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1/14/20, 9:00 AM
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Raffaella Schneider1/14/20, 9:15 AMTalk
The existence of massive stellar black hole binaries, with primary black hole (BH) masses greater than 30 -35 Msun was proven by the detection of the gravitational wave (GW) event GW150914 during the first LIGO/Virgo observing run (O1), and successively confirmed by seven additional GW signals discovered by independent analyses of the O1 and O2 data. Recently reported O3 alerts suggest that...
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Dr Lumen Boco (SISSA)1/14/20, 10:00 AMTalk
In this talk I will discuss a novel mechanism to grow supermassive black hole seeds in star-forming ETG progenitors at z >1. This envisages the migration and merging of stellar compact remnants, via gaseous dynamical friction, toward the central regions of such galaxies. I will show that this process can build up central BH masses of order 10^4 − 10^6 Msun in a timescale shorter than 10^8 yr,...
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Mr Alberto Mangiagli (University of Milan - Bicocca)1/14/20, 10:15 AMTalk
In current stellar evolutionary models, the occurrence of pair-instability supernovae plays a key role in shaping the resulting black hole (BH) mass population, preventing the formation of remnants between about $[60, \, 120] \rm M_\odot$.
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We develop a simple approach to describe BHs beyond the pair-instability gap, by convolving the initial mass function and star formation rate with the... -
Laura Sberna (Perimeter Institute)1/14/20, 10:30 AMTalk
We study the impact of mass accretion in the evolution of LIGO-like black hole binaries. Based on simulated catalogues of binary populations, we estimate that a fraction of the events will have a detectable imprint of Eddington-level accretion, when detected by LISA or by LISA and ground-based detectors (multiband). Accretion can also induce bias in the binary parameters, such as the masses...
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Francisco Duque (GRiT/CENTRA, Instituto Superior Técnico, Universidade de Lisboa)1/14/20, 10:45 AMTalk
The tidal deformability of compact objects by an external field has a detectable imprint in the gravitational waves emitted by a binary system, which is encoded in the so-called Tidal Love Numbers (TLNs). For a particular theory of gravity, the TLNs depend solely on the object's internal structure and, remarkably, they vanish for black holes in general relativity. This fact has gathered...
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Béatrice Bonga (Radboud University)1/14/20, 11:30 AMTalk
This will be an overview talk about the Bondi-Metzner-Sachs group, which is the symmetry group of asymptotically flat spacetimes. After having reviewed its main properties, I will discuss some applications such as the memory effect. Next, I will discuss the BMS algebra in other contexts such as higher dimensions and black hole horizons. The latter is conjectured to be key in solving the...
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Nikos Karnesis1/14/20, 2:15 PMTalk
The LISA Data Challenges (LDC) where established as a common ground with the aim of engaging the community to the open LISA data analysis questions. Since the first LDC, a lot of experience has been gained, and significant progress has been achieved. In this talk I will review this progress, and I will present the purpose and individual goals of the current LDCs. The status and future...
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Troels Harmark (Niels Bohr Institute)1/14/20, 3:00 PMTalk
Despite their potential importance for understanding astrophysical jets, physically realistic exact solutions for magnetospheres around Kerr black holes have not been found, even in the force-free approximation. Instead approximate analytical solutions such as the Blandford-Znajek (split-)monopole, as well as numerical solutions, have been constructed. In this talk we consider a new approach...
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Dr Richard Brito (Sapienza University of Rome)1/14/20, 3:15 PMTalk
Gravitational-wave observations of coalescing binary black holes allow for novel tests of the strong-field regime of gravity. Using the detections of the LIGO and Virgo collaborations, we place the first constraints on higher-order curvature corrections that arise in the effective-field-theory extension of general relativity where higher-order powers in the Riemann tensor are included in the...
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Christos Charmoussis (LPT-Orsay)1/14/20, 3:30 PMTalk
We will discuss an analytic hairy black hole in a subclass of scalar tensor theories
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Dr Antoine Lehébel (University of Nottingham)1/14/20, 4:15 PMTalk
In generic higher-order scalar-tensor theories which avoid the Ostrogradsky instability, the presence of a scalar field significantly modifies the propagation of matter perturbations, even in weakly curved backgrounds. This affects notably the speed of sound in the atmosphere of the Earth. It can also generate instabilities in homogeneous media. I will use this to constrain the viable...
