https://doi.org/10.1140/epjc/s10052-025-14980-7
Regular Article - Theoretical Physics
Exploring four-dimensional Brans–Dicke black holes charged with the Born–Infeld nonlinear source
Department of Physics, Razi University, Kermanshah, Iran
Received:
20
August
2025
Accepted:
21
October
2025
Published online:
30
October
2025
We derive new four-dimensional Brans–Dicke (BD) black holes (BHs) charged with Born–Infeld (BI) source and study their thermodynamics. Starting with the BD action sourced by BI nonlinear electrodynamics, we address the complexity of direct solutions by transforming the BD theory’s Jordan frame action to its conformally equivalent Einstein frame. Following Haghighi and Dehghani (Eur Phys J C 85:652, 2025), the BI parameter is allowed to vary under the conformal transformations (CTs). In the Einstein frame, the theory becomes Einstein–Born–Infeld-dilaton (EBId) gravity, yielding readily solvable field equations. Our exact solutions present two novel classes of EBId BHs with unusual asymptotes, capable of exhibiting extreme, as well as one, two, or three horizons. We compute thermodynamic quantities and confirm the first law of thermodynamics for these EBId BHs. Thermal stability is then analyzed using the canonical ensemble method, focusing on the BHs’ heat capacity (HC) signature. Reversing these transformations, we introduce Brans–Dicke–Born–Infeld (BDBI) BHs, which mirror the Einstein frame solutions. These BDBI BHs also exhibit horizon-less, one-horizon, two-horizon, three-horizon, and extreme forms. We demonstrate the validity of the first law of thermodynamics for the new BDBI BHs and extend the thermal stability analysis to them using the canonical ensemble method.
© The Author(s) 2025
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