### Conveners

#### Hořava–Lifshitz Gravity: Block 1

- Anzhong Wang (Baylor University)

#### Hořava–Lifshitz Gravity: Block 2

- Anzhong Wang (Baylor University)

### Description

This section will focus on classical and quantum aspects of Horava-Lifshitz gravity and some related gravitational theories, such as Einstein-aether theory and khronometric gravity, as well as their applications to cosmology and astrophysics.

We quantize the two-dimensional projectable Horava-Lifshitz gravity with a bi-local as well as space-like wormhole interaction. The resulting quantum Hamiltonian coincides with the one obtained through summing over all genus in the string field theory for two-dimensional causal dynamical triangulations. This implies that our wormhole interaction can be interpreted as a splitting or joining...

We investigate a autonomous system analysis in terms of new expansion-normalized variables for homogeneous and anisotropic Bianchi-I spacetimes in $f(R)$ gravity in the presence of anisotropic matter. It is demonstrated that with a suitable choice of the evolution parameter, the Einstein's equations are reduced to an autonomous 5-dimensional system of ordinary differential equations for the...

The Vector-Tensor theories are a class of alternative theories of gravity that differ from the standard General Relativity (GR) with the presence of a vector field besides the metric. They are studied in attempts to understand spontaneous Lorentz violation, to generate massive gravitons, and as models of dark matter and dark energy. In this talk, I outline how the nature of singularities and...

The nature of generic spacelike singularities in general relativity is connected with first principles, notably Lorentzian causal structure, scale invariance and general covariance. To bring a new perspective on how these principles affect generic spacelike singularities, we consider the initial singularity in spatially homogeneous Bianchi type VIII and IX vacuum models in Ho\v{r}ava-Lifshitz...

In this talk, we shall present our recent studies on a (3+1)-dimensional Ho\v{r}ava-Lifshitz gravity coupled with an anisotropic electromagnetic (EM) field. This model is generated by a Kaluza-Klein reduction of a (4+1)-dimensional Ho\v{r}ava-Lifshitz gravity and it exhibits a remarkable feature that the gravitational waves and the electromagnetic waves, in spite of Lorentz invariance...

We investigate Horava-Lifshitz Einstein- Aether gravity in light of the recent Event Horizon Telescope (EHT) observations of the M87*. The shape and size of the observed black hole shadow contains information of the geometry in its vicinity, and thus one can consider it as a potential probe to investigate different gravitational theories, since the involved calculation framework is enriched...

Relations between the neutron star moment of inertia, tidal Love number and quadrupole moment are known to be insensitive to the nuclear equation of state (the so-called I-Love-Q relations). Such universal relations are powerful for testing general relativity and beyond in the strong-field regime with neutron star observations. Horava-Lifshitz gravity is one such alternative theory of gravity...

Recently there has been a surge of interest in regularizing a $ D \to 4 $ limit of, the Einstein-Gauss-Bonnet (EGB) gravity, and the resulting regularized $4D$ EGB gravity has nontrivial dynamics. The theory admits spherically symmetric black holes generalizing the Schwarzschild black holes. Furthermore, the $4D$ non-relativistic Horava-Lifshitz theory of gravity also admits the identical...

The nonprojectable version of the Horava theory has a dynamics closer to general relativity than the projectable case, since it possesses the so-called Hamiltonian constraint. But the nonprojectable version is a field theory with second-class constraints, the Hamiltonian constraint being one of them. This feature poses challenges in understanding its quantization. The main unanswered question...

We develop the various solutions of Einstein-Aether theory of gravity through reconstruction approach. In order to discuss the current cosmic acceleration corresponding to our reconstructed models, we evaluate different cosmological parameters. Also, we also discuss the consistency of our results of cosmological parameters with current observational data for ensuring the viability of models.

Boundary conditions have physical consequences. On Lifshitz spacetimes, the Klein-Gordon equation gives rise to an initial-boundary value problem. This means that for a given suitable initial data, corresponding solutions might not exist. If they exist, then each boundary condition selects a different solution, thus yielding inequivalent dynamics. In this talk I will show that there is a...

We study non-rotating and isotropic strange quark stars in Lorentz-violating theories of gravity, and in particular in Hořava gravity and Einstein-æther theory. For quark matter we adopt both linear and non-linear equations-of-state, corresponding to the MIT bag model and color flavor locked state, respectively. The new structure equations describing hydrostatic equilibrium generalize the...

Einstein-aether theory is a vector-tensor theory with the vector (aether) field that is always timelike and unity. It is self-consistent (such as free of ghosts and instability), and satisfies all the experimental tests carried out so far. Its Cauchy problem is well posed, and energy is always positive (as far as the hypersurface-orthogonal aether field is concerned). In addition, BHs exist ...

It is expected that the quantum gravity should resolve the black-hole singularity problem, according to the finite action principle one may ask which of the microscopic actions remain finite for non-singular black holes and conversely interfere destructively for the singular ones. We also show that the finite action selection principle works for H-L gravity in the context of black holes (the...

The path integral approach yields a powerful framework in the quantum theory. It emphasizes Lorentz covariance and allows for the description of non-perturbative phenomena. In the path integral, one sums over all possible configurations of a field(s) Φ weighted by $e^{iS[Φ]}$, where S[Φ] is the classical action of the theory.

In the Minkowski path integral, the classical action approaching...