Spontaneous Lorentz Violation Research Articles

Novel features of Schwarzschild-like black hole of Lorentz violating bumblebee gravity

A possible avenue for observing quantum gravity (QG) effects at low energy scales is to introduce spontaneous Lorentz violation (LV) in new models of gravity theories. One such model in the literature is bumblebee gravity yielding Schwarzschild-like black hole and weak field Solar System observations involve LV corrections characterized by the parameter ℓ. Here we first show that these LV corrections have a novel genesis in the conical angle Δ = πb subtended at the origin of the spacetime of massless bumblebee gravity. Exploiting the resultant asymptotic light deflection angle πb −1 as a new input in the exact deflection formula, we next study the strong field lensing properties of the Schwarzschild-like black hole exploring how they differ from those of the Schwarzschild black hole of general relativity. It is shown that the angular image separation and ratio of fluxes could respectively be s ∼ e πℓ and r ∼ e−πℓ times those of the Schwarzschild black hole (ℓ = 0). However, the shadow of the Schwarzschild-like black hole is independent of ℓ suggesting that observations of shadow radii cannot reveal QG effects. Finally, we raise an interesting issue about the measurability of the LV corrections caused by strong field lensing. An appendix briefly outlines lensing by the spinning bumblebee black hole.

Kerr–Sen-like Lorentz violating black holes and superradiance phenomena

A Kerr–Sen-like black hole solution results from Einstein-bumblebee gravity. It contains a Lorentz violating (LV) parameter that enters when the bumblebee field receives vacuum expectation value through a spontaneously breaking of the symmetry of the classical action. The geometrical structure concerning the singularity of this spacetime is studied with reference to the parameters involved in the Kerr–Sen-like metric. We introduce this Einstein-bumblebee modified gravity to probe the role of spontaneous Lorentz violation on the superradiance scattering phenomena and the instability associated with it. We observe that for the low-frequency range of the scalar wave the superradiance scattering gets enhanced when the Lorentz-violating parameter ell takes the negative values and it reduces when values of ell are positive. The study of the black hole bomb issue reveals that for the negative values of ell , the parameter space of the scalar field instability increase prominently, however, for its positive values, it shows a considerable reduction. We also tried to put constraints on the parameters contained in the Kerr–Sen-like black hole by comparing the deformation of the shadow produced by the black hole parameters with the observed deviation from circularity and the angular deviation from the M87* data.

Spontaneous Lorentz Violation from Infrared Gravity

In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between this modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended uncertainty relations is validated by comparing the predictions concerning a deformed Hawking temperature derived from the two models. Moreover, starting from the experimental bounds on the gravity sector of the SME, we derive the most stringent constraint achieved so far on the value of the free parameter in the extended Heisenberg uncertainty principle.

Spontaneous Lorentz violation and asymptotic flatness

The Standard Model Extension (SME) is a generic parametrization for Lorentz violation and the phenomenological consequences of the minimal gravity sector of the SME are usually studied using a post-Newtonian expansion that requires spacetime to be asymptotically flat. However, there is a term in this sector for which these approximations are unable to make predictions; this is known as the $t$ puzzle. The present paper studies a model of spontaneous Lorentz violation in the minimal gravity sector of the SME in a static and spherically symmetric situation, when no additional matter fields are present. It is shown that, under the above mentioned assumptions, $t$ is the only term in the minimal gravity sector for which no asymptotically flat solutions exist. This stems from the fact that the $t$ term fixes the asymptotic behavior of all the pieces of the curvature tensor.

Extra equation of gravity induced by spontaneous local Lorentz symmetry breakdown

A model of spontaneous Lorentz violation in four dimension is given, which seems to provide a Lorentz invariant effective theory. An SU(2) Yang-Mills gauge field and an auxiliary U(1) vector field generate gravity and other interactions when they have vacuum expectation values. The emergent gravity is equivalent to conventional general relativity up to the third order terms in the Lagrangian. The coupling to matter, including spin-1/2 fermions, is also given correctly to this level. It remains to be seen whether this formalism reproduces the properties of black holes and other consequences obtained from Einstein's theory.

On the quantum equivalence of an antisymmetric tensor field with spontaneous Lorentz violation

We present an explicit proof that a minimal model of rank-2 antisymmetric field with spontaneous Lorentz violation and a classically equivalent vector field model are also quantum equivalent by calculating quantum effective actions of both theories. We comment on the issues encountered while checking quantum equivalence in curved spacetime.

Quantum aspects of antisymmetric tensor field with spontaneous Lorentz violation

We study the quantization of a simple model of antisymmetric tensor field with spontaneous Lorentz violation in curved spacetime. We evaluate the 1-loop corrections at first order of metric perturbation, using a general covariant effective action approach. We revisit the issue of quantum equivalence, and find that it holds for non-Lorentz-violating modes but breaks down for Lorentz violating modes.

