We consider the mass-radius bounds for spherically symmetric static compact objects in the de Rham-Gabadadze-Tolley (dRGT) Massive Gravity theories, free of ghosts. In this type of gravitational theories the graviton, the quantum of gravity, may have a small, but non-vanishing mass. We derive the hydrostatic equilibrium and mass continuity equations in the Lorentz-violating Massive gravity in the presence of a cosmological constant and for a non-zero graviton mass. The case of the constant density stars is also investigated by numerically solving the equilibrium equations. The influence of the graviton mass on the global parameters (mass and radius) of these stellar configurations is also considered. The generalized Buchdahl relations, giving the upper and lower bounds of the mass-radius ratio are obtained, and discussed in detail. As an application of our results we obtain gravitational redshift bounds for compact stellar type objects in the Lorentz-violating dRGT Massive Gravity, which may (at least in principle) be used for observationally testing this theory in an astrophysical context.
We revisit the problem of gravity coupled to a background metric $η_{μν}$, looking for ghost free interactions. It is known that elimination of the Boulware-Desewr ghost is equivalent to a certain Hessian condition on the interacting potential. We elaborate on this equation and provide a proof that dRGT potential is the unique interaction between the spacetime metric and a background field $η_{μν}$ which is both Lorentz invariant and ghost free. Our approach is fully non-perturbative using only the ADM formulation of general relativity.
In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory. We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the Einstein-Hilbert action plus the dRGT potential terms. In this vacuum, there are five (three from Goldstone modes) propagating degrees of freedom which form polarizations of a massive spin 2 particle, an extra healthy heavy scalar (Higgs) mode and no Boulware-Deser ghost mode. We further show that the action can be derived in a limit from a topological de Sitter inva…
The dynamics of binary pulsars can be used to test different aspects of gravitation. This is particularly important to constrain alternatives to general relativity in regimes which are not probed by other methods. In this short contribution, I will describe the case of theories of gravity without Lorentz invariance. The latter are important in the context of quantum gravity and modify the laws of gravity at basically all scales.
I discuss progress towards "bootstrapping" a Lorentz-violating gravity theory: namely, extending a linear Lorentz-violating theory of a rank-2 tensor to a non-linear theory by coupling this field to its own stress-energy tensor.
If the kinetic interactions of a Lorentz-invariant massive graviton are Einstein-Hilbert, then the only possible potential terms free from the Boulware-Deser ghost are those of de Rham, Gabadadze and Tolley (dRGT). We point out there are other possibilities if the kinetic terms are not required to be Einstein-Hilbert. We construct pseudo-linear ghost-free potentials, terms that derive in a natural way from the linear theory. The simplicity of this approach allows us to construct diffeomorphism non-invariant higher-derivative interaction terms that do not introduce ghosts. We conjecture that th…
Lorentz-Violating (Regular) Black Holes in Einstein Gravity
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）
The fundamental issues of microcausality and energy positivity conditions are important to be investigated in the context of spontaneous Lorentz violating theories. We check the microcausality and energy positivity conditions for a free rank-2 antisymmetric tensor field with spontaneous Lorentz violating term and a classically equivalent vector theory from dispersion relations and propagators, and find that the two theories lead to different conditions. While the antisymmetric tensor theory satisfies energy positivity condition and can satisfy microcausality condition for a particular choice o…
In this paper, we obtain dispersion relations corresponding to plane wave solutions in various Lorentz-breaking extensions of gravity with dimensions 3, 4, 5 and 6. We demonstrate that these dispersion relations display an usual Lorentz-invariant mode when the corresponding additive term involves higher derivatives.
Black holes in Lorentz violating gravity, such as Einstein--Aether or Horava--Lifshitz Gravity, are drastically different from their general relativistic siblings. Although they allow for superluminal motion in their vicinity, they still exhibit an absolute causal boundary in the form of a universal horizon. By working in the tunneling picture for a gravitating scalar field, we show that universal horizons emit Hawking radiation in a manner akin to standard results in General Relativity, with a temperature controlled by the high-energy behavior of the dispersion relation of the gravitating fie…
We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension. We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) model and the Standard-Model Extension. As part of the analysis,we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.
Lorentz symmetry is an important concept in modern physics. Precision pulsar timing was used to put tight constraints on the coefficients for Lorentz violation in the pure-gravity sector of the Standard-Model Extension (SME). We extend the analysis to Lorentz-violating matter-gravity couplings, utilizing three small-eccentricity relativistic neutron star (NS) -- white dwarf (WD) binaries. We obtain compelling limits on various SME coefficients related to the neutron, the proton, and the electron. These results are complementary to limits obtained from lunar laser ranging and clock experiments.
Lorentz-violating theories of gravity typically contain constrained vector fields. We show that the lowest-order coupling of such vectors to $\mathrm{U}(1)$-symmetric scalars can naturally give rise to baryogenesis in a manner akin to the Affleck-Dine mechanism. We calculate the cosmology of this new mechanism, demonstrating that a net $B-L$ can be generated in the early Universe, and that the resulting baryon-to-photon ratio matches that which is presently observed. We discuss constraints on the model using solar system and astrophysical tests of Lorentz violation in the gravity sector. Gener…
The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativistic point-particle lagrangians are derived that reproduce the momentum-velocity and dispersion relations of quantum wave packets. The correspondence to Finsler structures is established, and some properties of the resulting Riemann-Finsler spaces are investigated. The results prov…
