Explanation of Missing Mass Problem with General Relativity and Dark Matter Identification
Discover how the missing mass problem in the universe can potentially be explained through general relativity, dark matter, and dragging phenomena. Explore key ideas, theoretical frameworks, and empirical measures discussed at the 15th International Workshop on the Identification of Dark Matter in Italy.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
15th International Workshop on the Identification of Dark Matter GSSI, L Aquila, Italy, 8 - 12 July 2024 GR & DM Introduction How dragging and general relativity could explain the missing mass problem Theoretical Framework Empirical Measures Federico Re, federico.re@unimib.it Conclusions Dipartimento di Fisica Giuseppe Occhialini, Universit di Milano-Bicocca Collaboration: Massimo Dotti, Sergio Cacciatori, Vittorio Gorini, Francesco Haardt, Davide Astesiano, Marco Galoppo, David Wiltshire, Frederic Hessman 1/17
KEY IDEAS Strategies for the Missing Mass Problem KI #1: all the MMP have gravitational nature Most natural idea: Existing invisible mass Is the Missing Mass a clue of misunderstanding in gravity? Galaxy rotation curves Virial of clusters Gravitational lensing Temperature of hot gases Bullet clusters CMB anisotropies SNIa redshift measures Etc All gravitational attractions or space-time distortions, i.e. gravitational wells Dark matter: MaCHOs? Hot DM (sterile neutrinos)? Cold DM (WIMPs)? Attempts to modify the Newtonian Gravity (MOND) Introduction Theoretical Framework Milgrom 1983, Bekenstein&Milgrom 1984, Bekenstein 2004 Empirical Measures Conclusions KI #2: GR is already a modified gravity 2/17
KEY IDEAS GR is more than post-Newtonian corrections KI #3: GR allows non- Newtonian phenomena in low energy r gime ?00 ?0? ?0? ???, Intuition: GR = Newton + post-Newtonian corrections ?? = where?0?dragging term KI #4: galaxy surrounded by dragging vortex supporting rotation curve Galactic dynamics in low energy r gime: Sub-relativistic speeds Weak forces Astesiano+3 2022 Introduction Carlotto-Shoen shielding metrics Geons (solitonic GW) Theoretical Framework Balasin&Grumiller 2008 Crosta+ 2020 Astesiano+5 2022 Re&Galoppo 2024 PN terms have magnitude ~?2 Negligible corrections ?2: Empirical Measures A galaxy is an extended source: Not globally Newtonian Ciotti 2022, Lasenby+ 2023, Costa+ 2023, Glampedakis&Jones 2023 Costa&Nat rio 2023 Re-weight DM amount in disc galaxies Conclusions DM phenomena = fake DM from GR + true DM 3/17
KEY IDEAS Low energy limit and non-commutativity Widespread intuition: Switch the order: Start with full Einstein Eqs Require small metric perturbations (classical limit): ?? = ???+ ? 2 ?? They don t commute! Then expand formulas at the lowest order in Low Energy Limit (LEL) Introduction ??: Then deduce Einstein Eqs Theoretical Framework Find in Newtonian limit: 4??? = + ? Find non-negligible corrections to Newtonian eqs!: 4??? = + ????? ???, Empirical Measures ?2 ?2 , Conclusions 4/17
,? MODEL Metric and source Lewis Papapetrou Weyl metric: ?2?? + ???2+ ? 2? 2 2 ?? ?,?2= ?2? ?2?2??2+ ? ?2??2+ ??2 12??+ ?? Perfect fluid: ?? = ???? No velocity dispersion: ??= ? Introduction Balasin&Grumiller 2008 Crosta+ 2020 Galoppo+ 2022 Beordo+2024 Generalization of BG metric Theoretical Framework Empirical Measures In Low Energy Limit (LEL): ? ??? ?2, ????= ?2 ? = 1 + ? Conclusions ?2 with finite ?? dragging speed , ? ?2= ? ?2 ?2 , ?2 ?2 . 5/17
