Thermodynamics of static solutions in ( n + 1 )-dimensional quintic quasitopological gravity

Based on the fact that some important theories like string and M theories predict spacetime with higher dimensions, so, in this paper, we aim to construct a theory of quintic quasitopological gravity in higher dimensions ( n ≥ 5 ). This ( n + 1 )-dimensional quintic quasitopological gravity can also lead to the most second-order linearized field equations in the spherically symmetric spacetimes. These equations cannot be solved exactly, and so we obtain a new class of ( n + 1 )-dimensional static solutions with numeric methods. For large values of mass parameter m , these solutions yield to black holes with two horizons in AdS and flat spacetimes. For dS solutions, there are two values, m ext and m cri , which yield to a black hole with three horizons for m ext < m < m cri . We also calculate thermodynamic quantities for this black hole such as entropy and temperature and check the first law of thermodynamics. Finally, we analyze the thermal stability of the ( n + 1 )-dimensional static black hole at the horizon r + . Unlike dS solutions, AdS ones have thermal stability for each value of k , but flat solutions are stable with just k = 1.