General Relativity and Gravitation最新文献

We prove that the black to white hole transition theorized in several papers can be described as a change in the topology of the event horizon. We also show, using the theory of cobordism due to Milnor and Wallace, how to obtain the full manifold containing the transition.

The parallel theory of relativity predicts conserved energy–momentum currents for an arbitrary metric, without invoking Killing symmetries. By treating the reference frame as an independent variational field and requiring it to carry no energy, the theory naturally unifies Einstein’s two formulations of gravity and yields uniquely defined covariant charges. In isotropic and homogeneous cosmology, the canonical time direction selected by the reference frame coincides with the Kodama vector, and the associated Noether energy reproduces the Misner–Sharp mass.

We provide a short introduction to “Lorentzian metric spaces” i.e., spacetimes defined solely in terms of the two-point Lorentzian distance. As noted in previous work, this structure is essentially unique if minimal conditions are imposed, such as the continuity of the Lorentzian distance and the relative compactness of chronological diamonds. The latter condition is natural for interpreting these spaces as low-regularity versions of globally hyperbolic spacetimes. Confirming this interpretation, we prove that every Lorentzian metric space admits a Cauchy time function. The proof is constructive for this general setting and it provides a novel argument that is interesting already for smooth spacetimes.

I review the scientific and epistemological intuition behind Lemaître’s primeval atom hypothesis of 1931 and argue this resonates with the observer-centric interpretation of the no-boundary hypothesis developed in the years 2010. A sufficiently refined but realistic model of the observer as a quantum system described by the theory strongly affects the no-boundary probability distribution. In the context of inflation, it changes the dominant saddle from one with minimal inflation to one where the universe starts out in the regime of eternal inflation.

We present a detailed analysis that may significantly impact understanding the relationship between structure formation in the late-epoch Universe and dark energy as described by the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological constant density ({{widehat{Omega }}_Lambda }). Our geometrical approach provides a non-perturbative technique that allows the standard FLRW observer to evaluate a measurable, scale-dependent distance functional between her idealized FLRW past light cone and the actual physical past light cone. From the point of view of the FLRW observer, gathering data from sources at cosmological redshift ({widehat{z}}), this functional generates a geometry-structure-growth contribution ({Omega _Lambda ({widehat{z}})}) to ({{widehat{Omega }}_Lambda }). This redshift-dependent contribution erodes the interpretation of ({{widehat{Omega }}_Lambda }) as representing constant dark energy. In particular, ({Omega _Lambda ({widehat{z}})}) becomes significantly large at very low ({widehat{z}}), where structures dominate the cosmological landscape. At the pivotal galaxy cluster scale, where cosmological expansion decouples from the local gravitation dynamics, we get ({Omega _Lambda ({widehat{z}})/{widehat{Omega }}_Lambda },=,O(1)), showing that late-epoch structures provide an effective field contribution to the FLRW cosmological constant that is of the same order of magnitude of its assumed value. We prove that ({Omega _Lambda ({widehat{z}})}) is generated by a scale-dependent effective field governed by structures formation and related to the comparison between the idealized FLRW past light cone and the actual physical past light cone. These results are naturally framed in mainstream FLRW cosmology; they do not require the existence of exotic fields and provide a natural setting for analyzing the coincidence problem, leading to an interpretative shift in the current interpretation of constant dark energy.

The Lyra geometry provides an interesting approach to develop purely geometrical scalar-tensor theories. Here we present a theory on Lyra manifolds which contains generalizations of both Brans-Dicke gravity and Einstein-Gauss-Bonnet scalar-tensor theory. We show that the symmetry group of gravitational theories on the Lyra geometry comprises not only coordinate transformations but also local transformations of length units, so that the Lyra function is a conformal factor which locally fixes the unit of length. The Lyra geometry is thus the generalization of Riemannian geometry which properly includes spacetime-dependent length units. By performing a Lyra transformation to a frame in which the length unit is globally fixed, we show that General Relativity (GR) is obtained from the Lyra Scalar-Tensor Theory (LyST). Through the same procedure, it is found that Brans-Dicke gravity and the Einstein-Gauss-Bonnet scalar-tensor theory are obtained from their Lyra counterparts. It might be possible that any known scalar-tensor theory can be naturally geometrized by considering a particular Lyra frame, for which the scalar field is the function which locally controls the unit of length. The Jordan-Einstein frame conundrum is also assessed from the perspective of Lyra transformations: we show that the Lyra geometry makes explicit that the two frames are only different representations of the same theory, so that in the Einstein frame the unit of length varies locally. The Lyra formalism is then better suited for exploring scalar-tensor gravity, since in its well-defined structure the conservation of the energy-momentum tensor and geodesic motion are assured in the Einstein frame.