Mariafelicia De Laurentis

This book offers an excellent introduction to General Relativity and Cosmology. It is designed to serve as a self-contained text for graduate and advanced undergraduate students and also to provide a basic text for PhD courses. Each of the four parts of the book, two basic and two advanced, can be used as an independent module. In the first part, the main concepts of General Relativity are presented, while the second offers an introduction to the astrophysical applications. The third part is advanced, and discusses the extensions of General Relativity; the contents represent ideal material for a short course at PhD level. The final part of the book provides an introduction to Relativistic Cosmology and its applications. Throughout the text, all mathematical calculations are explained clearly, in step by step detail. Whenever appropriate, the reader is guided to further specialized sources of information.
http://www.springer.com/de/book/9783319327464

Radio-astronomical observations of the supermassive black-hole candidate in the galactic center will soon offer the possibility to study gravity in its strongest regimes and to test different models for these compact objects. Studies based on semi-analytic models and strong-field images of stationary plasma configurations around boson stars have stressed the difficulty to distinguish them from black holes. We here report on the first general-relativistic magnetohydrodynamic simulations of accretion onto a nonrotating boson star and employ general-relativistic radiative-transfer calculations to revisit the appearance of an accreting boson star. We find that the absence of an event horizon in a boson star leads to important differences in the dynamics of the accretion and results in both the formation of a small torus in the interior of the boson star and in the absence of an evacuated high-magnetization funnel in the polar regions. Synthetic reconstructed images considering realistic astronomical observing conditions show that differences in the appearance of the two compact object are large enough to be detectable. These results, which also apply to other horizonless compact objects, strengthen confidence in the ability to determine the presence of an event horizon via radio observations and highlight the importance of self-consistent multidimensional simulations to study the compact object at the galactic center.

Our Galactic Center, Sagittarius A* (Sgr A*), is believed to harbour a supermassive black hole (BH), as suggested by observations tracking individual orbiting stars. Upcoming sub-millimetre very-long-baseline-interferometry (VLBI) images of Sgr A* carried out by the Event-Horizon-Telescope Collaboration (EHTC) are expected to provide critical evidence for the existence of this supermassive BH. We assess our present ability to use EHTC images to determine if they correspond to a Kerr BH as predicted by Einstein's theory of general relativity (GR) or to a BH in alternative theories of gravity. To this end, we perform general-relativistic magnetohydrodynamical (GRMHD) simulations and use general-relativistic radiative transfer (GRRT) calculations to generate synthetic shadow images of a magnetised accretion flow onto a Kerr BH. In addition, and for the first time, we perform GRMHD simulations and GRRT calculations for a dilaton BH, which we take as a representative solution of an alternative theory of gravity. Adopting the VLBI configuration from the 2017 EHTC campaign, we find that it could be extremely difficult to distinguish between BHs from different theories of gravity, thus highlighting that great caution is needed when interpreting BH images as tests of GR.

The Noether Symmetry Approach can be used to construct spherically symmetric solutions in f(R) gravity. Specifically, the Noether conserved quantity is related to the gravitational mass and a gravitational radius that reduces to the Schwarzschild radius in the limit f(R)→R.. We show that it is possible to construct the M−R relation for neutron stars depending on the Noether conserved quantity and the associated gravitational radius. This approach enables the recovery of extreme massive stars that could not be stable in the standard Tolman-Oppenheimer-Volkoff based on General Relativity. Examples are given for some power law f(R) gravity models.

To date, the most precise tests of general relativity have been achieved through pulsar timing, albeit in the weak-field regime. Since pulsars are some of the most precise and stable "clocks" in the Universe, present observational efforts are focused on detecting pulsars in the vicinity of supermassive black holes (most notably in our Galactic Centre), enabling pulsar timing to be used as an extremely precise probe of strong-field gravity. In this paper a mathematical framework to describe test-particle dynamics in general black hole spacetimes is presented, and subsequently used to study a binary system comprising a pulsar orbiting a black hole. In particular, taking into account the parameterization of a general spherically symmetric black hole metric, general analytic expressions for both the advance of the periastron and for the orbital period of a massive test particle are derived. Furthermore, these expressions are applied to four representative cases of solutions arising in both general relativity and in alternative theories of gravity. Finally, this framework is applied to the Galactic Centre S-stars and four distinct pulsar toy models. It is shown that by adopting a fully general-relativistic description of test-particle motion which is independent of any particular theory of gravity, observations of pulsars can help impose better constraints on alternative theories of gravity than is presently possible.

