VandyGRAF

Vanderbilt initiative for gravity, waves, and fluids

VandyGRAF Initiative

VandyGRAF Initiative

The Vanderbilt Initiative for Gravity, Waves, and Fluids is an interdisciplinary research venture providing mathematicians, physicists, and astrophysicists with the resources and space to connect and collaboratively work on problems of outstanding scientific merit, such as:

  • General relativity: theoretical, mathematical, numerical, or experimental, including, but not restricted to, black holes, gravitational radiation, and multimessenger astrophysics.
  • Fluid mechanics: theoretical, mathematical, numerical, or experimental, including, but not restricted to, relativistic fluids far from equilibrium.
  • Evolution of partial differential equations related to fluids and gravity, including, but not restricted to, the geometric analysis of waves and fluids.
  • The physics and mathematics of neutron star mergers and high-energy nuclear collisions.

VandyGRAF Seminar Series

All VandyGRAF talks will take place in the Chapel in the 17th&Horton building, unless indicated below.

Marcelo Disconzi, Vanderbilt University, September 19, 12:30 pm

The mathematics of general-relativistic stars

Astronomy is arguably the oldest scientific discipline. Precise measurements of the motion of celestial bodies date back to the ancient Babylonians, Chinese, Greeks, and indigenous peoples outside Eurasia. Starting in the 19th century, systematic applications of physical principles to the formation and dynamics of stars marked the birth of astrophysics as a subfield of physics. Present-day astrophysics employs an array of theoretical and observational tools to construct sophisticated and predictive models of the origin, evolution, and death of stars. While stars can be largely described within Newtonian physics, some of their most interesting properties, such as bounds on their mass-radius ratio, their potential collapse into a black hole, or effects of viscosity on gravitational waves emitted by mergers of neutron stars, can only be studied via applications of general relativity. Moreover, as a matter of principle, we ought to be able to fully understand stars as general-relativistic phenomena. The mathematical treatment of stars within general relativity, however, has lagged. Little progress has been made on this front since the discovery of the Tolman-Oppenheimer-Volkoff (TOV) equations and the Oppenheimer-Snyder solution in the late ‘30s. The former describes a static (i.e., time independent), perfectly spherically symmetric star, whilst the latter describes the collapse of a perfectly spherically symmetric star with no pressure into a black hole. Despite being landmark results in general relativity, both situations are highly idealized. Inferences about generic properties of general-relativistic stars derived from such models are, therefore, a priori unjustified.

In this talk, I will discuss the problem of formulating a sound mathematical theory of general-relativistic star evolution based on the Einstein-Euler system. After setting up the problem, I will explain its main challenges, but also how a great deal of rich physics and mathematics is involved in its study. A fundamental difficulty involves understanding the mathematics of the fluid-vacuum interface which separates the body of the star from vacuum. This interface displays a singular behavior which is not amenable to current mathematical techniques. This difficulty, however, can be circumvented if we consider stars that are spherically symmetric but not static. This corresponds to a dynamic (i.e., time-dependent) generalization of the TOV equations.

K. E. Saavik Ford, American Museum of Natural History, Dept. of Astrophysics,
September 26, 12:30 pm, Room A1013

The AGN Channel for Stellar Mass Binary Black Hole Mergers

Active Galactic Nuclei (AGN) have historically been studied and understood strictly as gas disks accreting onto supermassive black holes. However, we now understand that there are ‘things’ in AGN accretion disks-specifically stars and stellar mass black holes. Based on our understanding of the physics of ‘things in disks’ (largely derived for protoplanetary systems), we can predict the detectable signatures of these ‘things’, including binary black hole (BBH) mergers (detectable via gravitational waves-GW), tidal disruption events (TDEs), changing look AGN (CL-AGN) and quasi-periodic eruptions (QPEs), among others. Understanding the signatures of ‘things in disks’ will enable us to reverse engineer the parameters of both AGN disks and nuclear star clusters (NSCs) as a function of redshift. This is especially valuable for NSCs, which are usually poorly observationally constrained at redshifts other than zero. Looking ahead, we will see that ‘things’ in AGN disks are especially important for our understanding of Rubin and LISA observations, both of which will produce haystacks of data requiring careful searches for shiny, but possibly sharp, needles.