,? MODEL Metric and source 2? 2 2 ?2?? + ???2+ ? ??= ? ?? ?,?2= ?2? ?2?2??2+ ? ?2??2+ ??2, 12??+ ??, ?? = ???? ,? family of exact solutions. Fully generated by the choice of functions ?,0 and ? Introduction ???+ ??2 Grad-Shafranov operator, ? 1 = 0 s.t. = ??2 and ?,? +?2 Theoretical Framework 2?2 ? ??? 2 ? ? ? Velocity Field Equation (VFE) ? Empirical Measures ?2 2 ??2, 12 ? ? ???= ? 2?? + ? = ?2 ?2? , Conclusions ???= ?? + ?2 ??2, s.t. ? = ? ?? 8 ?? =?22 ?2 ?2?2 ?2+ ?2 2 s.t. ? ? ? ???= 4?? Astesiano+3 2022 Astesiano+5 2022 Re&Galoppo 2024 6/17
,? MODEL What speed? Zero Angular Momentum Observers (ZAMO): 1= ?????, ?? where = ??? ? ? 1 2= ? 3= ? 0= ?? ??+ ??, ?? ?2??, ?? ?2??; ? ??? ??? dragging angular speed Introduction 1 ?? ?? Measures speed ??=?? 0 ??=? In LEL: 2 = ?? ? ? ??? Theoretical Framework Stationary (not static!) Observers: ?2 ?? ???, ?? Empirical Measures ? ? 1=? 0= ? 2= ? 3= ? ?? ?2??, ?? ?2??, ?? ?2?? ? Conclusions 1 ?? ?? Measures speed ??=?? 1? In LEL: ?? ? ~10 3 0 ??= ?? ?2? 1 ?? ?? 0 0= ??? ? Dragging speed: ??=?? In LEL: ?? ? ~10 3 Re&Galoppo 2024 0 ?? 7/17
,? MODEL What speed? ?? 1+ ????? Measure rotation curves with redshift. In SR, for a edge-on galaxy: 1 + ? = 1 + ?2 1 ?2 A still observer at spatial infinity measures 1 + ???= ??? In LEL: 1 + ? 1 + ??? ? 2 1 ?1 + ? ?2 ? + ? Introduction Astesiano+5 2022, Re&Galoppo 2024 Theoretical Framework ????? Analog if measure our speed from the CMB dipole. According SR: ??,10 = 2 ? 3? Inside a dragging metric we see ? ? 1 + ??? ??10 ? ?2 ? Empirical Measures ??? ?3? In LEL: ??,10 2 ??,10= Conclusions Re, Galoppo, Dotti (coming soon) We measure the speed ??, but the dynamics is determined by the angular momentum, proportional to the (different!) speed ?? ?? ?? 8/17
PHANTOM DARK MATTER Corrections on required density 8 ?? =?22 ?2 ?2?2 ?2+ ?2 2 In 2 8 ?? 4?? ??? ?? 2? ??? ? ??? ? ??+ ? ??? ? ?? LEL: 4?? ? ? ?? ??? +?? +?? Introduction Cfr non-linear gravitomagnetic formalism: ? , ? ? ? = ?2+ ? = 0 ? = ?2 ? = 2 ?2 16?? ?2 ??? Theoretical Framework ?2 ?2 2?2 4??? , being ??= ?? ? momentum density Empirical Measures ? ? ?2 ? ? ? ?3 Conclusions We don t measure directly ? We measure ??. With ? less ? less ? ? = ? + ? ? ? ??? Re&Galoppo 2024 9/17
PHANTOM DARK MATTER Corrections on gravitational lensing Gauss-Bonnet ( ? = 1) Introduction Gravitomagnetism: ? + ? ? ? , ? ? Asymmetric geodesics: ? ?0 ? Far from the centre: ?,?,?,?< 0 Theoretical Framework ?= Empirical Measures Conclusions ??+ ?? ??+ ??|???? 2? ?,??0 ? ? Galoppo+ 2022 Re&Galoppo 2024 ? 10/17
ESTIMATION OF DRAGGING SPEED With Newtonian ad-hoc term 2 2 8 ? ??+ ???? 8 ?? ,? 2+ 2?? Fraction1 ? of DM explained by dragging ??= ?? ?2 ?2 ,? ?2 ? 2 ? = 1 ?? 0: spherically symmetric Newtonian model with 100% of DM 4 ? ??+ ??? = 2????,? +?? Introduction ?2 ? Theoretical Framework 2 NFW, ??? ? ? ??? exponential, ??? ???0 Evaluate for MW: ?? ??0? ?? 2.1 kpc, ??? 5.69 kpc, ? 220 km/s, ???0 6.4% ??0 1 + ??? Empirical Measures At ? ?.? kpc: ? ? ,? ? ? ?? km/s Conclusions Example: ? = 12 ??? ,0 35 km/s in our neighborhood Re&Galoppo 2024 11/17
