Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1509.03095

Causal Space-Times on a Null Lattice

Martin Schaden
View original source ↗Read source document ↗Export metadata ↓

Abstract

I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are constructed from local Lorentz symmetry considerations only. For smooth configurations, the local lattice actions reduce to the Hilbert-Palatini action, a cosmological term and the three topological terms of dimension four of Pontyagin, Euler and Nieh-Yan. Consistency conditions for a topologically hypercubic complex with null 4-simplexes are derived and a topological lattice theory that enforces these non-local constraints is constructed. The lattice integration measure is derived from an \SLC-invariant integration measure by localization of the non-local structure group. This measure is unique up to a density that depends on the local 4-volume. It can be expressed in terms of manifestly coordinate invariant geometrical quantities. The density provides an invariant regularization of the lattice integration measure that suppresses configurations with small local 4-volumes. Amplitudes conditioned on geodesic distances between local observables have a physical interpretation and may have a smooth ultraviolet limit. Numerical studies on small lattices in the unphysical strong coupling regime of large imaginary cosmological constant suggest that this model of triangulated causal manifolds is finite. Two topologically different triangulations of space-time are discussed: a single, causally connected universe and a duoverse with two causally disjoint connected components. In the duoverse, two hypercubic sublattices are causally disjoint but the local curvature depends on fields of both sublattices. This may simulate effects of dark matter in the continuum limit.

Explore related subjects

gr-qc

Keep this discovery

BibTeXRIS

Martin Schaden. 2015-09-10. Causal Space-Times on a Null Lattice. https://arxiv.org/abs/1509.03095

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

gr-qc↗
arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