Covariant and manifestly projective invariant formulation of Thomas-Whitehead gravity

被引:1
|
作者
Grover, Tyler [1 ]
Stiffler, Kory [1 ]
Vecera, Patrick [2 ]
机构
[1] Univ Iowa, Dept Phys & Astron, Iowa City, IA 52242 USA
[2] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
关键词
COADJOINT ORBITS; EINSTEIN-METRICS; SYMMETRIES; GEOMETRY; FERMIONS; TENSOR; GAUGE;
D O I
10.1103/PhysRevD.110.084058
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
Thomas-Whitehead (TW) gravity is a recently formulated projectively invariant extension of Einstein- Hilbert gravity. Projective geometry was used long ago by Thomas et al. to succinctly package equivalent paths encoded by the geodesic equation. Projective invariance in gravity has further origins in string theory through a geometric action constructed from the method of coadjoint orbits using the Virasoro algebra. A projectively invariant connection arises from this construction, a part of which is known as the diffeomorphism field. TW gravity exploits projective Gauss-Bonnet terms in the action functional to endow the diffeomorphism field with dynamics, while allowing the theory to collapse to general relativity in the limit that the diffeomorphism field vanishes and the connection becomes Levi-Civita. In the original formulation of TW gravity, the diffeomorphism field is projectively invariant but not tensorial and the connection is projectively invariant but not affine. In this paper we reformulate TW gravity in terms of projectively invariant tensor fields and a projectively invariant covariant derivative, derive field equations respecting these symmetries, and show that the field equations obtained are classically equivalent across formulations. This provides a "Rosetta Stone" between this newly constructed covariant and projective invariant formulation of TW gravity and the original formulation that was manifestly projective invariant, but not covariant.
引用
收藏
页数:25
相关论文
共 50 条
  • [42] Manifestly gauge-invariant cosmological perturbation theory from full loop quantum gravity
    Han, Muxin
    Li, Haida
    Liu, Hongguang
    PHYSICAL REVIEW D, 2020, 102 (12)
  • [44] COVARIANT AND GAUGE-INVARIANT FORMULATION OF THE SACHS-WOLFE EFFECT
    RUSS, H
    SOFFEL, MH
    XU, CM
    DUNSBY, PKS
    PHYSICAL REVIEW D, 1993, 48 (10): : 4552 - 4556
  • [45] Covariant gauge-invariant perturbations in multifluid f (R) gravity
    Abebe, Amare
    Abdelwahab, Mohamed
    de la Cruz-Dombriz, Alvaro
    Dunsby, Peter K. S.
    CLASSICAL AND QUANTUM GRAVITY, 2012, 29 (13)
  • [46] Covariant master theory for novel Galilean invariant models and massive gravity
    Gabadadze, Gregory
    Hinterbichler, Kurt
    Khoury, Justin
    Pirtskhalava, David
    Trodden, Mark
    PHYSICAL REVIEW D, 2012, 86 (12):
  • [47] MANIFESTLY COVARIANT CANONICAL FORMULATION OF THE YANG-MILLS FIELD-THEORIES .1. GENERAL FORMALISM
    KUGO, T
    OJIMA, I
    PROGRESS OF THEORETICAL PHYSICS, 1978, 60 (06): : 1869 - 1889
  • [48] MANIFESTLY LORENTZ COVARIANT FORMULATION OF THE EINSTEIN-PODOLSKY-ROSEN PROBLEM USING THE TOMONAGA-SCHWINGER FORMALISM
    GHOSE, P
    HOME, D
    PHYSICAL REVIEW A, 1991, 43 (11): : 6382 - 6385
  • [49] ZEROS OF COVARIANT VECTOR-FIELDS FOR THE POINT GROUPS - INVARIANT FORMULATION
    JARIC, MV
    MICHEL, L
    SHARP, RT
    JOURNAL DE PHYSIQUE, 1984, 45 (01): : 1 - 27
  • [50] Covariant formulation of BPS black holes and the scalar weak gravity conjecture
    Dall'Agata, Gianguido
    Morittu, Matteo
    JOURNAL OF HIGH ENERGY PHYSICS, 2020, 2020 (03)