The paradox of a free falling radiating charged particle in a gravitational field, is a well-known fascinating conceptual challenge that involves classical electrodynamics and general relativity. We discuss this paradox considering the emission of radiation as a consequence of an explicit space/time symmetry breaking involving the electric field within the trajectory of the particle seen from an external observer. This occurs in certain particular cases when the relative motion of the charged particle does not follow a geodesic of the motion dictated by the explicit Lagrangian formulation of the problem and thus from the metric of spacetime. The problem is equivalent to the breaking of symmetry within the spatial configuration of a radiating system like an antenna: when the current is not conserved at a certain instant of time within a closed region then emission of radiation occurs [1]. Radiation from a system of charges is possible only when there is explicit breaking of symmetry in the electric field in space and time.

The recently reported gravitational wave events GW150914 and GW151226 caused by the merg- ers of binary black holes [1–3] provide a formidable way to set constraints on alternative metric theories of gravity in the strong field regime. In this paper, we develop an approach where an arbitrary theory of gravity can be parametrised by an effective coupling Geff and an effective grav- itational potential Φ(r). The standard Newtonian limit of General Relativity is recovered as soon as Geff → GN and Φ(r) → ΦN. The upper bound on the graviton mass and the gravitational interaction length, reported by the LIGO-VIRGO collaboration, can be directly recast in terms of the parameters of the theory which allows an analysis where the gravitational wave frequency modulation sets constraints on the range of possible alternative models of gravity. Numerical results based on published parameters for the binary black hole mergers are also reported. Comparison of the observed phase of the GW150914 and GW151226 with the modulated phase in alternative theories of gravity does not give reasonable constraints due the large uncertainties in the estimated parameters for the coalescing black holes. In addition to these general considerations, we obtain limits for the frequency dependence of the α parameter in scalar tensor theories of gravity.

Einstein's General Theory of Relativity (GR) successfully describes gravity. The most fundamental predictions of GR are black holes (BHs), but in spite of many convincing BH candidates in the Universe, there is no conclusive experimental proof of their existence using astronomical observations. Are BHs real astrophysical objects? Does GR hold in its most extreme limit or are alternatives needed? The prime target to address these fundamental questions is in the center of our own Galaxy, which hosts the closest and best-constrained supermassive BH candidate in the Universe, Sagittarius A* (Sgr A*). Three different types of experiments hold the promise to test GR in a strong-field regime using observations of Sgr A* with new-generation instruments. The first experiment aims to image the relativistic plasma emission which surrounds the event horizon and forms a "shadow" cast against the background, whose predicted size (~50 microarcseconds) can now be resolved by upcoming VLBI experiments at mm-waves such as the Event Horizon Telescope (EHT). The second experiment aims to monitor stars orbiting Sgr A* with the upcoming near-infrared interferometer GRAVITY at the Very Large Telescope (VLT). The third experiment aims to time a radio pulsar in tight orbit about Sgr A* using radio telescopes (including the Atacama Large Millimeter Array or ALMA). The BlackHoleCam project exploits the synergy between these three different techniques and aims to measure the main BH parameters with sufficient precision to provide fundamental tests of GR and probe the spacetime around a BH in any metric theory of gravity. Here, we review our current knowledge of the physical properties of Sgr A* as well as the current status of such experimental efforts towards imaging the event horizon, measuring stellar orbits, and timing pulsars around Sgr A*.

To explain the extremely high energy release, > 10 53 erg, suggested by the observations of some Gamma-Ray Bursts (GRBs), we propose a new energy extraction mechanism from the rotational energy of a Kerr-Newman black hole (BH) by a massive photon field. Numerical studies show that this mechanism is stable with respect to the black hole rotation parameter, a, with a clear dependence on the BH mass, M, and charge, Q, and can extract energies up to 10 54 erg. The controversial " energy crisis " problem of GRBs that does not show evidence for collimated emission may benefit from this energy extraction mechanism. With these results we set a lower bound on the coupling between electromagnetic and gravitational fields.

Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f(T) gravity, where f(T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f(T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f(T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f(T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f(T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f(R) gravity, trying to enlighten the subject of which formulation might be more suitable for quantization ventures and cosmological applications.

