Doubly special relativity provides an intriguing scenario for studying possible modifications of special relativity. To the leading order of quantum corrections, the scenario is characterized simply by several free parameters in boost generators, dispersion relation and momentum addition law. In this scenario, we work out finite-boost transformations in 3 þ 1 dimensions. Constraints on parameters are obtained from compatibility analysis, in agreement with other studies. Combining two successive noncollinear boosts, we also obtain the Wigner rotation angle in this scenario. Our analysis is restricted mainly to the case of the commutative addition law.

The black hole information paradox is related to the area of event horizon, and potentially to the volume and singularity behind it. One example is the complexity/volume duality conjectured by Stanford and Susskind. Accepting the proposal of Christodoulou and Rovelli, we calculate the maximal volume inside regular black holes, which are free of curvature singularity, in asymptotically flat and anti-de Sitter spacetimes respectively. The complexity/volume duality is then applied to anti-de Sitter regular black holes. We also present an analytical expression for the maximal volume outside the de Sitter horizon.

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