H2020Индивидуална стипендия2017–2019

QuEST · Quantum Energy Conditions and Singularity Theorems

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2017-09-01 → 2019-08-31
Финансиране от ЕС: 195 455 €
Участници: 1
Схема: MSCA-IF-EF-ST

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Накратко на български

Сингулярностите в пространството-времето, като тези в черните дупки или при Големия взрив, се изследват чрез нови математически доказателства за квантовата материя. Работата по тях помага да се разбере произходът на Вселената и връзката между гравитацията и останалите сили.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Quantum Energy Conditions and Singularity Theorems

In the context of general relativity, a singularity is defined as a boundary point of spacetime beyond which no extension is possible, and a singularity theorem is a proof that singularities are inevitable under certain conditions. Although singularities were discovered early in the history of general relativity in solutions to Einstein’s field equations, the question of whether singularities occur in the physical universe (e.g., inside black holes or at the big bang) remains open and continues to intrigue both mathematicians and physicists. Work on singularities can help answer questions on the origin of our Universe and give insights into a complete theory that would unify gravity with other forces. Fifty years ago, Hawking and Penrose developed the first general singularity theorems in classical General Relativity. These theorems showed that singularities exist in any spacetime that satisfies certain properties. Some of these properties are mild assumptions on spacetime geometry but others depend on matter content and are more problematic. For example, Hawking assumed a Strong Energy Condition (SEC) asserting positivity of the effective energy density (EED). Unfortunately quantised matter as described by quantum field theory (QFT) allows states that violate these energy conditions and so it is necessary to try to prove singularity theorems under weaker assumptions. The main goal of the research project was to establish mathematically rigorous singularity theorems for quantized matter fields based on quantum energy inequalities (QEIs) that constrain local averages of quantities like the EED. Final period conclusions: During the project considerable progress was made towards deriving singularity theorems for quantised matter, and work is nearly complete on a Hawking-type singularity theorem using hypotheses satisfied by a quantum field theory. Along the way, we have derived a classical singularity theorem for the Einstein-Klein-Gordon system, a QSEI for nonminimally coupled scalar fields and a new method for proving singularity theorems (of both types) with weakened energy conditions. Additional results were derived during the duration of the project or are expected in the near future and they are discussed below.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

The proposed project explores an important open question in mathematical physics today: the occurrence of singularities in spacetime - places where the usual understanding of physics breaks down. For example, singularities may exist at the center of black holes, or have occurred at the beginning of the universe. Singularity theorems, developed over the past 50 years following pioneering work of Penrose and Hawking, are mathematically rigorous results that imply that singularities are inevitable provided the matter content of the universe obeys a suitable energy conditions. Although forms of matter described by quantum field theory can violate the original energy conditions, recent developments provide hope that singularity theorems can be proved even in this case. To date, however, no known singularity theorem fully corresponds to the behaviour of quantum fields or takes into account the backreaction of the quantum field on the spacetime. The goal of this project is to establish singularity theorems for quantised matter using recent work by the researcher and the supervisor as a base. This will be approached in several ways (a) new quantum energy inequalities will be proved that are suitable for use in singularity theorems; (b) new singularity theorems will be proved using a transversely smeared version of the averaged null energy condition; (c) analogues of singularity theorems will be investigated in the context of semiclassical gravity. The combination of the complementary expertise of the researcher and the supervisor is essential to the success of this project. Moreover the researcher will receive training from the supervisor in mathematically rigorous approaches to quantum field theory and relativity, which will broaden her knowledge and expertise. This project will help to resolve a major problem in mathematical physics today and provide insight into how the universe works.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITY OF YORK · YORK NORTH YORKSHIREКоординаторОбединеното кралство