In this work we present a procedure to infer the mass of progenitors and remnants of Gamma Ray Bursts (GRB), starting from the observed energy EGRBiso emitted isotropically and considering the associated emission of Gravitational Waves (GW) EGWiso in the different phases. We assume that the GW energy of the progenitor EGWPROG is emitted partially during a star collapse, and the residual energy is related to the GW energy emitted by the remnant. We take a sample of 237 Long GRB, and use an hybrid Montecarlo procedure to explore, for each of them, a region of possible solutions of EGWiso as a function of the masses, radii, oblateness, rotation frequencies of progenitor and remnant and the fraction of energy k emitted as GW by the GRB. We discriminate between a Neutron Star (NS) or Black Hole (BH) for the remnant and obtain interesting values for the GW emitted by the remnant NS or BH, for the conversion factor k of and for the masses and radii of GRB progenitor stars. We also obtain remnant populations with mean masses, mean GW frequencies and GRB frequency of GW emission in agreement with the most accepted models.

Cosmological inflation is discussed in the framework of $F(R,{\cal G})$ gravity where $F$ is a generic function of the curvature scalar $R$ and the Gauss-Bonnet topological invariant
$\cal G$. The main feature that emerges in this analysis is the fact that this kind of theory can exhaust all the curvature budget related to curvature invariants without considering derivatives of $R,$ $R_{\mu\nu}$, $R^{\lambda}_{\sigma\mu\nu}$ etc. in the action.  Cosmological dynamics results driven by two effective masses (lenghts) related to the $R$ scalaron and the $\cal G$ scalaron working respectively at early and very early epochs of cosmic evolution. In this sense, a double inflationary scenario naturally emerges.

In the framework of a Varying Speed of Light theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. We find that the Wheeler-DeWitt equation for the Friedmann-Lema\^{\i}tre-Robertson-Walker metric is completely equivalent to a Sturm-Liouville problem provided that the related eigenvalue and the cosmological constant be identified. The explicit calculation is performed with the help of a variational procedure with trial wave functionals related to the Bessel function of the second kind $K_{\nu }\left( x\right) $. We find the existence of a family of eigenvalues associated to a negative power of the scale. Furthermore, we show that at the inflationary scale such a family of eigenvalues does not appear.

We consider curvature-teleparallel F(R,T) gravity, where the gravitational Lagrangian density is given by an arbitrary function of the Ricci scalar R and the torsion scalar T. Using the Noether Symmetry Approach, we show that the functional form of the F(R,T) function, can be determined by the presence of symmetries . Furthermore, we obtain exact solutions through to the presence of conserved quantities and the reduction of cosmological dynamical system. Example of particular cosmological models are considered.

The issues of quintessence and cosmic acceleration can be discussed in
the framework of $F(R, {\cal G})$ theories of gravity where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant.
It is possible to show that such an approach exhausts all the curvature content related to the Riemann tensor giving rise to a fully geometric approach to dark energy.

We develop the Regge-Wheeler formalism for f(R)-gravity theories. In particular as a first step we shown that a Schwarzchild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and will therefore remain stable if subject to a small nonspehrical perturbation.

We show here how it is possible to relate the cosmographic parameters (namely the deceleration$q_0$, the jerk $j_0$, the snap $s_0$ and the lerk $l_0$ parameters) to the present day values of f(R,G) and its derivatives thus offering a new tool to constrain such higher order models. Our analysis thus offers the possibility to relate the model independent results coming from cosmography to the theoretically motivated assumptions of f(R,G) cosmology

Inflation and dark energy are two of the most relevant aspects of modern cosmology. These different epochs provide the universe is passing through accelerated phases soon after the Big-Bang and at present stage of its evolution. In this review paper, we discuss that both eras can be, in principle, described by a geometric picture, under the standard of f(R) gravity. We give the fundamental physics motivations and outline the main ingredients of f(R) inflation, quintessence and cosmography. This wants to be a quick summary of f(R) paradigm without claiming of completeness.

A geometrical approach to produce the mass of particles is derived. The results could be suitably tested at LHC. Starting from a 5D unification scheme, we show that all the known interactions could be induced by a symmetry breaking of the non-unitary \(GL(4)\)-group of diffeomorphisms. The further gravitational degrees of freedom, emerging from the reduction mechanism in 4D, eliminate the hierarchy problem generating a cut-off comparable with electroweak scales.

