Black holes and black strings in M-theory on Calabi–Yau threefolds with four Kähler parameters

Abstract Combining toric geometry techniques and $$\mathcal {N}=2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> supergravity formalisms, we study 5D black branes in the M-theory compactification on a four parameter Calabi–Yau threefold. First, we investigate 5D BPS and non-BPS black holes that are derived by wrapping M2-branes on non-holomorphic 2-cycles in such a toric Calabi–Yau manifold. Concretely, we provide the allowed electric charge regions of BPS and non-BPS black hole states that are obtained by surrounding M2-branes over appropriate 2-cycles. Then, we approach the black hole thermodynamic behavior by computing the entropy and the temperature. By evaluating the recombination factor, we examine the stability of such non-BPS black holes. Precisely, we find stable and unstable solutions depending on the allowed electric charge regions. After that, we study 5D black strings by wrapping M5-branes on non-holomorphic dual 4-cycles in the proposed toric Calabi–Yau manifold by focusing on the stability behaviors. In the allowed regions of the moduli space of the non-BPS stringy solutions, we find stable and unstable states depending on the magnetic charge values.