Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions

General Teleparallel theories assume that curvature is vanishing in which case gravity can be solely represented by torsion and/or nonmetricity. Using differential form language, we express the Riemannian Gauss-Bonnet invariant concisely in terms of two General Teleparallel Gauss-Bonnet invariants, a bulk and a boundary one. Both terms are boundary terms in four dimensions. We also find that the split is not unique and present two possible alternatives. In the absence of nonmetricity our expressions coincide with the well-known Metric Teleparallel Gauss-Bonnet invariants for one of the splits. Next, we focus on the description where only nonmetricity is present and show some examples in different spacetimes. We finish our discussion by formulating novel modified Symmetric Teleparallel theories constructed with our new scalars.

[1]  S. Capozziello,et al.  The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity , 2023, 2308.03632.

[2]  E. Saridakis,et al.  Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology , 2023, 2308.00652.

[3]  D. Doneva,et al.  Distinctive Features of Hairy Black Holes in Teleparallel Gauss-Bonnet Gravity , 2023, 2307.14720.

[4]  S. Capozziello,et al.  The role of the boundary term in $f(Q,B)$ symmetric teleparallel gravity , 2023, 2307.13280.

[5]  T. Koivisto,et al.  General teleparallel metrical geometries , 2023, International Journal of Geometric Methods in Modern Physics.

[6]  D. Doneva,et al.  Spontaneous scalarization of black holes in Gauss-Bonnet teleparallel gravity , 2022, Physical Review D.

[7]  S. Bahamonde,et al.  Black hole solutions in scalar-tensor symmetric teleparallel gravity , 2022, Journal of Cosmology and Astroparticle Physics.

[8]  J. Serra,et al.  Causality constraints on black holes beyond GR , 2022, Journal of High Energy Physics.

[9]  K. Yagi,et al.  Constraints on Einstein-dilation-Gauss-Bonnet gravity from black hole-neutron star gravitational wave events , 2022, Physical Review D.

[10]  Simone Kuhn,et al.  Revisiting cosmologies in teleparallelism , 2021, Classical and Quantum Gravity.

[11]  S. Kuhn,et al.  Black holes in f(Q) gravity , 2021, Physical Review D.

[12]  M. Hohmann.  General covariant symmetric teleparallel cosmology , 2021, Physical Review D.

[13]  M. Hendry,et al.  Teleparallel gravity: from theory to cosmology , 2021, Reports on progress in physics. Physical Society.

[14]  E. Saridakis,et al.  First evidence that non-metricity f(Q) gravity could challenge ΛCDM , 2021, Physics Letters B.

[15]  N. Frusciante.  Signatures of f(Q) gravity in cosmology , 2021, 2101.09242.

[16]  C. Herdeiro,et al.  Spin-Induced Scalarized Black Holes. , 2020, Physical review letters.

[17]  T. Koivisto,et al.  Cosmological perturbations in modified teleparallel gravity models: boundary term extension , 2020, 2009.02168.

[18]  M. Gangopadhyay,et al.  Inflation with a quartic potential in the framework of Einstein-Gauss-Bonnet gravity , 2020, Physical Review D.

[19]  N. Franchini,et al.  Spin-Induced Black Hole Spontaneous Scalarization. , 2020, Physical review letters.

[20]  Robie A. Hennigar,et al.  On taking the D → 4 limit of Gauss-Bonnet gravity: theory and solutions , 2020, 2004.09472.

[21]  P. Creminelli,et al.  Hairy black-holes in shift-symmetric theories , 2020, Journal of High Energy Physics.

[22]  P. Rudra,et al.  String-inspired Teleparallel cosmology , 2020, Nuclear Physics B.

[23]  Y. Pang,et al.  Horndeski gravity as D → 4 limit of Gauss-Bonnet , 2020, 2003.11552.

[24]  Luca Santoni,et al.  Black hole ringdown as a probe for dark energy , 2019, Physical Review D.

[25]  T. Koivisto,et al.  General teleparallel quadratic gravity , 2019, Physics Letters B.

[26]  E. Saridakis,et al.  Conformal gravity and transformations in the symmetric teleparallel framework , 2019, Physical Review D.

[27]  J. Jim'enez,et al.  Cosmology in f(Q) geometry , 2019, 1906.10027.

[28]  Chunshan Lin,et al.  Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime. , 2019, Physical review letters.

[29]  L. Heisenberg,et al.  The Geometrical Trinity of Gravity , 2019, Universe.

[30]  E. Berti,et al.  Self-interactions and spontaneous black hole scalarization , 2019, Physical Review D.

[31]  C. Charmousis,et al.  Cosmological instability of scalar-Gauss-Bonnet theories exhibiting scalarization , 2019, Journal of Cosmology and Astroparticle Physics.

[32]  Damianos Iosifidis.  Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories , 2019, 1902.09643.

[33]  V. Oikonomou,et al.  Ghost-free Gauss-Bonnet theories of gravity , 2018, Physical Review D.

[34]  C. Boehmer,et al.  Teleparallel theories of gravity: illuminating a fully invariant approach , 2018, Classical and Quantum Gravity.

[35]  L. Gualtieri,et al.  Black holes and binary mergers in scalar Gauss-Bonnet gravity: Scalar field dynamics , 2018, Physical Review D.

[36]  S. Capozziello,et al.  Noether symmetries and boundary terms in extended Teleparallel gravity cosmology , 2018, Classical and Quantum Gravity.

