Lorentzian geometrical structures with global time, Gravity and Electrodynamics

We investigate Lorentzian structures in the four-dimensionalspace-time, supplemented either by a covector field of thetime-direction or by a scalar field of the global time. Furthermore,we propose a new metrizable model of the gravity. In contrast to theusual Theory of General Relativity where all ten components of thesymmetric pseudo-metrics are independent variables, the presentedhere model of the gravity essentially depend only on singlefour-covector field, restricted to have only three-independentcomponents. However, we prove that the Gravitational field, ruled bythe proposed model and generated by some massive body, resting andspherically symmetric in some coordinate system, is given by apseudo-metrics, which coincides with thewell known Schwarzschild metric from the General Relativity. TheMaxwell equations and Electrodynamics are also investigated in theframes of the proposed model. In particular, we derive the covariantformulation of Electrodynamics of moving dielectrics andpara/diamagnetic mediums.

Lie theory for asymptotic symmetries in general relativity: The BMS Group

We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi--Metzner--Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Finally, we verify the Trotter property as well as the commutator property. As an outlook, we comment on the situation of related asymptotic symmetry groups. In particular, the much more involved situation of the Newman--Unti group is highlighted, which will be studied in future work.

Joule–Thomson expansion in charged AdS black hole surrounded by a cosmological fluid in Rainbow Gravity

In this work, we analyze the Joule–Thomson expansion in an AdS Reissner–Nordström black hole, surrounded by an average cosmological fluid, in Rainbow Gravity. We plot the graphs corresponding to the inversion temperature curves and numerically calculate the ratio between the minimum of the inversion temperature and the critical temperature, with the aim of investigating how Rainbow Gravity alters such behaviors compared to General Relativity.

General Relativity and Causality, Reasoning from Metaphysics, and E. J. Lowe’s Ontology

The paper aims to show the importance of reasoning “from metaphysics” in the course of a consistent interpretation of the “against neoscholasticism” thesis (J. Ladyman). The idea that “the subject of metaphysics is metaphysical possibilities, and science determines which of them are actually achieved” (E. J. Lowe, J. Katz, etc.) reinforces the role of reasoning “from metaphysics” within the field of metaphysics of science. The general theory of relativity violates the common prevailing intuition that “causality is the subject of local physical interaction” (J. Bigelow). Interpretation of causality in terms of “forces” and “coming into” within the framework of E. J. Lowe's ontology makes it possible to talk about causality in terms of “finding” and “going out” of existence of the corresponding modes of objects connected by a formal “causal relationship”. The transition to E. J. Lowe's ontology helps not only to overcome the intuition of the locality of causality, but also reveals in its own way, for example, such seemingly simple common intuitions as the dependence of the truth of propositions on time or the understanding of time as a dimension. All this once again brings us back to the understanding of the importance of the fact that a scientist, constructing or interpreting a scientific theory, as a rule, uses non-trivial philosophical assumptions that should be the subject of its own philosophical analysis.

Nonconservative Unimodular Gravity: Gravitational Waves

Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation: The symmetry properties of unimodular gravity are governed by the transverse diffeomorphisms. Nevertheless, if the conservation of the energy–momentum tensor is imposed in unimodular gravity, the general relativity theory is recovered with an additional integration constant which is associated to the cosmological term Λ. However, if the energy–momentum tensor is not conserved separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in a nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model. As our main result, we verify that gravitational waves in the nonconservative version of unimodular gravity are strongly amplified during the evolution of the universe.

Brown-York charges at null boundaries

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor Tij takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.