Mathematicians crack formula for measuring curved spacetime
Researchers have developed a new geometric measurement tool that works under looser conditions than previous methods, opening doors to better models of curved spacetime. The discovery could strengthen theoretical foundations for gravitational physics and help refine how scientists predict physical behavior in extreme environments.
Originaltitel: A volume-renormalized mass for asymptotically hyperbolic manifolds
<p>We define a geometric quantity for asymptotically hyperbolic manifolds, which we call the volume-renormalized mass. It is essentially a linear combination of the ADM mass surface integral and a renormalization of the volume. We show that the volume-renormalized mass is well-defined and diffeomorphism invariant under weaker fall-off conditions than required to ensure that the renormalized volume and the ADM mass surface integral are well-defined separately. We prove several positivity results for the volume-renormalized mass. We also use it to define a renormalized Einstein–Hilbert action and a renormalized expander entropy which is nondecreasing under the Ricci flow. Further, we show that local maximizers of the entropy are local minimizers of the volume-renormalized Uaeusmass.</p>