Jorge Bellorín

On the consistency of the Horava Theory

With the goal of giving evidence for the theoretical consistency of the Hořava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Hořava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant λ. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of λ deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model. There have been a lot of interest about Hořava’s proposal of a new theory of gravity which in principle has a renormalizable quantum version [1] (an important part of the conceptual and technical basis was previously developed in Ref. [2]). To build such a theory, Hořava has proposed to abandon the principle of space-time relativity as a fundamental symmetry of nature, reducing the freedom to perform coordinate transformations to those transformations that preserve some preferred universal time-like foliation. The advantage of this scheme is that one can include higher spatial-derivative terms in the Lagrangian that render the theory renormalizable. According to Hořava’s point of view, jorgebellorin@usb.ve arestu@usb.ve

Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings

We perform the characterization program for the supersymmetric configurations and solutions of the supergravity theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general non-Abelian gaugings. By using the conditions yielded by the characterization program, new exact supersymmetric solutions are found in the SO(4, 1)/SO(4) model for the hyperscalars and with SU(2) × U(1) as the gauge group. The solutions contain also non-trivial vector and massive tensor fields, the latter being charged under the U(1) sector of the gauge group and with self-dual spatial components. These solutions are black holes with AdS2 × S3 near horizon geometry in the gauged version of the theory and for the ungauged case we found naked singularities. We also analyze supersymmetric solutions with only the scalars x of the vector/tensor multiplets and the metric as the non-trivial fields. We find that only in the null class the scalars x can be non-constant and for the case of constant x we refine the classification in terms of the contributions to the scalar potential.

Consistent Hořava gravity without extra modes and equivalent to general relativity at the linearized level

We consider a Horava theory that has a consistent structure of constraints and propagates two physical degrees of freedom. The Lagrangian includes the terms of Blas, Pujolas and Sibiryakov. The theory can be obtained from the general Horavas formulation by setting lambda = 1/3. This value of lambda is protected in the quantum formulation of the theory by the presence of a constraint. The theory has two second-class constraints that are absent for other values of lambda. They remove the extra scalar mode. There is no strong-coupling problem in this theory since there is no extra mode. We perform explicit computations on a model that put together a z = 1 term and the IR effective action. We also show that the lowest-order perturbative version of the IR effective theory has a dynamics identical to the one of linearized general relativity. Therefore, this theory is smoothly recovered at the deepest IR without discontinuities in the physical degrees of freedom.

Closure of the algebra of constraints for a non-projectable Ho\v{r}ava model

We perform the Hamiltonian analysis for a nonprojectable Horava model whose potential is composed of R and R{sup 2} terms. We show that Diracs algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Horava theory, the validity of the full nonprojectable theory still remains unanswered.

ON THE CONSISTENCY OF THE HOŘAVA THEORY

With the goal of giving evidence for the theoretical consistency of the Hořava theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Hořava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant λ. Since this constant breaks the general covariance under spacetime diffeomorphisms, it is believed that arbitrary values of λ deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model.

Quantization of the Hořava theory at the kinetic-conformal point

The Horava theory depends on several coupling constants. The kinetic term of its Lagrangian depends on one dimensionless coupling constant lambda. For the particular value lambda = 1/3 the kinetic term becomes conformal invariant, although the full Lagrangian does not have this symmetry. For any value of lambda the nonprojectable version of the theory has second-class constraints which play a central role in the process of quantization. Here we study the complete nonprojectable theory, including the Blas-Pujolas-Sibiryakov interacting terms, at the kinetic-conformal point lambda = 1/3. The generic counting of degrees of freedom indicates that this theory propagates the same physical degrees of freedom of General Relativity. We analyze this point rigorously taking into account all the z=1,2,3 terms that contribute to the action describing quadratic perturbations around the Minkowski spacetime. We show that the constraints of the theory and equations determining the Lagrange multipliers are strongly elliptic partial differential equations, an essential condition for a constrained phase-space structure in field theory. We show how their solutions lead to the two independent tensorial physical modes propagated by the theory. We also obtain the reduced Hamiltonian. These arguments strengthen the consistency of the theory. We find the restrictions on the space of coupling constants to ensure the positiveness of the reduced Hamiltonian. We obtain the propagator of the physical modes, showing that there are not ghosts and that the propagator effectively acquires the z=3 scaling for all physical degrees of freedom at the high energy regime. By evaluating the superficial degree of divergence, taking into account the second-class constraints, we show that the theory is power-counting renormalizable. ...

Nonperturbative analysis of the constraints and the positivity of the energy of the complete Hořava theory

We perform a non-perturbative analysis to the Hamiltonian constraint of the lowest-order effective action of the complete Hoyrava theory, which includes a (@i lnN) 2 term in the Lagrangian. We cast this constraint as a partial differential equation for N and show that the solution exists and is unique under a condition of positivity for the metric and its conjugate momentum. We interpret this condition as the analog of the positivity of the spatial scalar curvature in general relativity. From the analysis we extract several general properties of the solution for N: an upper bound on its absolute value and its asymptotic behavior. In particular, we find that the asymptotic behavior is different to that of general relativity, which has consequences on the evolution of the initial data and the calculus of variations. Similarly, we proof the existence and uniqueness of the solution of the equation for the Lagrange multiplier of the theory. We also find a relationship between the expression of the energy and the solution of the Hamiltonian constraint. Using it we prove the positivity of the energy of the effective action under consideration. Minkowski spacetime is obtained from Hoyrava theory at minimal energy.

Solutions with throats in Hořava gravity with cosmological constant

By combining analytical and numerical methods we find that the solutions of the complete Horava theory with negative cosmological constant that satisfy the conditions of staticity, spherical symmetry and vanishing of the shift function are two kinds of geometry: (i) a wormhole-like solution with two sides joined by a throat and (ii) a single side with a naked singularity at the origin. We study the second-order effective action. We consider the case when the coupling constant of the (partial ln N)^2 term, which is the unique deviation from general relativity in the effective action, is small. At one side the wormhole acquires a kind of deformed AdS asymptotia and at the other side there is an asymptotic essential singularity. The deformation of AdS essentially means that the lapse function N diverges asymptotically a bit faster than AdS. This can also be interpreted as an anisotropic Lifshitz scaling that the solutions acquire asymptotically.

Wormholes and naked singularities in the complete Hořava theory

We find the static spherically symmetric solutions (with vanishing shift function) of the complete nonprojectable Horava theory explicitly, writing the space-time metrics as explicit tensors in local coordinate systems. This completes previous works of other authors that have studied the same configurations. The solutions depend on the coupling constant alpha of the (partial_i ln N)^2 term. The lambda = 1/3 case of the theory does not possess any extra mode, hence the range of alpha is in principle not limited by the linear stability of any extra mode. We study the full range of alpha, both in the positive and negative sectors. We find the same wormhole solutions and naked singularities that were found for the Einstein-aether theory in a sector of the space of alpha. There also arise wormholes in other sector of alpha. Our coordinate systems are valid at the throats of the wormholes. We also find the perturbative solutions for small alpha. We give this version of the solutions directly on the original radial coordinate r, which is particularly suitable for representing the exterior region of solutions with localized sources.

Einstein’s quadrupole formula from the kinetic-conformal Hořava theory

We analyze the radiative and nonradiative linearized variables in a gravity theory within the family of the nonprojectable Hořava theories, the Hořava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory, we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein’s quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.