English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

General Relativity, while ultimately based on the Einstein equations, also allows one to quantitatively study some aspects of the theory without explicitly solving the Einstein equations. These geometrical notions of the theory provide an insight to the nature of more general spacetimes. In this thesis, the Raychaudhuri equation, the choice of the coordinate system, the notions of surface gravity and of entropy, and restrictions on negative energy densities on the form of the Quantum Interest Conjecture, will be discussed. First, using the Kodama vector, a geometrically preferred coordinate system is built. With this coordinate system the usual quantities, such as the Riemann and Einstein tensors, are calculated. Then, the notion of surface gravity is generalized in two different ways. The first generalization is developed considering radial ingoing and outgoing null geodesics, in situations of spherical symmetry. The other generalized surface gravity is a three-vector obtained from the spatial components of the redshifted four acceleration of a suitable set of fiducial observers. This vectorial surface gravity is then used to place a bound on the entropy of both static and rotating horizonless objects. This bound is obtain mostly by classical calculations, with a minimum use of quantum field theory in curved spacetime. Additionally, several improved versions of the Raychaudhuri equation are developed and used in different scenarios, including a two congruence generalization of the equation. Ultimately semiclassical quantum general relativity is studied in the specific form of the Quantum Inequalities, and the Quantum Interest Conjecture. A variational proof of a version of the Quantum Interest Conjecture in (3 + 1)–dimensional Minkowski space is provided.

Kodama Time, Entropy Bounds, the Raychaudhuri Equation, and the Quantum Interest Conjecture