We study static (electrically)-charged solutions of Eddington-inspired Born-Infeld (EiBI) theory of gravity in general D-dimensional spacetime. We consider both linear (Maxwell) as well as nonlinear electrodynamics for the matter fields. In this particular work, the nonlinear theory we specifically consider is the Born-Infeld (BI) electrodynamics. The solutions describe higherdimensional black holes in EiBI gravity. For the linear Maxwell field, we show that the electric field is still singular for D > 4. This singularity is cured when EiBI is coupled to the BI electrodynamics. We obtain EiBI-BI black hole solutions in the limit ofα ≡ 4κb 2 /λ = 1 and 2. We also investigate their thermodynamical property. We show that all solutions satisfy the first-law of black hole thermodynamics, from which their corresponding ADM mass can be extracted. It is found that κ imposes a charge screening that makes the corresponding Hawking temperature experiences some sudden jump from charged-type to the Schwarzschild-type at some critical value of κ. Thermodynamical stability reveals that the EiBI-BI black holes can exist with smaller horizon than their Reissner-Nordstrom (RN) counterparts. * Electronic address: byon.nugraha@ui.ac.id † Electronic address: hramad@ui.ac.id arXiv:1810.08780v4 [gr-qc] 5 Apr 2019Black hole has been an intriguing phenomenon in gravitational physics that fascinates both theoretical physicists as well as astronomers. In General Relativity (GR), the theoretical existence of black holes is inevitable. Observationally, the recent detection of gravitational waves is a solid proof that such object does exist physically [1].Although as a modern cosmological framework general relativity is very successful, several large-scale or strong-field regime phenomena (such as the accelerated expansion of the universe, the big bang singularity, etc) demands a more satisfactory explanation. This is the main reason behind the vast modern literature on modified-gravitational theories beyond GR. Among many excellent alternative theory of gravity, the Eddington-inspired Born-Infeld (EiBI) theory proposed by Banados and Ferreira recently enjoys widespread attention [2].
Constructed based on the old proposal of Eddington gravitational action [3] combined withthe nonlinearity of the Born-Infeld (BI) theory [4], this particular theory resurrects the popular old-Born-Infeld gravity models [5,6]. This theory offers interesting solutions to some theoretical and cosmological problems, like the freedom from ghosts and instabilities [7], or the non-singularity of big bang and big crunch [8,9] (however, see the discussions in [10][11][12]). In nuclear astrophysics the EiBI model finds its (perhaps) most active elaboration since coupling it to the NS equation of state (EOS) enables one to obtain the observed mass of the Neutron Star (NS) while simultaneously solves the "hyperon puzzle" (see, for example, [13,14] and references therein). For a comprehensive review on EiBI gravity, see [15].Despite the extensive investigation on the astroph...