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Register a new userPure Lorentz spin connection theories and uniqueness of General Relativity
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General Relativity can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type $f(Fwedge F)$, where $F$ is the curvature 2-form of the spin connection. A theory from this class with a generic $f$ is known to propagate eight degrees of freedom: a massless graviton, a massive graviton and a scalar. General Relativity in this formalism avoids extra degrees of freedom because the function $f$ is special and leads to the appearance of six extra primary constraints on the phase space variables. Our main new result is that there are other theories of the type $f(Fwedge F)$ that lead to six extra primary constraints. However, only in the case of GR the dynamics is such that these six primary constraints get supplemented by six secondary constraints, which gives the end result of two propagating degrees of freedom. This is how uniqueness of GR manifests itself in this ``pure spin connection formalism. The other theories we discover are shown to give examples of irregular dynamical systems. At the linear level around (anti-)de Sitter space they have two degrees of freedom, as General Relativity, with the extra ones manifesting themselves only non-linearly.
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The junction conditions for General Relativity in the presence of domain walls with intrinsic spin are derived in three and higher dimensions. A stress tensor and a spin current can be defined just by requiring the existence of a well defined volume element instead of an induced metric, so as to allow for generic torsion sources. In general, when the torsion is localized on the domain wall, it is necessary to relax the continuity of the tangential components of the vielbein. In fact it is found that the spin current is proportional to the jump in the vielbein and the stress-energy tensor is proportional to the jump in the spin connection. The consistency of the junction conditions implies a constraint between the direction of flow of energy and the orientation of the spin. As an application, we derive the circularly symmetric solutions for both the rotating string with tension and the spinning dust string in three dimensions. The rotating string with tension generates a rotating truncated cone outside and a flat space-time with inevitable frame dragging inside. In the case of a string made of spinning dust, in opposition to the previous case no frame dragging is present inside, so that in this sense, the dragging effect can be shielded by considering spinning instead of rotating sources. Both solutions are consistently lifted as cylinders in the four-dimensional case.
The properties of Lorentz transformations in de Sitter relativity are studied. It is shown that, in addition to leaving invariant the velocity of light, they also leave invariant the length-scale related to the curvature of the de Sitter spacetime. The basic conclusion is that it is possible to have an invariant length parameter without breaking the Lorentz symmetry. This result may have important implications for the study of quantum kinematics, and in particular for quantum gravity.
We explore General Relativity solutions with stealth scalar hair in general quadratic higher-order scalar-tensor theories. Adopting the assumption that the scalar field has a constant kinetic term, we derive in a fully covariant manner a set of conditions under which the Euler-Lagrange equations allow General Relativity solutions as exact solutions in the presence of a general matter component minimally coupled to gravity. The scalar field possesses a nontrivial profile, which can be obtained by integrating the condition of constant kinetic term for each metric solution. We demonstrate the construction of the scalar field profile for several cases including the Kerr-Newman-de Sitter spacetime as a general black hole solution characterized by mass, charge, and angular momentum in the presence of a cosmological constant. We also show that asymptotically anti-de Sitter spacetimes cannot support nontrivial scalar hair.
We study the spontaneously induced general relativity (GR) from the scalar-tensor gravity. We demonstrate by numerical methods that a novel inner core can be connected to the Schwarzschild exterior with cosmological constants and any sectional curvature. Deriving an analytic core metric for a general exterior, we show that all the nontrivial features of the core, including the locally holographic entropy packing, are universal for the general exterior in static spacetimes. We also investigate whether the f(R) gravity can accommodate the nontrivial core.
The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators.
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