We review the hypothesis of the existence of gravitational magnetic monopoles (H-pole for short) defined in analogy with the Diracs hypothesis of magnetic monopoles in electrodynamics. These hypothetical dual particles violate the equivalence principle and are accelerated by a gravitational field. We propose an expression for the gravitational force exerted upon an H-pole. According to GR ordinary matter (which we call E-poles) follows geodesics in a background metric. The dual H-poles follows geodesics in an effective metric.
We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter wave, microwave, optical, and Mossbauer clock tests, yields comprehensive limits on spin-independent Einstein equivalence principle-violating standard model extension terms at the $10^{-6}$ level.
We review matter wave and clock comparison tests of the gravitational redshift. To elucidate their relationship to tests of the universality of free fall (UFF), we define scenarios wherein redshift violations are coupled to violations of UFF (type II), or independent of UFF violations (type III), respectively. Clock comparisons and atom interferometers are sensitive to similar effects in type II and precisely the same effects in type III scenarios, although type III violations remain poorly constrained. Finally, we describe the Geodesic Explorer, a conceptual spaceborne atom interferometer that will test the gravitational redshift with an accuracy 5 orders of magnitude better than current terrestrial redshift experiments for type II scenarios and 12 orders of magnitude better for type III.
The recent LIGO detection of gravitational waves from black-hole binaries offers the exciting possibility of testing gravitational theories in the previously inaccessible strong-field, highly relativistic regime. While the LIGO detections are so far consistent with the predictions of General Relativity, future gravitational-wave observations will allow us to explore this regime to unprecedented accuracy. One of the generic predictions of theories of gravity that extend General Relativity is the violation of the strong equivalence principle, i.e. strongly gravitating bodies such as neutron stars and black holes follow trajectories that depend on their nature and composition. This has deep consequences for gravitational-wave emission, which takes place with additional degrees of freedom besides the tensor polarizations of General Relativity. I will briefly review the formalism needed to describe these extra emission channels, and show that binary black-hole observations probe a set of gravitational theories that are largely disjoint from those that are testable with binary pulsars or neutron stars.
We study the variational principle on a Hilbert-Einstein action in an extended geometry with torsion taking into account non-trivial boundary conditions. We obtain an effective energy-momentum tensor that has its source in the torsion, which represents the matter geometrically induced. We explore about the existence of magnetic monopoles and gravitational waves in this torsional geometry. We conclude that the boundary terms can be identified as possible sources for the cosmological constant and torsion as the source of magnetic monopoles. We examine an example in which gravitational waves are produced during a de Sitter inflationary expansion of the universe.
We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a curved and time-dependent spatial metric. It is this requirement that forces the gravitational mass to be equal to the inertial mass. We identify the symmetry responsible for the equivalence principle as the remnant of time-reparameterization symmetry of the relativistic theory. We also clarify the transformation properties of the Schroedinger wave-function under arbitrary changes of frame.