Studies of singularities, black holes, and gravitational radiation

The National Science Foundation Division of Physics awarded Oakland University $150,000 as a project grant on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support theoretical research on singularities, black holes, and gravitational radiation through the period of performance ending July 31, 2029.

The funded work encompasses three research projects. The first examines the properties of singularities formed during gravitational collapse, specifically the forces experienced by observers approaching a singularity. The second investigates smoothing mechanisms that produced the observed uniformity in density, pressure, and other properties throughout the early universe, comparing inflation during rapid post-Big Bang expansion against contraction mechanisms preceding the Big Bang. The third project conducts numerical simulations of gravitational collapse using a tetrad formulation of the vacuum Einstein field equations, employing harmonic time slicing and adaptive mesh refinement to explore both spacelike and null components of black hole singularities without symmetry constraints, while also simulating mechanisms responsible for homogeneity and isotropy in early-universe conditions.

Work is performed in Rochester, Michigan at Oakland University, a public research institution that maintains a research portfolio concentrated in life sciences and engineering with substantial engagement across the federal research funding landscape.

Abstract

Inside a black hole, the object continues to become smaller and smaller under the influence of its own gravity until IT becomes a point with infinite density and infinite gravitational field called a singularity. One project supported by this award involves working out the properties of the singularities formed in gravitational collapse, and in particular, the forces felt by any observer who approaches the singularity. One striking feature of the early universe is that the density, pressure, and all other properties are almost exactly the same at all points in space. IT is not thought that this uniformity just happened: rather, IT is expected that the very early universe was highly non-uniform and that IT became uniform through some kind of smoothing mechanism. A second project will investigate two different possible smoothing mechanisms: one occurs during a period of extremely rapid expansion shortly after the big bang. The other occurs during a contracting phase of the universe that precedes the big bang. IT is thought that the singularity inside a black hole has both a spacelike piece and a null piece. This project will perform numerical simulations of gravitational collapse to explore the properties of both parts of the singularity. The simulation makes use of a tetrad formulation of the vacuum einstein field equations. The spacetimes simulated have no symmetry, and the code has both parallelism and adaptive mesh refinement provided by pretorius? Pamr package. The code will use harmonic time slicing so that the surfaces of constant time approach arbitrarily close to the singularity without hitting IT. This project will also perform numerical simulations to study mechanisms that make conditions in the early universe homogeneous and isotropic. In particular, a comparison between the standard cosmological mechanism of inflation, which occurs during a period of rapid expansion, and the ``ekpyrotic?? Mechanism, which occurs during a period of contraction preceding the big bang, will be performed. The codes use a tetrad formalism, no symmetry, and parallelism, and adaptive mesh refinement provided by pamr. The codes use constant mean curvature slicing, so that when the universe becomes uniform, the slices become the standard cosmological time slices. 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.- subawards are not planned for this award.