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Lagrangian description of lightlike p-branes is presented in two equivalentforms - a Polyakov-type formulation and a dual to it Nambu-Goto-typeformulation. Next, the properties of lightlike brane dynamics in genericgravitational backgrounds of spherically symmetric and axially symmetric typeare discussed in some detail: "horizon straddling" and "mass inflation" effectsfor codimension-one lightlike branes and ground state behavior ofcodimension-two lightlike "braneworlds".

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