Antisymmetric tensor propagator with spontaneous Lorentz violation

In this work, we study the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime. For a smooth quadratic potential, the spectrum of the theory exhibits massless and massive excitations. We show that the equations of motion for the free field obey some constraints which lead to the massive mode being nonpropagating at leading order. Besides, there exists a massless mode in the theory which can be identified with the usual Kalb-Ramond field, carrying only one on-shell degree of freedom. The same conclusion holds when one analyses the pole structure of its Feynman propagator. A new complete set of spin-type operators is found, which was the requirement to evaluate the propagator of the Kalb-Ramond field modified by the presence of a nonzero vacuum expectation value responsible for the Lorentz violation.

Is There Any Symmetry Left in Gravity Theories with Explicit Lorentz Violation?

It is well known that a theory with explicit Lorentz violation is not invariant under diffeomorphisms. On the other hand, for geometrical theories of gravity, there are alternative transformations, which can be best defined within the first-order formalism and that can be regarded as a set of improved diffeomorphisms. These symmetries are known as local translations, and among other features, they are Lorentz covariant off shell. It is thus interesting to study if theories with explicit Lorentz violation are invariant under local translations. In this work, an example of such a theory, known as the minimal gravity sector of the Standard Model Extension, is analyzed. Using a robust algorithm, it is shown that local translations are not a symmetry of the theory. It remains to be seen if local translations are spontaneously broken under spontaneous Lorentz violation, which are regarded as a more natural alternative when spacetime is dynamic.

Fermionic Lorentz violation and its implications for interferometric gravitational-wave detection

The recent direct detection of gravitational waves reported by Advanced LIGO has inspired the current article. In this context, a particular Lorentz-violating framework for classical, massive particles is the focus. The latter is characterized by a preferred direction in spacetime comprised of CPT-odd components with mass dimension 1. Curvature effects in spacetime, which are caused by a propagating gravitational wave, are assumed to deform the otherwise constant background field. In accordance with spontaneous Lorentz violation, a particular choice for the vector field is taken, which was proposed elsewhere. The geodesic equations for a particle that is subject to this type of Lorentz violation are obtained. Subsequently, their numerical solutions are computed and discussed. The particular model considered leads to changes in the particle trajectory whose impact on interferometric gravitational-wave experiments such as LIGO will be studied.

Dynamical ambiguities in models with spontaneous Lorentz violation

Spontaneous Lorentz violation is a viable mechanism to look for Planck scale physics. In this work, we study spontaneous Lorentz violation models, in flat spacetime, where a vector field produces such a violation and matter is modeled by a complex scalar field. We show that it is possible to construct a Hamilton density for which the evolution respects the dynamical constraints. However, we also find that the initial data, as required by standard field theory, does not determine the fields evolution in a unique way. In addition, we present some examples where the physical effects of such ambiguities can be recognized. As a consequence, the proposals in which the electromagnetic and gravitational interactions emerge from spontaneous Lorentz violation are challenged.

Spacetime symmetry breaking and Einstein-Maxwell theory

A vector model with a hybrid form of spacetime symmetry breaking consisting of explicit diffeomorphism breaking but spontaneous local Lorentz violation is presented. The combined effects of these symmetry breakings give rise to a theory obeying the Einstein-Maxwell equations in a preferred spatially homogeneous and isotropic frame, with photons emerging as massless Nambu-Goldstone modes. Interpretations and possible generalizations of this model are discussed, and comparisons are made to previous models describing photons as Nambu-Goldstone modes.

Spontaneous Lorentz violation: the case of infrared QED

It is by now clear that infrared sector of QED has an intriguingly complex structure. Based on earlier pioneering works on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the $U(1)$ charge group of QED to the "Sky" group incorporating the known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality. There it was shown that the "Sky" group is generated by the algebra of angle dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous breaking of Lorentz symmetry. We further elaborate this approach here and investigate in some detail the properties of charged particles dressed by the infrared photons. We find that Lorentz violation due to soft photons may be manifestly codified in an angle dependent fermion mass modifying therefore the fermion dispersion relations. The fact that the masses of the charged particles are not Lorentz invariant affects their spin content too.Time dilation formulae for decays should also get corrections. We speculate that these effects could be measured possibly in muon decay experiments.

Spontaneous Lorentz violation in gauge theories

Frohlich, Morchio and Strocchi long ago proved that the Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where the consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected “Sky” group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These Abelian considerations and model are extended to non-Abelian gauge symmetries. Basic issues regarding the observability of twisted non-Abelian gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are raised.

