Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0412070

Applications of geometric algebra to black holes and Hawking radiation

S. Setiawan
View original source ↗Read source document ↗Export metadata ↓

Abstract

We discuss the applications of Gauge Theory of Gravity (GTG) within the language of geometric algebra to black holes and Hawking radiation. Applications include the Unruh effect, the Dirac and Klein-Gordon equations in several backgrounds, such as the de Sitter and Rindler metrics as well as spherically and axially black hole backgrounds. The analysis is also generalised to allow the presence of magnetic monopoles. We rederive the Hawking temperature for all cases. The derivation of both the correct Fermi-Dirac and Bose-Einstein statistics as well as the Hawking temperature may suggest that the method of calculations we employ here - geometric algebra - is really powerful in dealing with the problems in various strong gravitational backgrounds.

Explore related subjects

physics.gen-phphysics.class-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. Setiawan. 2025-03-25. Applications of geometric algebra to black holes and Hawking radiation. https://arxiv.org/abs/physics/0412070

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

KEEP EXPLORING

Related papers

arXiv2026

Fermions can also produce super-radiation phenomena

According to traditional theory, it is believed that Fermions do not exhibit superradiation. However, when predetermined boundary conditions are in place, there is a possibility of combining the wave function of coupled Fermions, which can result in the emergence of superradiation phenomena. This article presents a novel perspective, proposing that Fermions have the potential to display superradiation phenomena. This implies that there is a broader scope for investigating superradiation and its relationship with boundary conditions.

physics.gen-ph↗
arXiv2026

All About the Galilean Group SGal(3)

We consider the Galilean group of affine transformations that preserve absolute time intervals between events in spacetime, as well as spatial distances between simultaneous events. The special Galilean group, SGal(3), is a 10-dimensional Lie group; we examine the structure of the group and its Lie algebra and discuss the representation of uncertainty on the group manifold. We also derive closed-form expressions for the $\LieGroupSGal{3}$ exponential and logarithmic maps, the Cayley and inverse Cayley maps, and the left Jacobian and its inverse. Along the way, we mention other groups, including the special orthogonal group, the special Euclidean group, and the group of extended poses, all of which are proper subgroups of the special Galilean group. We describe the role of time in Galilean relativity and touch on the relationship between temporal and spatial uncertainty.

physics.gen-ph↗
arXiv2026

Constraints on Rastall gravity from current observational data

We study the cosmological features of Rastall gravity, where the covariant energy-momentum conservation is modified to $\nabla_μT^μ_ν=λ\nabla_νR$ in curved spacetime. For this purpose, we obtain the modified field equations of Rastall model to linear order of perturbations, and then inspect the evolutionary behavior of cosmological observables, chiefly the matter power spectrum and the Hubble parameter, within the context of Rastall gravity. We also compare Rastall model with cosmological probes, namely cosmic microwave background, weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. According to our numerical results, Rastall gravity prefers lower growth of structures compared to the $Λ$CDM model, which indicates consistency with low-redshift large-scale structure probes. Moreover, numerical analysis reveals that Rastall gravity with a cosmological constant as the dark energy component suffers from the Hubble tension, like the $Λ$CDM model.

physics.gen-ph↗