Locally AdS$_{d-1}\times\mathbb{R}$ uniform black strings (UBS) in the presence of a massless scalar field are believed to avoid onset Gregory-Laflamme (GL) instability $d\ge4$ as no tachyonic modes exist spectrum Laplace-Beltrami operator. We present analytic and numerical evidence GL Lichnerowicz indicating that AdS$_{d-1}$ UBSs classically thermodynamically unstable at linear level $d>4$. In...

Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show th...