Embedding Branes in Flat Two-time Spaces

We show how non-near horizon, non-dilatonic $p$-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers.Comment: LaTex, 8 pages. Contribution to the TMR Conference on Quantum aspects of gauge theories, supersymmetry and unification. Paris, 1-7 September 199

Mass inflation in a D dimensional Reissner-Nordstrom black hole: a hierarchy of particle accelerators ?

We study the geometry inside the event horizon of perturbed D dimensional Reissner-Nordstrom-(A)dS type black holes showing that, similarly to the four dimensional case, mass inflation also occurs for D>4. First, using the homogeneous approximation, we show that an increase of the number of spatial dimensions contributes to a steeper variation of the metric coefficients with the areal radius and that the phenomenon is insensitive to the cosmological constant in leading order. Then, using the code reported in arXiv:0904.2669 [gr-qc] adapted to D dimensions, we perform fully non-linear numerical simulations. We perturb the black hole with a compact pulse adapting the pulse amplitude such that the relative variation of the black hole mass is the same in all dimensions, and determine how the black hole interior evolves under the perturbation. We qualitatively confirm that the phenomenon is similar to four dimensions as well as the behaviour observed in the homogeneous approximation. We speculate about the formation of black holes inside black holes triggered by mass inflation, and about possible consequences of this scenario.Comment: 8 pages, 6 figure

Gravitating Opposites Attract

Generalizing previous work by two of us, we prove the non-existence of certain stationary configurations in General Relativity having a spatial reflection symmetry across a non-compact surface disjoint from the matter region. Our results cover cases such that of two symmetrically arranged rotating bodies with anti-aligned spins in $n+1$ ($n \geq 3$) dimensions, or two symmetrically arranged static bodies with opposite charges in 3+1 dimensions. They also cover certain symmetric configurations in (3+1)-dimensional gravity coupled to a collection of scalars and abelian vector fields, such as arise in supergravity and Kaluza-Klein models. We also treat the bosonic sector of simple supergravity in 4+1 dimensions.Comment: 13 pages; slightly amended version, some references added, matches version to be published in Classical and Quantum Gravit

Synchronized stationary clouds in a static fluid

The existence of stationary bound states for the hydrodynamic velocity field between two concentric cylinders is established. We argue that rotational motion, together with a trapping mechanism for the associated field, is sufficient to mitigate energy dissipation between the cylinders, thus allowing the existence of infinitely long lived modes, which we dub stationary clouds. We demonstrate the existence of such stationary clouds for sound and surface waves when the fluid is static and the internal cylinder rotates with constant angular velocity $\Omega$. These setups provide a unique opportunity for the first experimental observation of synchronized stationary clouds. As in the case of bosonic fields around rotating black holes and black hole analogues, the existence of these clouds relies on a synchronization condition between $\Omega$ and the angular phase velocity of the cloud.Comment: v2: 7 pages, 4 figures. Accepted for publication in Physics Letters

Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.Comment: 37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4; version published in CQ

Einstein-Maxwell-scalar black holes: classes of solutions, dyons and extremality

Spherical black hole (BH) solutions in Einstein-Maxwell-scalar (EMS) models wherein the scalar field is non-minimally coupled to the Maxwell invariant by some coupling function are discussed. We suggest a classification for these models into two classes, based on the properties of the coupling function, which, in particular, allow, or not, the ReissnerNordstr¨om (RN) BH solution of electrovacuum to solve a given model. Then, a comparative analysis of two illustrative families of solutions, one belonging to each class is performed: dilatonic versus scalarised BHs. By including magnetic charge, that is considering dyons, we show that scalarised BHs can have a smooth extremal limit, unlike purely electric or magnetic solutions. In particular, we study this extremal limit using the entropy function formalism, which provides insight on why both charges are necessary for extremal solutions to exist.publishe

Chains of Boson Stars

We study axially symmetric multi-soliton solutions of a complex scalar field theory with a sextic potential, minimally coupled to Einstein's gravity. These solutions carry no angular momentum and can be classified by the number of nodes of the scalar field, $k_z$, along the symmetry axis; they are interpreted as chains with $k_z+1$ boson stars, bound by gravity, but kept apart by repulsive scalar interactions. Chains with an odd number of constituents show a spiraling behavior for their ADM mass (and Noether charge) in terms of their angular frequency, similarly to a single fundamental boson star, as long as the gravitational coupling is small; for larger coupling, however, the inner part of the spiral is replaced by a merging with the fundamental branch of radially excited spherical boson stars. Chains with an even number of constituents exhibit a truncated spiral pattern, with only two or three branches, ending at a limiting solution with finite values of ADM mass and Noether charge.Comment: 20 pages, 6 figure

Multipolar boson stars: macroscopic Bose-Einstein condensates akin to hydrogen orbitals

Boson stars are often described as macroscopic Bose-Einstein condensates. By accommodating large numbers of bosons in the same quantum state, they materialize macroscopically the intangible probability density cloud of a single particle in the quantum world. We take this interpretation of boson stars one step further. We show, by explicitly constructing the fully non-linear solutions, that static (in terms of their spacetime metric, $g_{\mu\nu}$) boson stars, composed of a single complex scalar field, $\Phi$, can have a non-trivial multipolar structure, yielding the same morphologies for their energy density as those that elementary hydrogen atomic orbitals have for their probability density. This provides a close analogy between the elementary solutions of the non-linear Einstein--Klein-Gordon theory, denoted $\Phi_{(N,\ell,m)}$, which could be realized in the macrocosmos, and those of the linear Schr\"odinger equation in a Coulomb potential, denoted $\Psi_{(N,\ell,m)}$, that describe the microcosmos. In both cases, the solutions are classified by a triplet of quantum numbers $(N,\ell,m)$. In the gravitational theory, multipolar boson stars can be interpreted as individual bosonic lumps in equilibrium; remarkably, the (generic) solutions with $m\neq 0$ describe gravitating solitons $[g_{\mu\nu},\Phi_{(N,\ell,m)}]$ without any continuous symmetries. Multipolar boson stars analogue to hybrid orbitals are also constructed.publishe