32 research outputs found
A Rotating Black Hole Solution for Shape Dynamics
Shape dynamics is a classical theory of gravity which agrees with general
relativity in many important aspects, but which possesses different gauge
symmetries and can present some fundamental global differences with respect to
Einstein spacetimes. Here, we present a general procedure for (locally) mapping
stationary, axisymmetric general relativity solutions onto their shape dynamic
counterparts. We focus in particular on the rotating black hole solution for
shape dynamics and show that many of the properties of the spherically
symmetric solution are preserved in the extension to the axisymmetric case: it
is also free of physical singularities, it does not form a space-time at the
horizon, and it possesses an inversion symmetry about the horizon which leads
to us to interpret the solution as a wormhole.Comment: 13 page
Contact Geometry and Quantum Mechanics
We present a generally covariant approach to quantum mechanics in which
generalized positions, momenta and time variables are treated as coordinates on
a fundamental "phase-spacetime." We show that this covariant starting point
makes quantization into a purely geometric flatness condition. This makes
quantum mechanics purely geometric, and possibly even topological. Our approach
is especially useful for time-dependent problems and systems subject to
ambiguities in choices of clock or observer. As a byproduct, we give a
derivation and generalization of the Wigner functions of standard quantum
mechanics.Comment: 7 pages, 1 figure, LaTeX, references added, journal versio
Double Kerr-Schild spacetimes and the Newman-Penrose map
The Newman-Penrose map, which is closely related to the classical double
copy, associates certain exact solutions of Einstein's equations with self-dual
solutions of the vacuum Maxwell equations. Here we initiate an extension of the
Newman-Penrose map to a broader class of spacetimes. As an example, we apply
principles from the Newman-Penrose map to associate a self-dual gauge field to
the Kerr-Taub-NUT-(A)dS spacetime and we show that the result agrees with
previously studied examples of classical double copies. The corresponding field
strength exhibits a discrete electric-magnetic duality that is distinct from
its (Hodge star) self-dual property.Comment: 14 pages + reference
Dynamical Henneaux-Teitelboim Gravity
We consider a modified gravity model which we call "dynamical
Henneaux-Teitelboim gravity" because of its close relationship with the
Henneaux-Teitelboim formulation of unimodular gravity. The latter is a fully
diffeomorphism-invariant formulation of unimodular gravity, where full
diffeomorphism invariance is achieved by introducing two additional
non-dynamical fields: a scalar, which plays the role of a cosmological
constant, and a three-form whose exterior derivative is the spacetime volume
element. Dynamical Henneaux-Teitelboim gravity is a generalization of this
model that includes kinetic terms for both the scalar and the three-form with
arbitrary couplings. We study the field equations for the cases of spherically
symmetric and homogeneous, isotropic configurations. In the spherically
symmetric case, we solve the field equations analytically for small values of
the coupling to obtain an approximate black hole solution. In the homogeneous
and isotropic case, we perturb around de Sitter space to find an approximate
cosmological background for our model.Comment: 10 pages, 2 figure
A generalized Hartle-Hawking wavefunction
The Hartle-Hawking wave function is known to be the Fourier dual of the
Chern-Simons or Kodama state reduced to mini-superspace, using an integration
contour covering the whole real line. But since the Chern-Simons state is a
general solution of the Hamiltonian constraint (with a given ordering), its
Fourier dual should provide the general solution (i.e. beyond mini-superspace)
of the Wheeler DeWitt equation representing the Hamiltonian constraint in the
metric representation. We write down a formal expression for such a wave
function, to be seen as the generalization beyond mini-superspace of the
Hartle-Hawking wave function. Its explicit evaluation (or simplification)
depends only on the symmetries of the problem, and we illustrate the procedure
with anisotropic Bianchi models and with the Kantowski-Sachs model. A
significant difference of this approach is that we may leave the torsion inside
the wave functions when we set up the ansatz for the connection, rather than
setting it to zero before quantization. This allows for quantum fluctuations in
the torsion, with far reaching consequences.Comment: 8 pages, 2 figure