"We discuss the Noether Symmetry Approach in the framework of Gauss - Bonnet
cosmology showing that the functional form of the $F(R, {\cal G})$ function, where $R$ is the Ricci scalar and ${\cal G}$ is the Gauss -Bonnet topological invariant,  can be determined by the presence of symmetries. Besides, the method allows to find out exact  solutions due to the reduction of cosmological dynamical system and the presence of conserved quantities. Some  cosmological models are worked out.  "

In the context of $f(\mathcal{R})$ gravity, dark energy is  a geometrical fluid with negative equation of state. Since the function $f(\mathcal{R})$ is not known \emph{a priori}, the need of a model independent reconstruction of its shape  represents a relevant technique to determine which $f(\mathcal{R})$ model  is really favored with respect to others. To this aim, we relate cosmography to a generic $f(\mathcal R)$ and its derivatives in order to provide a model independent investigation at redshift $z \sim 0$. Our analysis is  based on the use of three different cosmological distance definitions, in order to alleviate the duality problem, i.e. the problem of which cosmological distance to use with specific cosmic data sets. We therefore consider the luminosity, $d_L$, flux, $d_F$, and angular, $d_A$, distances and we find numerical constraints by the Union 2.1 supernovae compilation and measurement of baryonic acoustic oscillations, at $z_{BAO}=0.35$.  We notice that all distances reduce to the same expression, i.e. $d_{L;F;A}\sim\frac{1}{\mathcal H_0}z$, at first order. Thus, to fix the cosmographic series of observables, we impose the initial value of  $H_0$ by fitting $\mathcal H_0$  through supernovae only, in the redshift regime $z<0.4$. We find that the pressure of curvature dark energy fluid is slightly lower than the one related to the cosmological constant. This indicates that a possible evolving curvature dark energy realistically fills the current universe. Moreover, the combined use of $d_L,d_F$ and $d_A$ shows that the sign of the acceleration parameter agrees with theoretical bounds, while its variation, namely the jerk parameter, is compatible with $j_0>1$. Finally, we infer the functional form of $f(\mathcal{R})$ by means of a truncated polynomial approximation, in terms of fourth order scale factor  $a(t)$.

Symmetries play a crucial role in physics and, in particular, the Noether symmetries are a useful tool both to select models motivated at a fundamental level, and to find exact solutions for specific Lagrangians. In this work, we consider the application of point symmetries in the recently proposed metric-Palatini Hybrid Gravity in order to select the $f({\cal R})$ functional form and to find analytical solutions for the field equations and for the related Wheeler-DeWitt (WDW) equation. We show that, in order to find out integrable $f({\cal R})$ models, conformal transformations in the Lagrangians are extremely useful. In this context, we explore two conformal transformations of the forms $d\tau=N(a) dt$ and $d\tau=N(\phi) dt$. For the former conformal transformation, we found two cases of $f({\cal R})$ functions where the field equations admit Noether symmetries. In the second case, the Lagrangian reduces to a Brans-Dicke-like theory with a general coupling function. For each case, it is possible to transform the field equations by using normal coordinates to simplify the dynamical system and to obtain exact solutions. Furthermore, we perform quantization and derive the WDW equation for the minisuperspace model. The Lie point symmetries for the WDW equation are determined and used to find invariant solutions.

This paper is devoted to solve the galactic rotation problem for ESO138-G014 galaxy based on two theories: dark matter and modified newtonian dynamics (MOND). Here we did the rotation curve analysis with two possible choices for the dark matter density profile, namely Burkert and NFW profiles. The analysis shows the dark matter distribution favored to Burkert profile (cored dark matter). The standard hypothesis for most spiral galaxies are known to be embedded in dark matter haloes has now been overshadowed by modified newtonian dynamics, known as MOND, the leading alternative of dark matter. MOND addresses the problem of a new fundamental constant $a_{0}$, called the acceleration constant, at which acceleration scale of Newton’s second law fails to hold. In this respect, we investigate this issue by testing the rotation curve within the MOND framework or ``MOND RC" with the observations to obtain the reliable disk mass, $M_D$. We investigate whether ESO138-G014 is compatible with MOND or dark matter is still favorable for the galactic rotation problem

There are several approaches to extend General Relativity in order to explain the phenomena related
to the Dark Matter and Dark Energy.  These theories, generally called Extended Theories of Gravity, can be tested using observations coming
from relativistic binary systems as  PSR $J0348+0432$.  Using a class of analytical $f(R)$-theories,
one can construct the first time derivative of orbital period of the binary systems
starting from a quadrupolar gravitational emission.  Our aim is to
set boundaries on the parameters of the theory in order to understand if they are ruled out, or not, by the observations
on PSR $J0348+0432$.  Finally, we have computed an upper limit on the graviton mass showing that agree with constraint coming from
other observations.

