general relativistic effect where a massive object bends the light from a background source as it travels toward the observer. Dependent on the number of lenses, the observer views two or more images of the source. In gravitational microlensing these images have separations of less than a few milliarcseconds and so they remain unresolved with current capabilities. My students have so far focused on the theoretical aspect of gravitational microlensing, specifically on circumbinary systems with two stars and one planet. They explored the mathematical framework of the triple lens equation numerically, and produced theoretical light curves for different numbers of lenses. The project began with Bard student Eleanor Turrell who wrote her undergraduate thesis on the topic and continued with Holy Cross students Brett George and Patrycja Przewoznik who worked on it during the summer of 2020. (Relevant publications: [1])