Geometric obstruction of black holes

We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The completeness of the latter is then employed to rigorously prove the absence of static spherically symmetric black holes in more than three dimensions. The proof of these new results is preceded by a pedagogic review of the local aspects of sectional curvature bounds for Lorentzian manifolds, which extends and strengthens previous constructions.     

On isoperimetric surfaces in general relativity,II

We determine the optimal way to enclose volume in a class of domains inside certain Friedmann–Robertson–Walker metrics. The method employed is an adaptation of the Bray–Morgan isoperimetric comparison procedure to the Lorentzian setting. We also make some remarks on isoperimetric comparison in the Riemannian setting, for rotationally-symmetric space-like slices in non-vacuum space-times.     

A global conformal extension theorem for perfect fluid Bianchi space-times

A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.     

The exact behavior of electromagnetic Faraday rotation in crossing a gravitational sandwich wave in general relativity

We have analyzed the exact behavior of the polarization vector of a linearly polarized electromagnetic shock wave upon crossing a gravitational sandwich wave, by using Einstein's theory of general relativity. The Faraday rotation in the polarization vector of the electromagnetic field is induced in this nonlinear process. We show that the Faraday's angle highly depends on the electromagnetic parameter, gravitational parameter and the width of the gravitational sandwich wave.     

Generalised Chern–Simons actions for 3d gravity and κ-Poincaré symmetry

We consider Chern–Simons theories for the Poincaré, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern–Simons formulation of 3d gravity. We determine conditions under which κ-Poincaré symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern–Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that κ-Poincaré symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern–Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of κ-de Sitter symmetry, and carry out the first steps in that construction.     

Quantum hall conductivity in a Landau type model with a realistic geometry II

We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the integral or fractional quantization of the Hall conductivity depending on the value of NB/2π (N is the number of charge carriers and B is the magnetic field). When NB/2π is irrational, we show that monovaluated wave functions can be constructed only on the graph of a free group with two generators. When NB/2π is rational, the relevant space becomes a punctured Riemann surface. We finally discuss our results from a phenomenological viewpoint.     

Evidence for a gravitational Myers effect

An indication for the existence of a collective Myers solution in the non-abelian D0-brane Born-Infeld action is the presence of a tachyonic mode in fluctuations around the standard diagonal background. We show that this computation for non-abelian D0-branes in curved space has the geometric interpretation of computing the eigenvalues of the geodesic deviation operator for U(N)-valued coordinates. On general grounds one therefore expects a geometric Myers effect in regions of sufficiently negative curvature. We confirm this by explicit computations for non-abelian D0-branes on a sphere and a hyperboloid. For the former the diagonal solution is stable, but not so for the latter. We conclude by showing that near a Schwarzschild black hole one also finds a tachyonic mode in the fluctuation spectrum, signaling the possibility of a near-black-hole gravitationally induced Myers effect.     

MΦller＇s Energy of Kerr-NUT Metric

The energy distribution of the Kerr-NUT （Newman-Unti-Tamburino） spacetime is calculated using MΦller＇s energy-momentum complex within the framework of the Riemannian geometry.     

On principle of inertia in closed universe

If our universe is asymptotic to a de Sitter space, it should be closed with curvature in O(Λ)$O(\Lambda )$ in view of dS special relativity. Conversely, its evolution can fix on Beltrami systems of inertia in the ds-space without Einstein's ‘argument in a circle’. Gravity should be local ds-invariant based on localization of the principle of inertia.     

