|Luca Bombelli: Research Interests|
General Research Interests
Almost all of my research is in gravitational theory, although at times I also get interested in problems in other areas of theoretical physics and mathematical physics,1 especially if it seems that they will help me understand aspects of gravitation that are too difficult to tackle directly.
Gravitational physics as we understand it today is basically the study of the structure of spacetimes, but it has grown over the past few decades from a small area of research concerned mainly with mathematical properties of Einstein's theory of general relativity into a broad field whose theoretical aspects range from astrophysics and cosmology to quantum gravity, one of the most challenging boundaries of our current understanding of the nature of matter and spacetime. Gravitational physics has also developed a solid experimental side with the building of a variety of gravitational wave detectors, and with high-precision tests of gravitational effects on Earth and in orbit; it has found practical applications in the GPS system, as well as in the guidance of spacecraft.
Within gravitational physics, the subjects that interest me most are: Quantum gravity (semiclassical loop quantum gravity, causal sets, phenomenology); Lorentzian and Riemannian geometry and their relationships with discrete structures; and Classical phenomena such as general relativistic chaos and properties of waves and particles in curved spacetimes.
My main motivation for studying quantum gravity is to understand what the fundamental structure of spacetime looks like at the smallest scales, where the continuum picture that we are used to from our experience at large scales probably breaks down. The techniques I use in this work are canonical quantization of the theory of general relativity, and a combinatorial approach for a discrete form of spacetime structure.
About the Gravitational Theory Group
Research in gravitational physics at Ole Miss covers both classical and quantum aspects of gravitational theories. Among the classical aspects, of particular interest are the study of the predictions of the theory, with its highly nonlinear dynamics, for the motion of gravitating bodies, the emission of gravitational waves during the gravitational collapse of massive objects, and for the evolution of the early universe. The quantum aspects are motivated by the current attempts to construct a complete theory of quantum gravity and to understand the geometrical structure of spacetime at the smallest scales.
Classical General Relativity
The simplest systems subject to gravitational forces where one can look for relativistic effects not predicted by Newtonian gravitation are binary systems. In fact, some of the classical tests of relativity involve the dynamics of planets in the solar system. Members of the Ole Miss group have studied various aspects of the relativistic dynamics of gravitating binary systems, including the onset of chaos in the motion around perturbed black holes (this work has generated interest because of its potential consequences for the emitted pattern of gravitational radiation), and the effect of the global evolution of the universe on binary systems (the general issue had been around for a long time, and it is known that the effects are very small, but a qualitatively new contribution to the precession of the orbits was found).
Regarding the structure of the gravitating objects themselves, although they involve an infinite number of degrees of freedom, one can study many of their features using simplified models with a high degree of symmetry or lower-dimensional models of gravity, useful for addressing issues in classical gravity that are too difficult to study in four dimensions. Gravitational collapse in three dimensions, for example, can be discussed analytically for a variety of models. Although gravity in three dimensions does not have propagating degrees of freedom (there are no vacuum gravitational waves), black hole solutions with constant curvature have been found. These analytical solutions allow us to test and compare numerical methods, and to discuss in detail the nonlinear dynamics of the gravitational field.
In classical cosmology, Ole Miss researchers have studied the dynamics of models of the early universe, in which the evolution of the gravitational field itself is chaotic; this may have consequences for our understanding of how the present universe emerged from the initial state. In addition, the amplification of the metric quantum fluctuations which are created during inflation is expected to produce a cosmic background of gravitons which, if seen today as relics of the early universe, would give us unique information about the primordial state of our universe. Recent studies of Ole Miss researchers include inflationary graviton production in braneworld models, mixing of massless and massive modes of the tensor perturbation spectrum, and the enhancement of the massless spectral amplitudes.
Quantum Gravity – Theory
The theory of quantum gravity is still in the process of being built. However, several approaches are being actively developed and can be considered promising candidates for the theory. In particular, over the past two decades, two approaches have emerged as the leading ones because they have been developed to a considerable extent and include many features that should be present in a theory of quantum gravity: superstrings and loop quantum gravity.
The loop quantum gravity approach is one in which priority is given to a consistent, non-perturbative, rigorous quantization of gravity as a theory of the spacetime geometry, based on a canonical formalism; matter is then added when the theory is sufficiently well understood. Techniques developed over the past 10 years or so have put loop quantum gravity on a firm mathematical ground and have made it similar to theories of other interactions, particularly gauge theories. The aspects studied at Ole Miss are based mainly on geometrical aspects of this approach, in which the quantum geometry of spacetime at the smallest scales indicates that the continuum picture drawn from our experience at large scales breaks down. Problems studied here include calculating the macroscopic observational effects of the microscopic quantum geometry, and finding quantum states for gravity which have the property that the appear like a classical continuum at large scales.
1 Question: What is the difference between theoretical physics and mathematical physics? Answer: Theoretical physics is done by physicists who lack the necessary skills to do real experiments; mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics. [in D Mermin, Physics Today May 2004, p10]