Numerical Simulations of Spacetime Singularities
Spacetime singularities occur at the Big Bang and in black hole interiors. This talk describes the use of computer simulations to understand the nature of spacetime singularities. Both the vacuum Einstein equations and matter models are treated. Most of the simulations are done for the case of closed, inhomogeneous cosmologies. In this case, the simulations show that the BKL approximation, in which time derivatives are more important than space derivatives, is justified. The relevance of these results for black hole interiors is discussed.
Two Notions of Naturalness
I will distinguish two notions of naturalness in use in BSM physics and argue that recognizing this distinction has methodological consequences. One notion of naturalness is an “autonomy of scales” requirement: it prohibits sensitive dependence of an effective field theory’s low-energy observables on precise specification of the theory’s description of cutoff-scale physics. General structural features of effective field theory provide reasonably good justification for the role this notion of naturalness has played in BSM model building. A second, distinct notion construes naturalness as a statistical principle requiring that the values of the parameters in an effective field theory be “likely” for some appropriately chosen measure on some appropriately circumscribed space of models. These two notions are historically and conceptually related but are motivated by distinct theoretical considerations and admit of distinct solutions.