Gonçalo A. S. Dias

Thin-shell wormholes in

We construct thin-shell electrically charged wormholes in d-dimensional general relativity with a cosmological constant. The wormholes constructed can have different throat geometries, namely, spherical, planar, and hyperbolic. Unlike the spherical geometry, the planar and hyperbolic geometries allow for different topologies and in addition can be interpreted as higher-dimensional domain walls or branes connecting two universes. In the construction we use the cut-and-paste procedure by joining together two identical vacuum spacetime solutions. Properties such as the null energy condition and geodesics are studied. A linear stability analysis around the static solutions is carried out. A general result for stability is obtained from which previous results are recovered.

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A calculation of the entropy of static, electrically charged, black holes with spherical, toroidal, and hyperbolic compact and oriented horizons, in D spacetime dimensions, is performed. These black holes live in an anti-de Sitter spacetime, i.e., a spacetime with negative cosmological constant. To find the entropy, the approach developed by Solodukhin is followed. The method consists in a redefinition of the variables in the metric, by considering the radial coordinate as a scalar field. Then one performs a 2+(D-2) dimensional reduction, where the (D-2) dimensions are in the angular coordinates, obtaining a 2-dimensional effective scalar field theory. This theory is a conformal theory in an infinitesimally small vicinity of the horizon. The corresponding conformal symmetry will then have conserved charges, associated with its infinitesimal conformal generators, which will generate a classical Poisson algebra of the Virasoro type. Shifting the charges and replacing Poisson brackets by commutators, one recovers the usual form of the Virasoro algebra, obtaining thus the level zero conserved charge eigenvalue L_0, and a nonzero central charge c. The entropy is then obtained via the Cardy formula.

-dimensional general relativity: Solutions, properties, and stability

Unlike the trapping of time-harmonic water waves by fixed obstacles, the oscillation of freely floating structures gives rise to a complex nonlinear spectral problem. Still, through a convenient elimination scheme the system simplifies to a linear spectral problem for a self-adjoint operator in a Hilbert space. Under symmetry assumptions on the geometry of the fluid domain, we present conditions guaranteeing the existence of trapped modes in a two-layer fluid channel. Numerous examples of floating bodies supporting trapped modes are given.

Conformal entropy from horizon states: Solodukhin's method for spherical, toroidal and hyperbolic black holes in D-dimensional anti-de Sitter spacetimes

M d x √ −gLm . Here κ is proportional to Newton’s constant G, M is the d-dimensional spacetime manifold, g is the determinant of the spacetime metric gμν , δ μ1···μ2p ν1···ν2p is totally anti-symmetric in the upper and lower indices, R μν is the Riemann tensor, ǫ is proportional to the vacuum electric permitivity ǫ0, Ωd−2 is the surface area of the d−2 unit sphere, Fμν is the Maxwell tensor, J μ is the electromagnetic current, A is the vector potential, and Lm is the matter Lagrangian. The energy-momentum tensor derived from Lm will be that of a general perfect fluid. The free coefficients αp in the Lovelock theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. After writing the action and the Lagrangian for a total spacetime comprised of an interior and an exterior regions, with a thin shell as a boundary in between, one finds the Hamiltonian using the ADM decomposition of the spacetime metric ds = −(N)dt + gij(N dt+ dx)(N dt+ dx), where the gij are the canonical coordinates intrinsic to the (d−1)-dimensional time foliation, and π are the respective canonical momenta. The consequent ADM description of the action is I = ∫

Trapped modes around freely floating bodies in a two-layer fluid channel

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free ω parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω → ∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω = 0), and a theory representing a class of theories (ω = -3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates {M, P M }, M being the mass parameter and P M its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schrodinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.