Hairy rotating black string in the Einstein-Maxwell-Higgs system

We show numerically that the Abelian Higgs field equations in the background of a four-dimensional rotating charged black string have vortex solutions. These solutions which have axial symmetry show that the rotating black string can support the Abelian Higgs field as hair. We find that one encounters with an electric field coupled to the Higgs scalar field for the case of rotating black string. This electric field is due to an electric charge per unit length, which increases as the rotation parameter becomes larger. We also find that the vortex thickness decreases as the rotation parameter grows up. Finally we consider the self-gravity of the Abelian Higgs field and show that the effect of the vortex is to induce a deficit angle in the metric under consideration which decreases as the rotation parameter increases.Comment: 16 pages, 8 figures, references added, some minor corrections don

Thermodynamics of a Kerr Newman de Sitter Black Hole

We compute the conserved quantities of the four-dimensional Kerr-Newman-dS (KNdS) black hole through the use of the counterterm renormalization method, and obtain a generalized Smarr formula for the mass as a function of the entropy, the angular momentum and the electric charge. The first law of thermodynamics associated to the cosmological horizon of KNdS is also investigated. Using the minimal number of intrinsic boundary counterterms, we consider the quasilocal thermodynamics of asymptotic de Sitter Reissner-Nordstrom black hole, and find that the temperature is equal to the product of the surface gravity (divided by $2\pi$) and the Tolman redshift factor. We also perform a quasilocal stability analysis by computing the determinant of Hessian matrix of the energy with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles and obtain a complete set of phase diagrams. We then turn to the quasilocal thermodynamics of four-dimensional Kerr-Newman-de Sitter black hole for virtually all possible values of the mass, the rotation and the charge parameters that leave the quasilocal boundary inside the cosmological event horizon, and perform a quasilocal stability analysis of KNdS black hole.Comment: REVTEX4, 12 pages, 12 figures, references added and some points in Sec II have been clarified, version to appear in Can. J. Phy

Vortices in De Sitter Spacetimes

We investigate vortex solutions to the Abelian Higgs field equations in a four dimensional de Sitter spacetime background. We obtain both static and dynamic solutions with axial symmetry that are generalizations of the Nielsen-Olesen gauge vortices in flat spacetime. The static solution is located in the static patch of de Sitter space. We numerically solve the field equations in an inflationary (big bang) patch and find a time dependent vortex soution, whose effect to create a deficit angle in the spacetime. We show that this solution can be interpreted in terms of a renormalization group flow in accord with a generalized {$c$}-theorem, providing evidence in favour of a dS/CFT correspondence.Comment: 14 pages, 8 figures, two figures changed, typos corrected, conclusions and two new figures added, version to appear in PL

Horizonless Rotating Solutions in (n+1)(n+1)-dimensional Einstein-Maxwell Gravity

We introduce two classes of rotating solutions of Einstein-Maxwell gravity in $n+1$ dimensions which are asymptotically anti-de Sitter type. They have no curvature singularity and no horizons. The first class of solutions, which has a conic singularity yields a spacetime with a longitudinal magnetic field and $k$ rotation parameters. We show that when one or more of the rotation parameters are non zero, the spinning brane has a net electric charge that is proportional to the magnitude of the rotation parameters. The second class of solutions yields a spacetime with an angular magnetic field and $$ boost parameters. We find that the net electric charge of these traveling branes with one or more nonzero boost parameters is proportional to the magnitude of the velocity of the brane. We also use the counterterm method inspired by AdS/CFT correspondence and calculate the conserved quantities of the solutions. We show that the logarithmic divergencies associated to the Weyl anomalies and matter field are zero, and the $r$ divergence of the action can be removed by the counterterm method.Comment: 14 pages, references added, Sec. II amended, an appendix added. The version to appear in Phys. Rev.

