We consider astrophysical objects such as main-sequence stars, white-dwarfs and neutron stars in a noncommutative context. Noncommutativity is implemented via a deformed dispersion relation E 2 = p 2 c 2 (1 + λE) 2 + m 2 c 4 from which we obtain noncommutative corrections to the pressure, particle number and energy densities for radiation and for a degenerate fermion gas. The main implications of noncommutativity for the considered astrophysical objects are examined and discussed.

In this work, a minisuperspace model for the projectable Hořava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some particular cases where, due to HL gravity, there is a "potential barrier" nearby a = 0. For a vanishing cosmological constant, it is found a normalizable wave function of the universe. When the cosmological constant is non-vanishing, the WKB method is used to obtain solutions for the wave function of the universe. Using the Hamilton-Jacobi equation, one discusses how the transition from quantum to classical regime occurs and, for the case of a positive cosmological constant, the scale factor is shown to grow exponentially, hence recovering the GR behaviour for the late universe.Hořava-Lifshitz (HL) gravity is a quite original proposal for a ultraviolet (UV) completion of General Relativity (GR) [1], in which gravity turns out to be power-countable renormalizable at the UV fixed point. GR is supposed to be recovered at the infra-red (IR) fixed point, as the theory goes from high-energy scales to low-energy scales. In order to obtain a renormalizable gravity theory one abandons Lorentz symmetry at high-energies [1,2]. Even though the idea that the Lorentz symmetry is a low-energy symmetry has been previously considered [3], the novelty of the HL proposal is that the breaking of Lorentz symmetry occurs the very way as in some condensed matter models (cf. Ref.[1] and references therein), that is through an anisotropic scaling between space and time, namely r → b r and t → b z t, b being a scale parameter. The dynamical critical exponent z is chosen in order to ensure that the gravitational coupling constant is dimensionless, which makes possible a renormalizable interaction. As the Lorentz symmetry is recovered at the IR fixed point, z flows to z = 1 in this limit.The anisotropy between space and time leads rather naturally to the well known 3 + 1 Arnowitt-Deser-Misner (ADM) splitting [4], originally devised to express GR in a Hamiltonian formulation. Following Ref.[1], a foliation, parametrized by a global time t, is introduced. Since the global diffeomorphism is not valid anymore, one imposes a weaker form of this symmetry, the so-called foliation-preserving diffeomorphism. Choosing this approach, the lapse ADM function, N, is constrained to be function only of the time coordinate, i.e. N = N(t). This assumption satisfies the projectability condition [1]. In order to match GR, one could also choose N = N( r, t), a model dubbed non-projectable and which has been investigated in Refs. [5,6]. The next step involves getting a gravitational Lagrangian into this anisotropic scenario. For this purpose, the effective field theory (EFT) formalism is used: every term that is marginal or relevant at the UV fixed point (z = 1) is included and, at the IR fixed point, only z = 1 terms survives. GR is then presumably recovered. The number of terms that must be included splits HL gravity into two clas...

We investigate the conditions for which a d-dimensional perfect fluid solution is in hydrostatic equilibrium with a cosmological constant. We find a generalization of Buchdahl inequality and obtain an upper bound for the degree of compactification. Using the Tolman-Oppenheimer-Volkoff equation to get a lower bound for the degree of compactification we analyse the regions where the solution is in hydrostatic equilibrium. We obtain the inner metric solution and the pressure for the constant fluid density model.

We consider a harmonic oscillator (HO) with a time-dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency ω 0 , then, at t = 0, its frequency suddenly increases to ω 1 and, after a finite time interval τ , it comes back to its original value ω 0. Contrary to what one could naively think, this problem is quite a non-trivial one. Using algebraic methods, we obtain its exact analytical solution and show that at any time t > 0 the HO is in a vacuum squeezed state. We compute explicitly the corresponding squeezing parameter (SP) relative to the initial state at an arbitrary instant and show that, surprisingly, it exhibits oscillations after the first frequency jump (from ω 0 to ω 1), remaining constant after the second jump (from ω 1 back to ω 0). We also compute the time evolution of the variance of a quadrature. Last, but not least, we calculate the vacuum (fundamental state) persistence probability amplitude of the HO, as well as its transition probability amplitude for any excited state.

We show how to obtain a vanishing DC conductivity in 3-dimensional strongly coupled QFT's using a massive 2-form field in the bulk that satisfies a special kind of boundary condition. The real and imaginary parts of the AC conductivity are evaluated in this holographic setup and we show that the DC conductivity identically vanishes even for an arbitrarily small (though nonzero) value of the 2-form mass in the bulk. We identify the bulk action of the massive 2-form with an effective theory describing a phase in which magnetic monopoles have condensed in the bulk. Our results indicate that a condensate of magnetic monopoles in a 4-dimensional bulk leads to a vanishing DC holographic conductivity in 3-dimensional strongly coupled QFT's.