ESTIMATION OF DRAGGING SPEED With Newtonian ad-hoc term General-relativistic description Newtonian description Introduction Theoretical Framework Empirical Measures Conclusions 12/17
ESTIMATION OF DRAGGING SPEED Coming soon: more precise formulas with pressure! General-relativistic description Newtonian description Introduction Theoretical Framework Empirical Measures Conclusions Galoppo, Wiltshire, Re (coming soon) 13/17
EMPIRICAL MEASURES Counter-rotating matter Kuijken+ 1996, Corsini 2014 Some disc galaxies have counter-rotating stars or gas The counter-rotating component is also dragged!?++ ? ?? Re (coming soon) Introduction Consider geodesics for a test particle with tangent motion?? ?? ?? Theoretical Framework Without dragging (?? 0): depends only on the potential s.t.???= ? 2 ?2 ?? ? Geodesic ? symmetric? ?? 2 2 ??=?? Geodesic ?2 ?? ? ?2, ? Empirical Measures ? With dragging ?: ? ?? ?? Asymmetric Conclusions 2 ?? ? ??? ?+ ??, ? = ??+? ??? +?? ? ? ??? ?? ? ?? ?? ? Non-negligible deviation from Newton! 14/17 14/17
CONCLUSIONS What has been done and what remains to be done What we know: GR non-linearities allow solitonic solutions for the dragging terms Strong dragging implies non-negligible deviations from Newton A quite small dragging vortex sustains flat rotation curve It returns also a suitable correction on the gravitational lensing The dragging speed can be measured with counter-rotating matter components Introduction Theoretical Framework Future perspectives: Generalize equations (in LEL) for non-negligible pressure (bulge, elliptical galaxies ) Consequences of the dragging on CMB Measure the actual dragging with the counter-rotating matter Apply GR to other MMP (gravitational lensing, universe expansion ) Empirical Measures Conclusions Galoppo, Wiltshire, Re (coming soon) Stay tuned! Re, Galoppo, Dotti (coming soon) Re (coming soon) 15/17 Galoppo+ 2022; Re 2020, Re 2021, Vigneron&Buchert 2019, Buchert 2008
CONCLUSIONS Introduction Thanks for your attention! Theoretical Framework Empirical Measures Conclusions 16/17
CONCLUSIONS Minimal bibliography H. Balasin and D. Grumiller (2008), Non-newtonian behavior in weak field general relativity for extended rotating sources Int. J. Mod. Phys. D 17 475 488 arXiv:astro-ph/0602519 M. Crosta, M. Giammaria, M. G. Lattanzi, and E. Poggio (2020), On testing CDM and geometry-driven Milky Way rotation curve models with Gaia DR2 MNRAS 496 2107 2122 arXiv:1810.04445 W. Beordo, M. Crosta, M. G. Lattanzi, P. Re-Fiorentin and A. Spagna (2024), Geometry-driven and dark- matter-sustained Milky Way rotation curves with Gaia DR3 MNRAS 529 (4) 4681-4698 D. Astesiano, S. L. Cacciatori, V. Gorini, and F. Re (2022), Towards a full general relativistic approach to galaxies EPJ C 82 (6) 554 arXiv:2204.05143 D. Astesiano, S. L. Cacciatori, M. Dotti, F. Haardt, and F. Re (2022), Re-weighting dark matter in disc galaxies: a new general relativistic observational test arXiv:2204.05143 M. Galoppo, S. L. Cacciatori, V. Gorini, and M. Mazza (2022), Equatorial Lensing in the Balasin- Grumiller Galaxy Model arXiv:2212.10290 F. Re and M. Galoppo (2024), On GR dragging and effective galactic dark matter arXiv:2403.03227 Introduction Theoretical Framework Empirical Measures Conclusions 17/17
