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We study the near-horizon spacetime for isolated and dynamical trappinghorizons (equivalently marginally outer trapped tubes). The metric is expandedrelative to an ingoing Gaussian null coordinate and the terms of that expansionare explicitly calculated to second order. For the spacelike case, knowledge ofthe intrinsic and extrinsic geometry of the (dynamical) horizon is sufficientto determine the near-horizon spacetime, while for the null case (an isolatedhorizon) more information is needed. In both cases spacetime is allowed to beof arbitrary dimension and the formalism accomodates both general relativity aswell as more general field equations.  The formalism is demonstrated for two applications. First, spacetime isconsidered near an isolated horizon and the construction is both checkedagainst the Kerr-Newman solution and compared to the well-known near-horizonlimit for stationary extremal black hole spacetimes. Second, spacetime isexamined in the vicinity of a slowly evolving horizon and it is demonstratedthat there is always an event horizon candidate in this region. The geometryand other properties of this null surface match those of the slowly evolvinghorizon to leading order and in this approximation the candidate evolves in alocally determined way. This generalizes known results for Vaidya as well ascertain spacetimes known from studies of the fluid-gravity correspondence.

Spacetime near isolated and dynamical trapping horizons