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Dr Ippocratis Saltas (CEICO - Czech Academy of Sciences)1/14/20, 4:30 PMTalk
Generic extensions of General Relativity aiming to explain dark energy typically introduce fifth forces of gravitational origin. In this talk, I will explain how helioseismic observations can provide a powerful and novel tool towards precision constraints of fifth forces, as predicted by general theories for dark energy, and I will discuss the implications for cosmology.
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Dr Mario Herrero-Valea (SISSA)1/14/20, 4:45 PMTalk
Horava Gravity is a renormalizable theory of Quantum Gravity which is expected to flow to GR in the low energy limit. This naive expectation is obstructed by a strongly coupled interaction when the parameters of the Lagrangian flow to the general relativistic values. However, when closely studied, only self-interactions of the extra scalar mode of the theory are strongly coupled. When matter...
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Francois Foucart1/15/20, 9:15 AMTalk
The first detection of a binary neutron star star system through gravitational waves and electromagnetic signals (gamma-ray burst, kilonova, radio) recently demonstrated the feasibility and usefulness of multi-messenger astronomy. In this talk, I will provide an overview of the physics of neutron star-neutron star and black hole-neutron star mergers, and of what we can learn from gravitational...
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Dr Ali Seraj (ULB)1/15/20, 10:00 AMTalk
Asymptotically flat spacetimes admit infinite dimensional BMS symmetries which complete the Poincare symmetry algebra with super-translation and super-Lorentz generators. We show that each of these symmetries lead to a flux-balance equation at null infinity, which we compute to all orders in the post-Minkowskian expansion in terms of radiative multipole moments. The ten Poincare flux-balance...
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Manuel Hohmann (University of Tartu)1/15/20, 10:15 AMTalk
The parameterized post-Newtonian (PPN) formalism is an invaluable tool to assess the viability of gravity theories using a number of constant parameters. These parameters form a bridge between theory and experiment, as they have been measured in various solar system experiments and can be calculated for any given theory of gravity. The practical calculation, however, can become rather...
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Ms Mekhi Dhesi (University of Southampton)1/15/20, 10:30 AMTalk
We are working to provide accurate modelling of the dynamics and gravitational-wave signatures of black hole inspirals in the intermediate-mass-ratio regime (IMIRIs) (1:100-1:1000). In doing so we hope to bridge the gap between the accurate modelling of extreme-mass-ratio inspirals achieved through black hole perturbation theory, and that of comparable-mass inspirals using numerical...
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Mr Thanasis Giannakopoulos (Instituto Superior Técnico)1/15/20, 10:45 AMTalk
Characteristic formulations of General Relativity (GR) have advantages over more standard spacelike foliations in a number of situations. For instance, the Bondi-Sachs formalism is at the base of codes that aim to produce gravitational waveforms of high accuracy, exploiting the fact that null hypersurfaces reach future null infinity and hence avoid systematic errors of extrapolation...
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Daniela Doneva (University of Tuebingen)1/15/20, 11:30 AMTalk
Spontaneous scalarization is a very interesting mechanism endowing the compact object with nontrivial scalar field. This mechanism is designed to work only in the strong gravity regime while remaining the weak field regime practically unaltered. While scalarization was discussed mainly for neutrons stars in the last few decades, it was recently discovered that black holes in Gauss-Bonnet...
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Niels Warburton1/15/20, 2:15 PMTalk
As we face the task of modelling small mass-ratio binaries for LISA we, as a community, need to spend more time developing waveform models and less time writing and re-writing codes. Currently there exist multiple, scattered black hole perturbation codes developed by a wide array of individuals or groups over a number of decades. This project brings together some of the core elements of these...
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Dr Stephen Green (Albert Einstein Institute Potsdam)1/15/20, 3:00 PMTalk
We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed into a pure gauge part plus a zero mode (infinitesimal perturbation of the mass and spin) plus a perturbation arising from a certain scalar ("Debye-Hertz")...
