Galaxy Rotation Curves in Covariant Hořava-Lifshitz Gravity
Abstract
:1. Introduction
2. Static and Spherically Symmetric Solutions of Covariant HL Gravity
2.1. Action
2.2. Constraints and Equations of Motion
- The variation with respect to A gives , or equivalently:
- The variation with respect to ν gives:
- The variation with respect to N gives the Hamiltonian constraint:
- The variation with respect to n gives:
- The variation with respect to f gives:
2.3. Solutions
- n ≠ 0 and A = 0: leads to the Schwarzschild solution in the Painleve-Gullstrand coordinates (), and the Hamiltonian constraint is automatically satisfied;
- n ≠ 0 and A ≠ 0: corresponds to the situation with multiple solutions for A and n, on which this article focuses. Since , we have and , such that the Equations (11) and (13) give respectively:
3. Galaxy Rotation Curves
3.1. Gravitational Potential
3.2. Navarro, Frenk and White Profile
Galaxy | a | v200 (km/s) | r200 (kpc) |
---|---|---|---|
NGC 2403 | 10.9 ± 0.6 | 106.1 ± 1.9 | 88.4 ± 2.6 |
NGC 3198 | 11.2 ± 0.43 | 104.0 ± 0.7 | 86.6 ± 1.6 |
NGC 3521 | 14.0 ± 12.6 | 122.5 ± 20.4 | 102.0 ± 18 |
3.3. Pseudoisothermal Profile
Galaxy | Rc (kpc) | ρ0 (10−3M⊙pc−3) | r200 (kpc) |
---|---|---|---|
NGC 2403 | 2.51 ± 0.32 | 59.1 ± 14.3 | 88.4 ± 2.6 |
NGC 2841 | 1.36 ± 0.75 | 674.8 ± 736.4 | 159.0 ± 3.7 |
NGC 3621 | 5.88 ± 0.32 | 13.0 ± 1.1 | 106.6 ± 4.0 |
3.4. Vacuum Energy Contribution of the Auxiliary Field
4. Conclusions
Acknowledgments
Conflicts of Interest
References
- Hořava, P. Quantum gravity at a Lifshitz point. Phys. Rev. D 2009, 79. [Google Scholar] [CrossRef]
- Alexandre, J. Lifshitz-type quantum field theories in particle physics. Int. J. Mod. Phys. A 2011, 26, 4523. [Google Scholar] [CrossRef]
- Padilla, A. The good, the bad and the ugly .... of Hořava gravity. J. Phys. Conf. Ser. 2010, 259, 012033. [Google Scholar] [CrossRef]
- Mukohyama, S. Hořava-Lifshitz cosmology: A review. Class. Quantum Gravity 2010, 27, 223101. [Google Scholar] [CrossRef]
- Sotiriou, T.P. Hořava-Lifshitz gravity: A status report. J. Phys. Conf. Ser. 2011, 283, 012034. [Google Scholar] [CrossRef]
- Sotiriou, T.P.; Visser, M.; Weinfurtner, S. Quantum gravity without Lorentz invariance. J. High Energy Phys. 2009, 2009, 033. [Google Scholar] [CrossRef]
- Charmousis, C.; Niz, G.; Padilla, A.; Saffin, P.M. Strong coupling in Hořava gravity. J. High Energy Phys. 2009, 2009, 070. [Google Scholar] [CrossRef]
- Hořava, P.; Melby-Thompson, C.M. General covariance in quantum gravity at a Lifshitz point. Phys. Rev. D 2010, 82, 064027. [Google Scholar] [CrossRef]
- Abdalla, E.; da Silva, A.M. On the motion of particles in covariant Hořava-Lifshitz gravity and the meaning of the A-field. Phys. Lett. B 2012, 707, 311–314. [Google Scholar] [CrossRef]
- Lin, K.; Wang, A. Static post-Newtonian limits in non-projectable Hořava-Lifshitz gravity with an extra U(1) symmetry. ArXiv E-Prints 2013. [Google Scholar]
- Mukohyama, S. Dark matter as integration constant in Hořava-Lifshitz gravity. Phys. Rev. D 2009, 80, 064005. [Google Scholar] [CrossRef]
- Cardone, V.F.; Radicella, N.; Ruggiero, M.L.; Capone, M. The Milky Way rotation curve in Hořava-Lifshitz theory. ArXiv E-Prints 2010. [Google Scholar]
- Cardone, V.F.; Capone, M.; Radicella, N.; Ruggiero, M.L. Spiral galaxies rotation curves in the Hořava-Lifshitz gravity theory. ArXiv E-Prints 2012. [Google Scholar]
- Romero, J.M.; Bernal-Jaquez, R.; Gonzalez-Gaxiola, O. Is it possible to relate MOND with Hořava Gravity? Mod. Phys. Lett. A 2010, 25, 2501. [Google Scholar] [CrossRef]
- Alexandre, J.; Farakos, K.; Tsapalis, A. Liouville-Lifshitz theory in 3 + 1 dimensions. Phys. Rev. D 2010, 81, 105029. [Google Scholar] [CrossRef]