Matter-gravity scattering in the presence of spontaneous Lorentz violation

Considering quantum gravity within the framework of effective field theory, we investigated the consequences of spontaneous Lorentz violation for the gravitational potential. In particular, we focus our attention on the bumblebee models, in which the graviton couples to a vector $B_{\mu}$ that assumes a nonzero vacuum expectation value. The leading order corrections for the nonrelativistic potential are obtained from calculation of the scattering matrix of two scalar particles interacting gravitationally. These corrections imply anisotropic properties associated with the bumblebee background and also add a Darwin-like term for Newton's potential.

The price of neutrino superluminality continues to rise

We revisit the model building challenges that one faces when trying to reconcile the OPERA claim of neutrino superluminality with other observational constraints. The severity of the supernova bound and of the kinematical constraints of Cohen–Glashow type lead us to focus on scenarios where all types of particles are superluminal inside matter. In contrast to the Dvali–Vikman proposal, this matter effect needs to be very short-ranged to avoid constraints from experiments on the Earthʼs surface in low-density environments. Due to this short range, the interaction underlying such a matter effect would have to be far stronger than permitted by fifth-force bounds. As a conceivable way out we suggest to make the matter effect “binary”, i.e., dense matter does not directly trigger superluminality, but merely induces the transition to a different phase of some weakly coupled hidden sector. This phase exhibits spontaneous Lorentz violation or at least a stronger than usual mediation of some residual Lorentz violation to all matter. The effect has not been observed before since we have never before been able to measure the velocity of high-energy particles in dense matter with sufficient precision.

Graviton as a Goldstone boson: Nonlinear sigma model for tensor field gravity

Spontaneous Lorentz invariance violation (SLIV) realized through a nonlinear tensor field constraint Hμν2=±M2 (M is the proposed scale for Lorentz violation) is considered in tensor field gravity theory, which mimics linearized general relativity in Minkowski space–time. We show that such a SLIV pattern, due to which the true vacuum in the theory is chosen, induces massless tensor Goldstone modes some of which can naturally be associated with the physical graviton. When expressed in terms of the pure Goldstone modes, this theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. Nonetheless, all SLIV effects turn out to be strictly canceled in all the lowest order processes considered, provided that the tensor field gravity theory is properly extended to general relativity (GR). So, as we generally argue, the measurable effects of SLIV, induced by elementary vector or tensor fields, are related to the accompanying gauge symmetry breaking rather than to spontaneous Lorentz violation. The latter appears by itself to be physically unobservable, only resulting in a non-covariant gauge choice in an otherwise gauge invariant and Lorentz invariant theory. However, while Goldstonic vector and tensor field theories with exact local invariance are physically indistinguishable from conventional gauge theories, there might appear some principal distinctions if this local symmetry were slightly broken at very small distances in a way that could eventually allow one to differentiate between them observationally.

Lorentz violation with an antisymmetric tensor

Field theories with spontaneous Lorentz violation involving an antisymmetric 2-tensor are studied. A general action including nonminimal gravitational couplings is constructed, and features of the Nambu-Goldstone and massive modes are discussed. Minimal models in Minkowski spacetime exhibit dualities with Lorentz-violating vector and scalar theories. The post-newtonian expansion for nonminimal models in Riemann spacetime involves qualitatively new features, including the absence of an isotropic limit. Certain interactions producing stable Lorentz-violating theories in Minkowski spacetime solve the renormalization-group equations in the tadpole approximation.

Vector-field domain walls

We argue that spontaneous Lorentz violation may generally lead to metastable domain walls related to the simultaneous violation of some accompanying discrete symmetries. Remarkably, such domain-wall solutions exist for spacelike Lorentz violation and do not exist for the timelike violation. Because a preferred space direction is spontaneously induced, these domain walls have no planar symmetry and produce a peculiar static gravitational field at small distances, while their long-distance gravity appears the same as for regular scalar-field walls. Some possible applications of vector-field domain walls are briefly discussed.

Spontaneous Lorentz violation, negative energy, and the second law of thermodynamics

We reconsider the possibility of violating the generalized second law of thermodynamics in theories with spontaneous Lorentz violation. It has been proposed that this may be accomplished in particular with a black hole immersed in a ghost condensate background, which may be taken to break Lorentz invariance without appreciably distorting the space-time geometry. In this paper we show that there in fact exist solutions explicitly describing the flow of negative energy into these black holes, allowing for violation of the second law in a very simple way. This second law violation is independent of any additional assumptions such as couplings of the ghost condensate to secondary fields, and suggests that violation of the null energy condition may be the true source of pathology in these theories.