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Dr Kostas Glampedakis1/15/20, 3:15 PMTalk
In this talk we study the quasi-normal modes of spherically symmetric black holes in modified theories of gravity, allowing for couplings between the tensorial and scalar field degrees of freedom. Using the eikonal approximation and a largely theory-agnostic approach, we obtain analytical results for the fundamental mode of such black holes.
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Dr Swetha Bhagwat (La Sapienza)1/15/20, 3:30 PMTalk
Validating the no-hair theorem with a gravitational wave observation from a compact binary coalescence presents a compelling argument that the remnant object is indeed a black hole described by the classical general theory of relativity. Validating this theorem relies on performing a spectroscopic analysis of the post-merger signal and recovering the frequencies of either different angular...
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Nikolas Andreou (University of Nottingham)1/15/20, 4:15 PMTalk
Spontaneous scalarization is a mechanism that endows relativistic stars and black holes with a nontrivial configuration only when their spacetime curvature exceeds some threshold. The standard way to trigger spontaneous scalarization is via a tachyonic instability at the linear level, which is eventually quenched due to the effect of non-linear terms. At this work (Phys. Rev. D 99, 124022...
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Mr Alexandru Dima (SISSA)1/15/20, 4:30 PMTalk
We present a numerical investigation of the superradiant instability in spinning black holes surrounded by a plasma with density increasing when moving closer to the black hole. We try to understand whether superradiant instabilities are relevant or not for astrophysical black-holes surrounded by matter.
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Mr Nicola Franchini (Sissa)1/15/20, 4:45 PMTalk
A modified causal structure of black holes in theories beyond general relativity might have implications for the stability of such solutions. In this talk, we explore the horizon structure of black holes as perceived by scalar fields for generalized scalar-tensor theories, which exhibit derivative self-interactions. This means that the propagation of perturbations on nontrivial field...
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Maximiliano Isi1/16/20, 9:15 AM
Gravitational waves may allow us to experimentally probe the structure of black holes, with important implications for fundamental physics. One of the most promising ways to do so is by studying the spectrum of quasinormal modes emitted by the remnant from a binary black hole merger. This program, known as black hole spectroscopy, could allow us to test general relativity and the nature of...
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Miguel Bezares (SISSA)1/16/20, 10:00 AMTalk
The direct detection of gravitational waves (GWs) by the LIGO and VIRGO interferometric detectors has begun a new era of GW astronomy, allowing us to study the strong regime of gravity through GW signals produced by coalescence of compact objects. In this talk, I will present our numerical studies on coalescence of binary Exotic Compact Objects (ECOs) performed by solving the Einstein...
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Daniele Pranzetti (Perimeter Institute)1/16/20, 10:15 AMTalk
In this talk I will show how to derive an effective Hamiltonian constraint for the Schwarzschild geometry starting from the full loop quantum gravity Hamiltonian constraint and computing its expectation value on coherent states sharply peaked around a spherically symmetric geometry. I then use this effective Hamiltonian to study the interior region of a Schwarzschild black hole, where a...
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Mr Alexandre Toubiana (APC/IAP)1/16/20, 10:30 AMTalk
Black holes mimickers, e.g. neutron stars or boson stars, are compact objects with similar properties to black holes.
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The gravitational wave signal emitted by a binary of such putative objects during the inspiral phase is difficult to
distinguish from the one emitted by a black hole binary. Nevertheless, significant differences might appear in the
post merger signal. Inspired by the known... -
Sayak Datta (IUCAA)1/16/20, 10:45 AMTalk
With the observation of the multiple binary inspirals, we begin to question whether the components of the binary are black holes or some exotic compact objects (ECO). The black holeness or the deviation from it can be tested in several ways. The distinguishing feature of a black hole from other exotic compact objects is the presence of the horizon. This surface acts as a one-way membrane, that...
