Abstract:
The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom induced by quantum fields is considered for spacetimes with nontrivial topology of the kind ${\bf R}^{D-1} \times {\bf T}^1$, for varying $D$. It is shown that a dynamical origin for the Lorentzian signature is possible in the five-dimensional space ${\bf R}^4 \times {\bf T}^1$ with small torus radius (periodic boundary conditions), as well as in four-dimensional space with trivial topology. Hence, the possibility exists that the early universe might have been of the Kaluza-Klein type, \ie multidimensional and of Lorentzian signature.

Abstract:
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This provides an abstract mathematical setting in which one can study causality independent of geometry and differentiable structure.

Abstract:
A quantum causal topology is presented. This is modeled after a non-commutative scheme type of theory for the curved finitary spacetime sheaves of the non-abelian incidence Rota algebras that represent `gravitational quantum causal sets'. The finitary spacetime primitive algebra scheme structures for quantum causal sets proposed here are interpreted as the kinematics of a curved and reticular local quantum causality. Dynamics for quantum causal sets is then represented by appropriate scheme morphisms, thus it has a purely categorical description that is manifestly `gauge-independent'. Hence, a schematic version of the Principle of General Covariance of General Relativity is formulated for the dynamically variable quantum causal sets. We compare our non-commutative scheme-theoretic curved quantum causal topology with some recent $C^{*}$-quantale models for non-abelian generalizations of classical commutative topological spaces or locales, as well as with some relevant recent results obtained from applying sheaf and topos-theoretic ideas to quantum logic proper. Motivated by the latter, we organize our finitary spacetime primitive algebra schemes of curved quantum causal sets into a topos-like structure, coined `quantum topos', and argue that it is a sound model of a structure that Selesnick has anticipated to underlie Finkelstein's reticular and curved quantum causal net. At the end we conjecture that the fundamental quantum time-asymmetry that Penrose has expected to be the main characteristic of the elusive `true quantum gravity' is possibly of a kinematical or structural rather than of a dynamical character, and we also discuss the possibility of a unified description of quantum logic and quantum gravity in quantum topos-theoretic terms.

Abstract:
We present an exposition on the geometrization of the electromagnetic force. We show that, in noncommutative (NC) spacetime, there always exists a coordinate transformation to locally eliminate the electromagnetic force, which is precisely the Darboux theorem in symplectic geometry. As a consequence, the electromagnetism can be realized as a geometrical property of spacetime like gravity. We show that the geometrization of the electromagnetic force in NC spacetime is the origin of gravity, dubbed as the emergent gravity. We discuss how the emergent gravity reveals a novel, radically different picture about the origin of spacetime. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity. This spacetime picture turns out to be crucial for a tenable solution of the cosmological constant problem.

Abstract:
It is suggested that not only the curvature, but also the signature of spacetime is subject to quantum fluctuations. A generalized D-dimensional spacetime metric of the form $g_{\mu \nu}=e^a_\mu \eta_{ab} e^b_\nu$ is introduced, where $\eta_{ab} = diag\{e^{i\theta},1,...,1\}$. The corresponding functional integral for quantized fields then interpolates from a Euclidean path integral in Euclidean space, at $\theta=0$, to a Feynman path integral in Minkowski space, at $\theta=\pi$. Treating the phase $e^{i\theta}$ as just another quantized field, the signature of spacetime is determined dynamically by its expectation value. The complex-valued effective potential $V(\theta)$ for the phase field, induced by massless fields at one-loop, is considered. It is argued that $Re[V(\theta)]$ is minimized and $Im[V(\theta)]$ is stationary, uniquely in D=4 dimensions, at $\theta=\pi$, which suggests a dynamical origin for the Lorentzian signature of spacetime.

Abstract:
A new class of electrically charged wormholes is described in which the outer two sphere is not spanned by a compact coorientable hypersurface. These wormholes can therefore display net electric charge from the source free Maxwell's equation. This extends the work of Sorkin on non-space orientable manifolds, to spacetimes which do not admit a time orientation. The work is motivated by the suggestion that quantum theory can be explained by modelling elementary particles as regions of spacetime with non-trivial causal structure. The simplest example of an electrically charged spacetime carries a spherical symmetry.

Abstract:
In proto-neutron stars with strong magnetic fields, the cross section for $\nu_e$ ($\bar\nu_e$) absorption on neutrons (protons) depends on the local magnetic field strength due to the quantization of energy levels for the $e^-$ ($e^+$) produced in the final state. If the neutron star possesses an asymmetric magnetic field topology in the sense that the magnitude of magnetic field in the north pole is different from that in the south pole, then asymmetric neutrino emission may be generated. We calculate the absorption cross sections of $\nue$ and $\bnue$ in strong magnetic fields as a function of the neutrino energy. These cross sections exhibit oscillatory behaviors which occur because new Landau levels for the $e^-$ ($e^+$) become accessible as the neutrino energy increases. By evaluating the appropriately averaged neutrino opacities, we demonstrate that the change in the local neutrino flux due to the modified opacities is rather small. To generate appreciable kick velocity ($\sim 300$ km~s$^{-1}$) to the newly-formed neutron star, the difference in the field strengths at the two opposite poles of the star must be at least $10^{16}$~G. We also consider the magnetic field effect on the spectral neutrino energy fluxes. The oscillatory features in the absorption opacities give rise to modulations in the emergent spectra of $\nu_e$ and $\bar\nu_e$.

Abstract:
This Letter investigates the origin of the asymmetric magnetic field line geometry in the ergospheric disk (and the corresponding asymmetric powerful jet) in 3-D perfect magnetohydrodynamic (MHD) numerical simulations of a rapidly rotating black hole accretion system reported in \citet{pun10}. Understanding, why and how these unexpected asymmetric structures form is of practical interest because an ergospheric disk jet can boost the black hole driven jet power many-fold possibly resolving a fundamental disconnect between the energy flux estimates of powerful quasar jets and simulated jet power \citep{pun11}. The new 3-D simulations of \citet{bec09} that were run with basically the same code that was used in the simulation discussed in \citet{pun10} describe the "coronal mechanism" of accreting poliodal magnetic flux towards the event horizon. It was determined that reconnection in the inner accretion disk is a "necessary" component for this process. The coronal mechanism seems to naturally explain the asymmetric ergospheric disk field lines that were seen in the simulations. Using examples from the literature, it is discussed how apparently small changes in the reconnection geometry and rates can make enormous changes in the magnetospheric flux distribution and the resultant black hole driven jet power in a numerical simulation. Unfortunately, reconnection is a consequence of numerical diffusion and not a detailed (yet to be fully understood) physical mechanism in the existing suite of perfect MHD based numerical simulations. The implication is that there is presently great uncertainty in the flux distribution of astrophysical black hole magnetospheres and the resultant jet power.

Abstract:
It is known that de Sitter spacetime can be seen as the solution of field equation for completely isotropic matter. In the present paper a new class of exact solutions in spherical symmetry is found and discussed, such that the energy--momentum tensor has two 2--dimensional distinct isotropic subspaces.

Abstract:
Emergent gravity is based on the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as U(1) gauge theory is defined on a spacetime with symplectic structure. In this approach, the spacetime geometry is defined by U(1) gauge fields on noncommutative (NC) spacetime. Accordingly the topology of spacetime is determined by the topology of NC U(1) gauge fields. We show that the topology change of spacetime is ample in emergent gravity and the subsequent resolution of spacetime singularity is possible in NC spacetime. Therefore the emergent gravity approach provides a well-defined mechanism for the topology change of spacetime which does not suffer any spacetime singularity in sharp contrast to general relativity.