Radial stability in stratified stars

We formulate within a generalized distributional approach the treatment of the stability against radial perturbations for both neutral and charged stratified stars in Newtonian and Einstein's gravity. We obtain from this approach the boundary conditions connecting two any phases within a star and underline its relevance for realistic models of compact stars with phase transitions, owing to the modification of the star's set of eigenmodes with respect to the continuous case.Comment: 11 pages, no figures. Accepted for publication in Astrophys.

Energy decomposition within Einstein-Born-Infeld black holes

We analyze the consequences of the recently found generalization of the Christodoulou-Ruffini black hole mass decomposition for Einstein-Born-Infeld black holes [characterized by the parameters $(Q,M,b)$, where $M = M(M_{irr},Q,b)$, $b$ scale field, $Q$ charge, $M_{irr}$ "irreducible mass", physically meaning the energy of a black hole when its charge is null] and their interactions. We show in this context that their description is largely simplified and can basically be split into two families depending upon the parameter $b|Q|$. If $b|Q|\leq 1/2$, then black holes could have even zero irreducible masses and they always exhibit single, non degenerated, horizons. If $b|Q|>1/2$, then an associated black hole must have a minimum irreducible mass (related to its minimum energy) and has two horizons up to a transitional irreducible mass. For larger irreducible masses, single horizon structures raise again. By assuming that black holes emit thermal uncharged scalar particles, we further show in light of the black hole mass decomposition that one satisfying $b|Q|>1/2$ takes an infinite amount of time to reach the zero temperature, settling down exactly at its minimum energy. Finally, we argue that depending on the fundamental parameter $b$, the radiation (electromagnetic and gravitational) coming from Einstein-Born-Infeld black holes could differ significantly from Einstein-Maxwell ones. Hence, it could be used to assess such a parameter.Comment: 9 pages, 5 figures, accepted for publication in Phys. Rev.

Trirefringence in nonlinear metamaterials

We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.Comment: 6 pages, 2 figures, published versio

A local Lagrangian for MOND as modified inertia

We propose a local Lagrangian for a point particle where its inertia part is modified in the regime of small accelerations. For the standard gravitational central force, it recovers the deep MOdified Newtonian Dynamics (MOND) (accelerations $\ll a_0\approx 10^{-10}$m/s$^{2}$) equations of motion in the case of a circular orbit. Perturbations to that turn on higher derivative terms, leading to exponentially unstable solutions that must vanish in order to account for the very small scattering of the Tully-Fisher relation. Unstable solutions linearly growing with time remain valid for a characteristic timescale of at least 3 billion years. We show that vertical perturbations recover similar results to dark matter for old galaxies, but deviations could be present for young ones. We also present ways to probe our approach and describe some of its subtleties, such as the strong equivalence principle (violated in general), the center of mass motion of a composite body, and how in some cases it could overcome Ostrogradsky's instabilities (with naturally occurring piecewise Lagrangians). Our main conclusions regarding our MOND-like proposal are: (i) it constitutes a possible recipe where Ostrogradsky instabilities could be "tamed"; (ii) it is a falsifiable approach in various contexts and (iii) it might explain simultaneously some of the issues usual modified gravity MOND and dark matter phenomenologies have difficulties individually. These aspects seem relevant to start addressing practical ways to differentiate modified gravity MOND from modified inertia and give insights into alternative ways to tackle some astrophysical and cosmological puzzles.Comment: 19 pages, no figures New discussions (vertical perturbations and center of mass) and references adde

Phase transition effects on the dynamical stability of hybrid neutron stars

We study radial oscillations of hybrid non-rotating neutron stars composed by a quark matter core and hadronic external layers. At first, we physically deduce the junction conditions that should be imposed between two any phases in these systems when perturbations take place. Then we compute the oscillation spectrum focusing on the effects of slow and rapid phase transitions at the quark-hadron interface. We use a generic MIT bag model for quark matter and a relativistic mean field theory for hadronic matter. In the case of rapid transitions at the interface we find a general relativistic version of the reaction mode which has similar properties as its classical counterpart. We also show that the usual static stability condition $\partial M/\partial \rho_c\geq 0$, where $\rho_c$ is the central density of a star whose total mass is $M$, remains always true for rapid transitions but breaks down in general for slow transitions. In fact, for slow transitions we find that the frequency of the fundamental mode can be a real number (indicating stability) even for some branches of stellar models that verify $\partial M/\partial \rho_c \leq 0$. Thus, when secular instabilities are suppressed, as expected below some critical stellar rotation rate, it would be possible the existence of twin or even triplet stars with the same gravitational mass but different radii, with one of the counterparts having $\partial M/\partial \rho_c \leq 0$. We explore some astrophysical consequences of these results.Comment: 14 pages, 15 figures. Minor changes. Version accepted for publication in Ap

