Thermodynamics of static solutions in (n+1)-dimensional Quintic Quasitopological gravity

Abstract

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 ($n\ge 5$). 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 can not 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, $m_{\mathrm{ext}}$ and $m_{\mathrm{cri}}$, which yield to a black hole with three horizons for $m_{\mathrm{ext}}<m<m_{\mathrm{cri}}$. We also calculate thermodynamic quantities for this black hole such as entropy and temperature and check the first law of thermodynamics. Finally, we analyze thermal stability of the $(n+1)$-dimensional static black hole at the horizon $r_{+}$. Unlike dS solutions, AdS ones have thermal stability for each values of $k$, but flat solutions are stable with just $k=1$.

11 pages, 5 figures

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