Ricci flat rotating black branes with a conformally invariant Maxwell source

We consider Einstein gravity coupled to an $U(1)$ gauge field for which the density is given by a power of the Maxwell Lagrangian. In $d$-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as $d/4$. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking--Page phase transition in spite of conformally invariant Maxwell field.Comment: 13 pages, one figur

Charged rotating dilaton black branes in AdS universe

We present the metric for the $(n+1)$-dimensional charged rotating dilaton black branes with cylindrical or toroidal horizons in the background of anti-de Sitter spacetime. We find the suitable counterterm which removes the divergences of the action in the presence of the dilaton potential in all higher dimensions. We plot the Penrose diagrams of the spacetime and reveal that the spacetime geometry crucially modifies in the presence of the dilaton field. The conserved and thermodynamic quantities of the black branes are also computed.Comment: 13 pages, 3 figures, to appear in Gen. Relat. Gravi

Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity

In this paper, we study topological AdS black branes of $(n+1)$-dimensional Einstein-Maxwell-dilaton theory and investigate their properties. We use the area law, surface gravity and Gauss law interpretations to find entropy, temperature and electrical charge, respectively. We also employ the modified Brown and York subtraction method to calculate the quasilocal mass of the solutions. We obtain a Smarr-type formula for the mass as a function of the entropy and the charge, compute the temperature and the electric potential through the Smarr-type formula and show that these thermodynamic quantities coincide with their values which are calculated through using the geometry. Finally, we perform a stability analysis in the canonical ensemble and investigate the effects of the dilaton field and the size of black brane on the thermal stability of the solutions. We find that large black branes are stable but for small black brane, depending on the value of dilaton field and type of horizon, we encounter with some unstable phases.Comment: 21 pages, 21 figures, references updated, minor editing, accepted in EPJC (DOI: 10.1140/epjc/s10052-010-1483-3

Cosmological Black Holes on Branes

We examined analytically a cosmological black hole domain wall system. Using the C-metric construction we derived the metric for the spacetime describing an infinitely thin domain wall intersecting a cosmological black hole. We studied the behaviour of the scalar field describing a self-interacting cosmological domain wall and find the approximated solution valid for large distances. The thin wall approximation and the back raection problem were elaborated finding that the topological kink solution smoothed out singular behaviour of the zero thickness wall using a core topological and hence thick domain wall. We also analyze the nucleation of cosmological black holes on and in the presence of a domain walls and conclude that the domain wall will nucleate small black holes on it rather than large ones inside.Comment: 13 pages, Revtex, to be published in Phys.Rev. D1

Vortex Holography

We show that the Abelian Higgs field equations in the four dimensional anti de Sitter spacetime have a vortex line solution. This solution, which has cylindrical symmetry in AdS$_4$, is a generalization of the flat spacetime Nielsen-Olesen string. We show that the vortex induces a deficit angle in the AdS$_4$ spacetime that is proportional to its mass density. Using the AdS/CFT correspondence, we show that the mass density of the string is uniform and dual to the discontinuity of a logarithmic derivative of correlation function of the boundary scalar operator.Comment: LaTeX, 20 pages, 4 eps figures, references and two paragraphs added, to appear in Nucl. Phys.

Rotating Black Branes in the presence of nonlinear electromagnetic field

In this paper, we consider a class of gravity whose action represents itself as a sum of the usual Einstein-Hilbert action with cosmological constant and an $U(1)$ gauge field for which the action is given by a power of the Maxwell invariant. We present a class of the rotating black branes with Ricci flat horizon and show that the presented solutions may be interpreted as black brane solutions with two event horizons, extreme black hole and naked singularity provided the parameters of the solutions are chosen suitably. We investigate the properties of the solutions and find that for the special values of the nonlinear parameter, the solutions are not asymptotically anti-deSitter. At last, we obtain the conserved quantities of the rotating black branes and find that the nonlinear source effects on the electric field, the behavior of spacetime, type of singularity and other quantities.Comment: 7 pages, 5 figures, to appear in EPJ