[37]  L. Heisenberg,et al.  Teleparallel Palatini theories , 2018, Journal of Cosmology and Astroparticle Physics.

[38]  J. Morales,et al.  Gauss–Bonnet models with cosmological constant and non zero spatial curvature in $$D=4$$D=4 , 2017, 1711.09484.

[39]  E. Berti,et al.  Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling. , 2017, Physical review letters.

[40]  D. Doneva,et al.  New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories. , 2017, Physical review letters.

[41]  L. Heisenberg,et al.  Coincident general relativity , 2017, Physical Review D.

[42]  V. Oikonomou,et al.  Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution , 2017, 1705.11098.

[43]  Diego Sáez-Chillón Gómez,et al.  Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss–Bonnet term , 2017, 1705.03867.

[44]  H. Omer,et al.  Strings in Background Fields , 2016, 1612.01830.

[45]  S. Capozziello,et al.  Noether symmetries in Gauss–Bonnet-teleparallel cosmology , 2016, The European physical journal. C, Particles and fields.

[46]  C. Böhmer,et al.  Modified teleparallel theories of gravity: Gauss–Bonnet and trace extensions , 2016, The European Physical Journal C.

[47]  F. Pretorius,et al.  Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226 , 2016, 1603.08955.

[48]  S. Capozziello,et al.  f(T) teleparallel gravity and cosmology , 2015, Reports on progress in physics. Physical Society.

[49]  E. Saridakis,et al.  The covariant formulation of f(T) gravity , 2015, 1510.08432.

[50]  P. González,et al.  Teleparallel Equivalent of Lovelock Gravity , 2015, 1508.01174.

[51]  F. Vernizzi,et al.  Weakly broken galileon symmetry , 2015, 1505.00007.

[52]  T. Sotiriou,et al.  Black hole hair in generalized scalar-tensor gravity: An explicit example , 2014, 1408.1698.

[53]  E. Saridakis,et al.  Cosmological applications of $F(T,T_G)$ gravity , 2014, 1408.0107.

[54]  E. Saridakis,et al.  Dynamical behavior in f (T, TG) cosmology , 2014, 1404.7100.

[55]  E. Saridakis,et al.  Teleparallel equivalent of Gauss-Bonnet gravity and its modifications , 2014, 1404.2249.

[56]  T. Sotiriou,et al.  Black hole hair in generalized scalar-tensor gravity. , 2013, Physical review letters.

[57]  J. W. Maluf,et al.  The teleparallel equivalent of general relativity , 2013, 1303.3897.

[58]  M. Gasperini.  Theory of Gravitational Interactions , 2013 .

[59]  J. Polchinski,et al.  The a-theorem and the asymptotics of 4D quantum field theory , 2012, 1204.5221.

[60]  K. Yagi,et al.  New constraint on scalar Gauss-Bonnet gravity and a possible explanation for the excess of the orbital decay rate in a low-mass x-ray binary , 2012, 1204.4524.

[61]  L. Hui,et al.  No-hair theorem for the Galileon. , 2012, Physical review letters.

[62]  Z. Komargodski,et al.  On renormalization group flows in four dimensions , 2011, 1107.3987.

[63]  J. Yokoyama,et al.  Generalized G-Inflation —Inflation with the Most General Second-Order Field Equations— , 2011, 1105.5723.

[64]  T. Padmanabhan,et al.  Structure of Lanczos-Lovelock Lagrangians in critical dimensions , 2010, 1008.5154.

[65]  V. Cardoso,et al.  Are black holes in alternative theories serious astrophysical candidates? The Case for Einstein-Dilaton-Gauss-Bonnet black holes , 2009, 0902.1569.

[66]  Franco Fiorini,et al.  Born-Infeld gravity in Weitzenböck spacetime , 2008, 0812.1981.

[67]  J. Barrow,et al.  Cosmology of modified Gauss-Bonnet gravity , 2007, 0705.3795.

[68]  Franco Fiorini,et al.  Modified teleparallel gravity : Inflation without an inflaton , 2006, gr-qc/0610067.

[69]  E. Elizalde,et al.  Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem , 2005, hep-th/0601008.

[70]  S. Nojiri,et al.  Modified Gauss–Bonnet theory as gravitational alternative for dark energy , 2005, hep-th/0508049.

[71]  S. Nojiri,et al.  Gauss-Bonnet dark energy , 2005, hep-th/0504052.

[72]  Y. Obukhov,et al.  Metric-affine approach to teleparallel gravity , 2002, gr-qc/0212080.

[73]  J. M. Nester,et al.  Symmetric teleparallel general relativity , 1998, gr-qc/9809049.

[74]  N. Mavromatos,et al.  Dilatonic black holes in higher curvature string gravity. , 1996, Physical review. D, Particles and fields.

[75]  K. Maeda,et al.  Dilatonic black holes with Gauss-Bonnet term , 1996, gr-qc/9606034.

[76]  E. Bergshoeff,et al.  The quartic effective action of the heterotic string and supersymmetry , 1989 .

[77]  E. Fradkin,et al.  Effective Field Theory from Quantized Strings , 1985 .

[78]  F. Hehl,et al.  General Relativity with Spin and Torsion: Foundations and Prospects , 1976 .

[79]  D. Lovelock.  The four-dimensionality of space and the einstein tensor , 1972 .

[80]  D. Lovelock.  The Einstein Tensor and Its Generalizations , 1971 .