Related papers: Something about Inter-universal Teichmuller Theory

I will begin by conjecturing a cosmological generalization of black hole complementarity (also known as the central dogma). I will then discuss three theories and argue that they are inconsistent with second law of thermodynamics if the…

We obtain the equations of motions of the $f(T)$ theory considering the Lema\^itre-Tolman-Bondi's metric for a set of diagonal and non-diagonal tetrads. In the case of diagonal tetrads the equations of motion of the $f(T)$ theory impose a…

We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant…

This is a continuation of my work on Arithmetic Teichmuller Spaces (arXiv:2106.11452, arXiv:2210.11635, arXiv:2303.01662, arXiv:2305.10398). This paper establishes a number of important results including (1) a proof Mochizuki's Corollary…

We exploit the parallel between dynamical black holes and cosmological spacetimes to describe the evolution of Friedmann-Lema\^itre-Robertson-Walker universes from the point of view of an observer in terms of the dynamics of the apparent…

The classic black hole mechanics and thermodynamics are formulated for stationary black holes with event horizons. Alternative theories of gravity of interest for cosmology contain a built-in time-dependent cosmological "constant" and black…

We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.…

The discovery of cosmic acceleration has presented a unique challenge for cosmologists. As observational cosmology forges ahead, theorists have struggled to make sense of a standard model that requires extreme fine tuning. This challenge is…

A new cosmological theory is proposed in the theoretical framework of modified gravity theories which is based on a tachyonic field non-minimally coupled with a specific topological invariant constructed with third order contractions of the…

We study the impact of the expansion of the universe on a broad class of objects, including black holes, neutron stars, white dwarfs, and others. Using metrics that incorporate primordial inhomogeneities, the effects of a hypothetical…

Compton wavelength and Schwarzschild radius are considered here as limiting cases of a unified length scale. Using this length, it is shown that the Dirac equation and the Einstein equations for a point mass are limiting cases of an…

In this work we have studied the singular behaviour of gravitational theories with non symmetric connections. For this purpose we introduce a new criteria for the appearance of singularities based on the existence of black/white hole…

(Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {\it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of…

Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally…

In this work we extend the proof of Ryan Unger and Christoph Kehle's work, "Gravitational collapse to extremal black holes and the third law of black hole thermodynamics", to construct examples of black hole formation from regular,…

Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally "anti-de Sitter"…

The universe today, with structure such as stars, galaxies and black holes, seems to have evolved from a very homogeneous initial state. From this it appears as if the entropy of the universe is decreasing, in violation of the second law of…

A general theorem due to Howe of dual action of a classical group and a certain non-associative algebra on a space of symmetric or alternating tensors is reformulated in a setting of second quantization, and familiar examples in atomic and…

We show how the Weyl formalism allows metrics to be written down which correspond to arbitrary numbers of collinear accelerating neutral black holes in 3+1 dimensions. The black holes have arbitrary masses and different accelerations and…

A satisfactory formulation of the laws of physics entails that the future evolution of a physical system should be determined from appropriate initial conditions. The existence of Cauchy horizons in solutions of the Einstein field equations…