Lightlike p-Branes: Mass "Inflation" and Lightlike Braneworlds

Lagrangian description of lightlike p-branes is presented in two equivalent forms - a Polyakov-type formulation and a dual to it Nambu-Goto-type formulation. Next, the properties of lightlike brane dynamics in generic gravitational backgrounds of spherically symmetric and axially symmetric type are discussed in some detail: "horizon straddling" and "mass inflation" effects for codimension-one lightlike branes and ground state behavior of codimension-two lightlike "braneworlds".