Noncommutative geometry inspired rotating black string

Noncommutativity is an idea dating back to the early times of Quantum Mechanics and that string theory induced noncommutative (NC) geometry which provides an effective framework to study short distance spacetime dynamics. Also, string theory, a candidate for a consistent quantum theory of gravity, admits a variety of classical black hole solutions including black strings. In this paper, we study a NC geometry inspired rotating black string to cylindrical spacetime with a source given by a Gaussian distribution of mass. The resulting metric is a regular, i.e. curvature-singularity free, rotating black string, that in large $r$ limit interpolates Lemos \cite{lemos96} black string. Thermodynamical properties of the black strings are also investigated and exact expressions for the temperature, the entropy and the heat capacity are obtained. Owing to the NC correction in the solution, the thermodynamic quantities have been also modified and that the NC geometry inspired black string is always thermodynamically stable.Comment: 19 pages, 11 figure

Stationary black holes and stars in the Brans-Dicke theory with Λ>0\Lambda >0 revisited

It was shown a few years back that for a stationary regular black hole or star solution in the Brans-Dicke theory with a positive cosmological constant $\Lambda$, endowed with a de Sitter or cosmological event horizon in the asymptotic region, not only there exists no non-trivial field configurations, but also the inverse Brans-Dicke parameter $\omega^{-1}$ must be vanishing. This essentially reduces the theory to Einstein's General Relativity. The assumption of the existence of the cosmological horizon was crucial for this proof. However, since the Brans-Dicke field $\phi$, couples directly to the $\Lambda$-term in the energy-momentum tensor as well as $\Lambda$ acts as a source in $\phi$'s equation of motion, it seems reasonable to ask : can $\phi$ become strong instead and screen the effect of $\Lambda$, at very large scales, so that the asymptotic de Sitter structure is replaced by some alternative, yet still acceptable boundary condition? In this work we analytically argue that no such alternative exists, as long as the spacetime is assumed to be free of any naked curvature singularity. We further support this result by providing explicit numerical computations. Thus we conclude that in the presence of a positive $\Lambda$, irrespective of whether the asymptotic de Sitter boundary condition is imposed or not, a regular stationary black hole or even a star solution in the Brans-Dicke theory always necessitates $\omega^{-1}=0$, and thereby reducing the theory to General Relativity. The qualitative differences of this result with that of the standard no hair theorems are also pointed out.Comment: v3; 10pp, 4 figs; Accepted for publication in Physical Review D (Letter