Derivace vyššího řádu a nelokalita v gravitaci
| Název práce v češtině: | Derivace vyššího řádu a nelokalita v gravitaci |
|---|---|
| Název v anglickém jazyce: | Higher derivatives and nonlocality in gravity |
| Klíčová slova: | gravitační teorie|pole v zakřivených prostoročasech|derivace vyššího řádu|nelokalita|přesná a přibližná řešení|regularita |
| Klíčová slova anglicky: | gravitational theories|fields in curved spacetimes|higher derivatives|non-locality|exact and approximate solutions|regularity |
| Akademický rok vypsání: | 2022/2023 |
| Typ práce: | disertační práce |
| Jazyk práce: | čeština |
| Ústav: | Ústav teoretické fyziky (32-UTF) |
| Vedoucí / školitel: | Mgr. Ivan Kolář, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 07.09.2023 |
| Datum zadání: | 07.09.2023 |
| Datum potvrzení stud. oddělením: | 27.09.2023 |
| Zásady pro vypracování |
| The main goal of this project is to study higher-derivative and non-local gravitational theories or scalar field theories in curved spacetimes using advanced established as well as new mathematical techniques.
The research should focus on solving some of the following research problems: - Finding exact or approximate solutions of higher-derivative and non-local theories of gravity (e.g., black holes and gravitational waves) [5,6]. - Studying higher-derivative and non-local scalar field theories in curved backgrounds (e.g., maximally-symmetric and black-hole spacetimes) at the classical or quantum level [7,8]. - Investigating the regularity of solutions (spacetimes and scalar fields) by standard methods and from the viewpoint of (non-linear) distributions [9,10]. - Calculating Galilean and Carrollian limits of higher-derivative and non-local theories of gravity [11]. - Deriving new non-local theories arising from various approaches to non-commutative geometry [12]. |
| Seznam odborné literatury |
| [1] Phys. Rev. D 16, 953 (1977)
[2] Phys. Rev. D 94, 104005 (2016) [3] Phys. Rev. Lett. 108, 031101 (2012) [4] JHEP 02, 008 (2008) [5] Phys. Rev. Lett. 114, 171601 (2015) [6] Phys. Rev. D 103, 124067 (2021) [7] Phys. Rev. D 105, 084026 (2022) [8] Phys. Rev. D 100, 104008 (2019) [9] Gen. Rel. Grav. 8, 915 (1977) [10] Class. Quantum Grav. 23 R91 (2006) [11] SciPost Phys. 13, 055 (2022) [12] Int. J. Mod. Phys. A 24, 1229 (2009) |
| Předběžná náplň práce v anglickém jazyce |
| Terms with derivatives of higher order appear naturally in many effective descriptions of quantum gravity. They tend to resolve or mitigate issues related to ultraviolet incompleteness of general relativity such as the existence of spacetime singularities and quantum non-renormalizability. Higher-derivative theories of finite order suffer from Ostrogradsky instability, which manifests in the presence of ghost degrees of freedom at the linear level [1]. Gravitational theories can be rendered ghost-free if they reduce to general relativity at the linear level [2] or if they avoid Ostrogradsky's theorem by admitting non-local terms with derivatives of infinite order [3]. Non-local scalar field theories arise also from popular models of p-Adic string theory, string field theory, and non-commutative geometry [4].
The project aims to study various problems of gravitational theories and scalar field theories (in the presence of gravity) that contain higher derivatives of finite or infinite order (non-local theories). The research will focus on solving some of the following problems: exact and approximate solutions of higher-derivative theories of gravity [5,6], higher-derivative scalar field theories in curved spacetimes from the classical and quantum viewpoint [7,8], regularity of fields and curvature in the context of functions and (non-linear) distributions [9,10], Gallean and Carrollian limits of higher-derivative and non-local theories [11], non-local theories based on non-commutative geometry [12]. |