# Research 2014

## Nonperturbative neutron star models in f(R) theories of gravity

February 2014

Stoytcho S. Yazadjieva, Daniela D. Doneva, Kostas D. Kokkotas and Kalin V. Staykov

The f (R) theories of gravity are one of the most popular alternative explanations of dark energy. Naturally they were mainly investigated in a cosmological context. Every theory of gravity has to be able to pass various astrophysical tests as well. The neutron stars are one of the primary candidates to test the strong field regime of gravity due to the large amount of observational data. That is why studying neutron stars in f (R) theories and confronting them against the observations, is an inseparable part of the attempts to find a generalized theory of gravity that can naturally incorporate the dark energy phenomena.

Compact stars in f (R) theories were intensively studied in the past few years. Due to the complexity of the field equations though, the problem was considered primarily using a perturbative approach. Our goal was to drop this approximation and consider the full nonlinear set of equations. The results show that the perturbative approach is misleading. We have investigated the properties of the neutron star modes, their dynamics and astrophysical implications in detail, both in the static and the rotating case, and we have identified the potentially observable effects.

JCAP **1406,** 003 (2014), arXiv:1402.4469 [gr-qc]

JCAP **1410**, 006 (2014), arXiv:1407.2180 [gr-qc]

Phys. Rev. D **91**, 084018 (2015), arXiv:1501.04591 [gr-qc]

Eur. Phys. J. C **75, **607 (2015), arXiv:1508.07790 [gr-qc]

Phys. Rev. D 92, 043009 (2015) , arXiv:1503.04711 [gr-qc]

## Rapidly rotating neutron stars in alternative theories of gravity

May 2014

Daniela D. Doneva, Stoytcho S. Yazadjiev, Nikolaos Stergioulas, Kostas D. Kokkotas, Tilemachos M. Athanasiadis

Neutron stars are valuable alternatives to black holes in tests of strong-field gravity, because they can probe (and possibly rule out) those theories that are practically indistinguishable from general relativity in the weak-field regime but can lead to serious deviations when strong fields are considered. There are both theoretical and observation motivations for modifying general relativity. For example, generalized theories of gravity are very often employed as alternative explanation of the accelerated expansion of the Universe and the dark matter phenomenon. On the other hand, theoretical justifications come from theories trying to unify all fundamental forces of nature and from the quantum field theory in curved spacetime.

Rapidly rotating neutron stars were never examined until now in generalized theories of gravity. That is why we derived for the first time the relevant field equations and solved them numerically. Our results show that rapidly rotating neutron star models can differ significantly from their general relativistic counterparts, and the deviations are much larger compared to the static case. This opens a completely new window towards testing the strong field regime of gravity with rapidly rotating neutron stars.

Some astrophysical implications were considered, such as the effect of alternative theories of gravity on the quasiperiodic oscillations observed in the X-ray emission of accreting neutron stars. The results show that for rapid rotation the deviations from pure general relativity can be large thus leading to potentially observable effects.

Phys. Rev. **D 88**, 084060 (2013), arXiv:1309.0605 [gr-qc]

Phys. Rev.** D 90**, 044004 (2014), arXiv:1405.6976 [astro-ph.HE]

## I-Q relations for rapidly rotating neutron stars

January 2014

Daniela D. Doneva, Stoytcho S. Yazadjiev, Nikolaos Stergioulas, Kostas D. Kokkotas

The famous I-Love-Q relations connect the normalized neutron star moment of inertia I, quadrupole moment Q and the tidal Love number. The most important property of the I-Love-Q relations is that they are practically independent of the EOS for moderate magnetic fields. Several applications were proposed and one of the most important is braking the degeneracy between the spins and the quadrupole moment of neutron star inspirals, and testing alternative theories of gravity. A big portion of the studies are limited to the slowly rotating case. Even though this is a good approximation for a variety of objects, the extension to rapid rotation is also interesting and important.

We have shown that when considering sequences with fixed rotational frequency the equation of state universality is lost. This choice of the parameter is motivated by the observations – the rotational frequency is one of the very few parameters that can be determined with a good accuracy for a big portion of the observed neutron stars. Later studies show, though, that if one uses the normalized rotational frequency instead, the equation of state universality is preserved even for rapid rotation.

We have further explore the I-Q relations for rapidly rotating neutron stars in different alternative theories of gravity. While the results in some cases, such as scalar-tensor theories, have negligible deviations from pure general relativity, in other cases, such as the f(R) theories, the differences can be large thus providing a potential tool for constraining the strong field regime of gravity. But the overall conclusion is that in many cases the I-Love-Q relations will not be useful for testing the generalized theories of gravity due to the normalization of the quantity. If one uses the unnormalized relations, though, the deviations from pure general relativity can be clearly observed.

ApJ Letters **781**, L6 (2014), arXiv:1310.7436 [gr-qc]

Phys. Rev.** D 90**, 104021 (2014), arXiv:1408.1641 [gr-qc]

Phys. Rev. **D 92**, 064015 (2015), arXiv:1507.00378 [gr-qc]