The aim of the school is to bring together PhD students, Post-docs and researchers with interests in the new approaches and trends in Theoretical Cosmology. In particular, the lectures will be devoted to the so called back reaction in cosmology, the cosmic acceleration and the theory of cosmological perturbations. The lectures are also devoted to the formation of INFN researchers.

The biennial Conference of the  Italian Society of General Relativity and Gravitation (SIGRAV) is devoted to all aspects of gravitational physics, such as Classical and Quantum Gravity, Relativistic Astrophysics and Cosmology, as well as Experimental Gravity.
The five day Conference will host about twenty invited plenary talks and shorter invited and contributed talks in three parallel workshops. A science divulgation/outreach session will be hosted during the Conference.
The Conference will take place at the Osservatorio Astronomico di Capodimonte (Napoli), in the framework of the celebrations of 200 years since its foundation.
During the Conference, the AMALDI MEDAL and the SIGRAV Prizes will be awarded to outstanding Senior and Junior scientists.

"The meeting is in the Series of the DSU workshops previeusly held in Seoul (2005), Madrid (2006), Minnesota (2007), Cairo (2008), Melbourne (2009), Leon (2010), Beijing (2011) and Buzios, Rio de Janeiro (2012). For more info, seehttp://dark.ft.uam.es/dsu/  DSU are a series of international workshops bringing together a wide range of theorists and experimentalists to discuss current ideas on models of the dark side and relate them to current and future experiments. Topics covered include: dark matter, dark energy, cosmic rays, neutrino physics, cosmology, astrophysical analysis of galactic halos, physics beyond the standard model, etc.  Topics of the workshop:  Observational Cosmology. Planck results. Dark Energy: origin, evolution and observational properties. Observational properties of Galaxies. Dark Matter in Galaxies, Groups and Clusters. Old and New Dark Matter candidates. Direct and Indirect Dark Matter searches. Simulations in Galaxy/Cluster Formation. Abandoning the LCDM Universe paradigm? Ultra high energy cosmic rays. Modifying Newton-Einstein Theory of Gravity?
Scientific Organizing Committee:
Pyungwon Ko (KIAS, South Korea)
Carlos Muñoz (UAM/IFT, Spain)
Christiane Frigerio Martins (UFF Brasil)
Shaban Khalil (BUE, Egypt)
Keith Olive (Minnesota University, USA)
Csaba Balazs (Monash University, Australia)
David Delepine (Guanajauato University, Mexico)
Qaisar Shafi (Delaware University, USA)
Yu-Feng Zhou (KITPC/ITP-CAS, China)
Paolo Salucci (SISSA, Italy)

Local Organizing Committee:
Paolo Salucci (SISSA, Italy)
Andrea Lapi (SISSA, Italy)
Mariafelicia De Laurentis (SISSA, Italy)
Gigi Danese (SISSA, Italy)
Piero Ullio (SISSA, Italy)"

My beloved Filippo, I would have liked to share with you all my successes
and achievements, only with you. The "fate" separated us. I will always
take you into my heart and especially in my mind also, since all I did and
I do is offered to you. It has been donated to the love you gave me once
so that you could be proud of me. I will never forget every single moment
of my life spent with you. Thanks my sweetheart, I still continue loving
you.

f(R) gravity is an extension of Einstein's General Relativity derived from relaxing the hypotesis that the Hilbert-Einstein action for the gravitational field is strictly linear in the Ricci curvature scalar R, i.e. f(R)=R. In this sense, f(R) gravity represents a class of theories defined as arbitrary functions of R. It can be considered as the simplest example of Extended Theory of Gravity (Capozziello and De Laurentis, 2011)....

Starting from a 5D-Riemannian manifold, we show that a reduction mechanism to 4D-spacetimes reproduces Extended Theories of Gravity (ETGs) that are direct generalizations of Einstein's gravity. In this context, the gravitational degrees of freedom can be dealt under the standard of spacetime deformations. Besides, such deformations can be related to the mass spectra of particles. The intrinsic non-linearity of ETGs gives an energy-dependent running coupling, while torsion gives rise to interactions among spinors displaying the structure of the weak forces among fermions. We discuss how this scheme is compatible with the known observational evidence and suggest that eventual discrepancies could be detected in experiments, as ATLAS and CMS, today running at LHC (CERN). We finally discuss the consequences of the present approach in view of unification of physical interactions.