In this paper, the curvature structure of a (2+1)-dimensional black hole in
the massive-charged-Born-Infeld gravity is investigated. The metric that we
consider is characterized by four degrees of freedom which are the mass and
electric charge of the black hole, the mass of the graviton field, and a
cosmological constant. For the charged and neutral cases separately, we present
various constraints among scalar polynomial curvature invariants which could
invariantly characterize our desired spacetimes. Specially, an appropriate
scalar polynomial curvature invariant and a Cartan curvature invariant which
together could detect the black hole horizon would be explicitly constructed.
Using algorithms related to the focusing properties of a bundle of light rays
on the horizon which are accounted by the Raychaudhuri equation, a procedure
for isolating the black hole parameters, as the algebraic combinations
involving the curvature invariants, would be presented. It will be shown that
this technique could specially be applied for black holes with zero electric
charge, contrary to the cases of solutions of lower-dimensional non-massive
gravity. In addition, for the case of massive (2+1)-dimensional black hole, the
irreducible mass, which quantifies the maximum amount of energy which could be
extracted from a black hole through the Penrose process would be derived.
Therefore, we show that the Hawking temperatures of these black holes could be
reduced to the pure curvature properties of the spacetimes. Finally, we comment
on the relationship between our analysis and the novel roles it could play in
numerical quark-gluon plasma simulations and other QCD models and also black
hole information paradox where the holographic correspondence could be
exploited.Comment: v3; 25 pages; 11 figures; 105 reference