A brief history of gravitational wave research

For the benefit of the readers of this journal, the editors requested that we prepare a brief review of the history of the development of the theory, the experimental attempts to detect them, and the recent direct observations of gravitational waves (GWs). The theoretical ideas and disputes beginning with Einstein in 1916 regarding the existence and nature of gravitational waves and the extent to which one can rely on the electromagnetic analogy, especially the controversies regarding the quadrupole formula and whether gravitational waves carry energy, are discussed. The theoretical conclusions eventually received strong observational support from the binary pulsar. This provided compelling, although indirect, evidence for gravitational waves carrying away energy—as predicted by the quadrupole formula. On the direct detection experimental side, Joseph Weber started more than fifty years ago. In 1966, his bar for GW detection reached a strain sensitivity of a few times ${10}^{?16}$. His announcement of coincident signals (now considered spurious), stimulated many experimental efforts from room temperature resonant masses to cryogenic detectors and laser-interferometers. Now there are km-sized interferometric detectors (LIGO Hanford, LIGO Livingston, Virgo and KAGRA). Advanced LIGO first reached a strain sensitivity of the order of ${10}^{?22}$. During their first 130 days of observation (O1 run), with the aid of templates generated by numerical relativity, they did make the first detections: two 5-σ GW events and one likely event. Besides earth-based GW detectors, the drag-free sensitivity of the LISA Pathfinder has already reached to the LISA goal level, paving the road for space GW detectors. Over the whole GW spectrum (from aHz to THz) there are efforts for detection, notably the very-low-frequency band (pulsar timing array [PTA], 300 pHz – 100 nHz) and the extremely-low (Hubble)-frequency (cosmic microwave background [CMB] experiment, 1 aHz – 10 fHz).     

Regular Charged Solutions in Mφller＇s Tetrad Theory of Gravitation

We find the most general tetrads which give a regular charged spacetime in tetrad theory of gravitation. The metric is a static one and it includes the Schwarzschild and Fteissner Nordstrom black holes. The energy content contained in a sphere of radius R is calculated using the superpotential given by Mφller in the context of Weitzenbock spacetime.     

Metric-affine f(R) theories of gravity

General Relativity assumes that spacetime is fully described by the metric alone. An alternative is the so called Palatini formalism where the metric and the connections are taken as independent quantities. The metric-affine theory of gravity has attracted considerable attention recently, since it was shown that within this framework some cosmological models, based on some generalized gravitational actions, can account for the current accelerated expansion of the universe. However we think that metric-affine gravity deserves much more attention than that related to cosmological applications and so we consider here metric-affine gravity theories in which the gravitational action is a general function of the scalar curvature while the matter action is allowed to depend also on the connection which is not a priori symmetric. This general treatment will allow us to address several open issues such as: the relation between metric-affine f(R) gravity and General Relativity (in vacuum as well as in the presence of matter), the implications of the dependence (or independence) of the matter action on the connections, the origin and role of torsion and the viability of the minimal-coupling principle.     

Various topological excitations in the SO (4) gauge field in higher dimensions

Following the original analysis of Zhang and Hu for the 4-dimensional generalization of Quantum Hall effect, there has been much work from different viewpoints on the higher dimensional condensed matter systems. In this paper, we discuss three kinds of topological excitations in the SO (4) gauge field of condensed matter systems in 4-dimension—the instantons and anti-instantons, the ’t Hooft-Polyakov monopoles, and the 2-membranes. Using the ?-mapping topological theory, it is revealed that there are 4-, 3-, and 2-dimensional topological currents inhering in the SO (4) gauge field, and the above three kinds of excitations can be directly and explicitly derived from these three kinds of currents, respectively. Moreover, it is shown that the topological charges of these excitations are characterized by the Hopf indices and Brouwer degrees of ?-mapping.     

General covariance of the non-abelian DBI-action: checks and balances

We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a base-point independence constraint between matrix Riemann normal coordinate systems. First, we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose base-point independence using an auxiliary dN²-dimensional nonlinear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order 4, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action.     

Cosmological Models with Time Dependent G and Λ Coupling Scalars

A cosmological model in which the universe has its critical density and gravitational constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. An exact solution for matter distribution in cosmological models satisfying G=G₀(R/R₀)ⁿ is presented. Corresponding physical interpretations of the cosmological solutions are also discussed.     

A new class of plane symmetric solution

A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different energy conditions are studied. The classical stability of this solution is discussed. The junction conditions matching to Minkowski metric and Taub metric are analyzed respectively.     

Coordinates, observables and symmetry in relativity

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, which is naturally identified with the physical spacetime.     

On the Energy-Momentum Problem in Static Einstein Universe

The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.