Satellite Test of the Equivalence Principle as a Probe of Modified Newtonian Dynamics

The proposed Satellite Test of the Equivalence Principle (STEP) will detect possible violations of the Weak Equivalence Principle by measuring relative accelerations between test masses of different composition with a precision of one part in $10^{18}$. A serendipitous byproduct of the experimental design is that the absolute (common-mode) acceleration of the test masses is also measured to high precision as they oscillate along a common axis under the influence of restoring forces produced by the position sensor currents, which in drag-free mode lead to Newtonian accelerations as small as $10^{-14}$ g. This is deep inside the low-acceleration regime where Modified Newtonian Dynamics (MOND) diverges strongly from the Newtonian limit of General Relativity. We show that MOND theories (including those based on the widely-used $n$-family of interpolating functions as well as the covariant Tensor-Vector-Scalar formulation) predict an easily detectable increase in the frequency of oscillations of the STEP test masses if the Strong Equivalence Principle holds. If it does not hold, MOND predicts a cumulative increase in oscillation amplitude which is also detectable. STEP thus provides a new and potentially decisive test of Newton's law of inertia, as well as the equivalence principle in both its strong and weak forms.Comment: 5 pages, 3 figures; in press at Physical Review Letter

Stability of thin-shell interfaces inside compact stars

We use the thin-shell Darmois-Israel formalism to model and assess the stability of the interfaces separating phases, e.g. the core and the crust, within compact stars. We exemplify the relevance and non-triviality of this treatment in the simplest case of an incompressible star, in constant pressure phase transitions, and in the case of strange quark stars with crust.Comment: matches version published in Physical Review

The flexibility of optical metrics

We firstly revisit the importance, naturalness and limitations of the so-called optical metrics for describing the propagation of light rays in the limit of geometric optics. We then exemplify their flexibility and nontriviality in some nonlinear material media and in the context of nonlinear theories of the electromagnetism, both underlain by curved backgrounds, where optical metrics could be flat and impermeable membranes only to photons could be conceived, respectively. Finally, we underline and discuss the relevance and potential applications of our analyses in a broad sense, ranging from material media to compact astrophysical systems.Comment: 8 pages, some improvements in the physical content. Accepted for publication in Classical and Quantum Gravit

The influence of quantum vacuum friction on pulsars

We firstly revisit the energy loss mechanism known as quantum vacuum friction (QVF), clarifying some of its subtleties. Then we investigate the observables that could easily differentiate QVF from the classical magnetic dipole radiation for pulsars with braking indices (n) measured accurately. We show this is specially the case for the time evolution of a pulsar's magnetic dipole direction ($\dot{\phi}$) and surface magnetic field ($\dot{B}_0$). As it is well known in the context of the classic magnetic dipole radiation, $n<3$ would only be possible for positive $(\dot{B}_0/B_0 + \dot{\phi}/\tan\phi)$, which, for instance, leads to $\dot{B}_0>0$ ($\dot{\phi}>0$) when $\phi$ ($B_0$) is constant. On the other hand, we show that QVF can result in very contrasting predictions with respect to the above ones. Finally, even in the case $\dot{B}_0$ in both aforesaid models for a pulsar has the same sign, for a given $\phi$, we show that they give rise to different associated timescales, which could be another way to falsify QVF.Comment: 7 pages, 3 figures. Accepted for publication in Ap

Born-Infeld magnetars: larger production of gravitational waves due to larger toroidal magnetic fields

We discuss some aspects of Pereira et al. (2018) concerning magnetars described by nonlinear theories of the electromagnetism and make the case for the Born-Infeld Lagrangian. We focus on the increase of toroidal magnetic fields in these systems with respect to ordinary magnetars and the subsequent increase of gravitational wave production. In summary, nonlinear theories of the electromagnetism would make it more likely for the detection of gravitational waves with future detectors, which could constrain nonlinear aspects of electrodynamics not entirely possible on Earth-based particle accelerators.Comment: Contribution to the Proceedings of the VIII International Workshop on Astronomy and Relativistic Astrophysics - IWARA 201