Research in Classical and Quantum Gravity

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

This award supports research in gravitational physics at the University of California, Santa Barbara. Many of the deepest problems in theoretical physics revolve around combining Einstein’s theory of general relativity with quantum theory. The resulting theory is called “quantum gravity” and is needed to understand the origin of the universe, the nature of space and time on small scales, and what happens inside black holes. The research supported by this award will use the latest techniques and tools to try to answer some of these fundamental problems. An essential part of this award is the training of graduate students and postdoctoral researchers in the knowledge and techniques that are central to understanding and discovery in gravitational physics. Through a range of forums from public lectures, to informing media reporters, the Principal Investigators will disseminate the directions and results of their research to a broad audience. Society at large will benefit by increasing their understanding of science and the world they live in. This award involves three related programs of research. PI Horowitz will explore black holes at very low temperatures in more general situations than has been done before. This will include breaking some spatial symmetry (both with and without a cosmological constant) and including quantum corrections to general relativity. It has recently been shown that these black holes can have much larger tidal forces near their horizon than previously thought. PI Horowitz will investigate new examples and look for possible astrophysical applications. PI Marolf will explore evidence for and implications of the idea that gravitational systems have a finite density of states, meaning that in a finite region of space, they can have only a finite number of states with energy less than any chosen value. While this idea would explain the thermodynamic properties of black holes, it is well known to fail in perturbative treatments of quantum gravity. In particular, one can find black hole geometries with arbitrarily large volumes of space behind the horizon, and which can thus hold arbitrary numbers of independent states. A focus of PI Marolf’s work will be the study of toy models in which the density of states in the full theory is much smaller than that of the naive perturbative theory. Horowitz and Marolf will both study possible definitions of quantum gravity associated with Feynman’s reformulation of quantum mechanics as a sum of all possible histories. For gravitational systems, such histories are entire spacetimes and so are associated with both geometry and topology. If one considers positive definite metrics, the sum over topologies has recently been argued to lead to the above-described finite density of states. But relativity teaches us that the metric of a physical spacetime is not positive definite, and the desired so-called Lorentz-signature metrics are not compatible with general such topologies. This tension will be explored from a variety of viewpoints. The methods employed in all three programs of research will be primarily analytic, though these will be supplemented with numerical calculations on desktop computers. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.