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Register a new userNotes on R-charged black holes near criticality and gauge theory
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After reviewing the thermodynamics and critical phenomena associated with AdS black holes carrying multiple R-charges in various dimensions, we do a Bragg-Williams like analysis of the systems around its critical points. This leads us to propose an effective potential governing the equilibrium properties of the boundary gauge theory. We also study certain non-equilibrium phenomena associated with these gauge theories. In particular, we compute the conductivities and diffusion coefficients for theories with multiple R-charges in four, three and six dimensions.
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This is a continuation of our earlier work where we constructed a phenomenologically motivated effective action of the boundary gauge theory at finite temperature and finite gauge coupling on $S^3 times S^1$. In this paper, we argue that this effective action qualitatively reproduces the gauge theory representing various bulk phases of R-charged black hole with Gauss-Bonnet correction. We analyze the system both in canonical and grand canonical ensemble.
We study the phase structure and equilibrium state space geometry of R-charged black holes in $D = 5$, 4 and 7 and the corresponding rotating $D3$, $M2$ and $M5$ branes. For various charge configurations of the compact black holes in the canonical ensemble we demonstrate new liquid-gas like phase coexistence behaviour culminating in second order critical points. The critical exponents turn out to be the same as that of four dimensional asymptotically AdS black holes in Einstein Maxwell theory. We further establish that the regions of stability for R-charged black holes are, in some cases, more constrained than is currently believed, due to properties of some of the response coefficients. The equilibrium state space scalar curvature is calculated for various charge configurations, both for the case of compact as well as flat horizons and its asymptotic behaviour with temperature is established.
Using the symmetry of the near-horizon geometry and applying quantum field theory of a complex scalar field, we study the spontaneous pair production of charged scalars from near-extremal rotating, electrically and/or magnetically charged black holes. Analytical expressions for pair production, vacuum persistence and absorption cross section are found, and the spectral distribution is given a thermal interpretation. The pair production in near-extremal black holes has a factorization into the Schwinger effect in AdS and Schwinger effect in Rindler space, measuring the deviational from extremality. The associated holographical correspondence is confirmed at the 2-point function level by comparing the absorption cross section ratio as well as the pair production rate both from the gravity and the conformal field theories. The production of monopoles is discussed.
With the successes of $f(R)$ theory as a neutral modification of Einsteins general relativity (GR), we continue our study in this field and attempt to find general natural and charged black hole (BH) solutions. In the previous papers cite{Nashed:2020mnp,Nashed:2020tbp}, we applied the field equation of the $f(R)$ gravity to a spherically symmetric space-time $ds^2=-U(r)dt^2+frac{dr^2}{V(r)}+r^2 left( dtheta^2+sin^2theta dphi^2 right)$ with unequal metric potentials $U(r)$ and $V(r)$ and with/without electric charge. Then we have obtained equations which include all the possible static solutions with spherical symmetry. To ensure the closed form of system of the resulting differential equations in order to obtain specific solutions, we assumed the derivative of the $f(R)$ with respect to the scalar curvature $R$ to have a form $F_1(r)=frac{df(R(r))}{dR(r)} propto frac{c}{r^n}$ but in case $n>2$, the resulting black hole solutions with/without charge do not generate asymptotically GR BH solutions in the limit $crightarrow 0$ which means that the only case that can generate GR BHs is $n=2$. In this paper, we assume another form, i.e., $F_1(r)= 1-frac{F_0-left(n-3right)}{r^n}$ with a constant $F_0$ and show that we can generate asymptotically GR BH solutions for $n>2$ but we show that the $n=2$ case is not allowed. This form of $F_1(r)$ could be the most acceptable physical form that we can generate from it physical metric potentials that can have a well-known asymptotic form and we obtain the metric of the Einstein general relativity in the limit of $F_0to n-3$. We show that the form of the electric charge depends on $n$ and that $n eq 2$. Our study shows that the power $n$ is sensitive and why we should exclude the case $n=2$ for the choice of $F_1(r)$ presented in this study.
We investigate modifications of the Lifshitz black hole solutions due to the presence of Maxwell charge in higher dimensions for arbitrary $z$ and any topology. We find that the behaviour of large black holes is insensitive to the topology of the solutions, whereas for small black holes significant differences emerge. We generalize a relation previously obtained for neutral Lifshitz black branes, and study more generally the thermodynamic relationship between energy, entropy, and chemical potential. We also consider the effect of Maxwell charge on the effective potential between objects in the dual theory.
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