- Dutta, S.; Saridakis, E.N. Overall observational constraints on the running parameter λ of Hořava-Lifshitz gravity. J. Cosmol. Astropart. Phys. 2010, 2010, 013. [Google Scholar] [CrossRef]
- Lin, K.; Mukohyama, S.; Wang, A. Solar system tests and interpretation of gauge field and Newtonian prepotential in general covariant Hořava-Lifshitz gravity. Phys. Rev. D 2012, 86, 104024. [Google Scholar] [CrossRef]
- Da Silva, A.M. An alternative approach for general covariant Hořava-Lifshitz gravity and matter coupling. Class. Quantum Gravity 2011, 28, 055011. [Google Scholar] [CrossRef]
- Klusoň, J. Hamiltonian analysis of nonrelativistic covariant restricted-foliation-preserving diffeomorphism invariant Hořava-Lifshitz gravity. Phys. Rev. D 2011, 83, 044049. [Google Scholar] [CrossRef]
- Blas, D.; Pujolas, O.; Sibiryakov, S. On the extra mode and inconsistency of Hořava gravity. J. High Energy Phys. 2009, 2009, 029. [Google Scholar] [CrossRef]
- Bogdanos, C.; Saridakis, E.N. Perturbative instabilities in Hořava gravity. Class. Quantum Gravity 2010, 27, 075005. [Google Scholar] [CrossRef]
- Koyama, K.; Arroja, F. Pathological behaviour of the scalar graviton in Hořava-Lifshitz gravity. J. High Energy Phys. 2010, 2010, 061. [Google Scholar] [CrossRef]
- Blas, D.; Pujolas, O.; Sibiryakov, S. Comment on “Strong coupling in extended Hořava-Lifshitz gravity”. Phys. Lett. B 2010, 688, 350–355. [Google Scholar] [CrossRef]
- Papazoglou, A.; Sotiriou, T.P. Strong coupling in extended Hořava-Lifshitz gravity. Phys. Lett. B 2010, 685, 197–200. [Google Scholar] [CrossRef] [Green Version]
- Alexandre, J.; Pasipoularides, P. Spherically symmetric solutions in covariant Hořava-Lifshitz gravity. Phys. Rev. D 2011, 83, 084030. [Google Scholar] [CrossRef]
- Greenwald, J.; Satheeshkumar, V.H.; Wang, A. Black holes, compact objects and solar system tests in non-relativistic general covariant theory of gravity. J. Cosmol. Astropart. Phys. 2010, 2010, 007. [Google Scholar] [CrossRef]
- De Naray, R.K.; McGaugh, S.S.; de Blok, W.J.G. Mass models for low surface brightness galaxies with high resolution optical velocity fields. Astrophys. J. 2008, 676, 920. [Google Scholar] [CrossRef]
- Lokas, E.L.; Mamon, G.A. Properties of spherical galaxies and clusters with an nfw density profile. Mon. Not. R. Astron. Soc. 2001, 321, 155–166. [Google Scholar] [CrossRef]
- Navarro, J.F.; Frenk, C.S.; White, S.D.M. The structure of cold dark matter halos. Astrophys. J. 1996, 462, 563–575. [Google Scholar] [CrossRef]
- De Blok, W.J.G.; Walter, F.; Brinks, E.; Trachternach, C.; Oh, S.-H.; Kennicutt, R.C., Jr. High-resolution rotation curves and galaxy mass models from THINGS. Astron. J. 2008, 136, 2648. [Google Scholar] [CrossRef]
- Lynden-Bell, D. Statistical mechanics of violent relaxation in stellar systems. Mon. Not. R. Astron. Soc. 1967, 136, 101–121. [Google Scholar] [CrossRef]
- Dutta, S.; Saridakis, E.N. Observational constraints on Hořava-Lifshitz cosmology. J. Cosmol. Astropart. Phys. 2010, 2010, 013. [Google Scholar] [CrossRef]
© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
Share and Cite
Alexandre, J.; Kostacinska, M. Galaxy Rotation Curves in Covariant Hořava-Lifshitz Gravity. Galaxies 2014, 2, 1-12. https://doi.org/10.3390/galaxies2010001
Alexandre J, Kostacinska M. Galaxy Rotation Curves in Covariant Hořava-Lifshitz Gravity. Galaxies. 2014; 2(1):1-12. https://doi.org/10.3390/galaxies2010001
Chicago/Turabian StyleAlexandre, Jean, and Martyna Kostacinska. 2014. "Galaxy Rotation Curves in Covariant Hořava-Lifshitz Gravity" Galaxies 2, no. 1: 1-12. https://doi.org/10.3390/galaxies2010001