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Luciano Rezzolla1/16/20, 11:30 AMTalk
I will briefly discuss how the first image of a black hole was obtained
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by the EHT collaboration. In particular, I will describe the theoretical
aspects that have allowed us to model the dynamics of the plasma
accreting onto the black hole and how such dynamics was used to generate
synthetic black-hole images. I will also illustrate how the comparison
between the theoretical images and the... -
Marcos Valdes1/16/20, 4:15 PMTalk
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Mr Nikolaos Chatzarakis (Aristotle University of Thessaloniki)Poster
Following the generalised form of non-stationary axisymmetric space-time (Chandrasekhar 1983), we assume a bifocale elliptic symmetry and attempt to show that this particular metric can be a solution to Einstein's field equations. We discuss the form of the metric and the curvature implied, as well as its possible physical meaning and applications.
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Mr Giovany Cruz (CINVESTAV)Poster
A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The term `simultaneous' is imported from variational calculus and refers to the fact that extremization of the action produces at once both the ?first and second variation of a given geometrical action for the brane. The action depends on a pair of independent field variables, the brane...
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Dr Andrea Maselli (Sapienza University of Rome)Poster
Black-hole spectroscopy is arguably the most promising tool to test
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gravity in extreme regimes and to probe the ultimate nature of black
holes with unparalleled precision. These tests are currently limited by
the lack of a ringdown parametrization that is both robust and accurate.
We develop an observable-based parametrization of the ringdown of
spinning black holes beyond general... -
Prof. Niels Obers (Nordita & Niels Bohr Institute)Poster
I will discuss an action principle for non-relativistic gravity, as has recently been obtained from a covariant large speed of light expansion of Einstein's theory of gravity. This action reproduces Newtonian gravity as a special case, but goes beyond it by allowing for gravitational time dilation while retaining a non-relativistic causal structure. As a consequence, it can be shown that the...
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Prof. Sandipan Sengupta (IIT Kharagpur)Poster
We present a smooth extension of the Schwarzschild exterior geometry, where the singular interior is superceded by a vacuum phase with vanishing metric determinant. Unlike the Kruskal-Szekeres continuation, this explicit solution to the first-order field equations in vacuum has no singularity in the curvature two-form fields, no horizon and no global time. The underlying non-analytic structure...
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Kunihito Uzawa (Kwansei Gakuin University)Poster
We discuss the weak gravity conjecture (WGC) from black hole entropy in the Einstein-Maxwell-dilaton system or string theory. The WGC is strongly motivated by theorems forbidding global symmetries which arise in the vanishing-charge limit, and implies the fact that not only all non-BPS black holes but also extremal one without supersymmetry should be able to decay. It is shown that the large...
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Dmitry Gal'tsov (Moscow state University)Poster
We show that the non-minimal conformally-coupled (CC) scalar-tensor theory and the Palatini theory with kinetic coupling of the scalar to the Ricci tensor (PKC) are the same. This is demonstrated by showing that both theories coincide in the Einstein frame. Using this duality as generating technique, we construct the PKC counterpart to the BBMB black hole of the CC theory. It turns out to be...
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Ilia Musco (University of Geneva)Poster
Primordial black holes can form in the early Universe from the collapse of cosmological perturbations after the cosmological horizon crossing. They are possible candidates for the dark matter as well as for the seeds of supermassive black holes observed today in the centre of galaxies. If the perturbation is larger than a certain threshold, depending on the equation of state and on the...
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Ms Federica Sassano (Sapienza University of Rome)Poster
In the last decade, many observations of bright quasars at $z > 5$, have revealed the existence of Supermassive Black Holes (SMBHs), giants of billion solar masses shining close to their Eddington limit. The mechanism of their
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formation at these early epochs represents currently an open problem in galaxy evolution.
Several scenarios have been proposed to overcome this problem, such as the... -
Dr Orlenys Troconis (International Centre for Theoretical Physics)Poster
Neutron stars are one of the most compact and densest astrophysical objects known in nature, they result from the supernova explosion of a massive star. Many of the neutron stars have very strong magnetic fields, which lead to the emission of radio and X-ray radiation. This work is devoted to study the effects of strong magnetic fields in the structure of neutron stars, within the framework of...
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Viktor GakisPoster
The Teleparallel equivalent of General Relativity, where the connection is curvatureless, offers an alternative but equivalent way of describing gravity. In accordance to GR-based modified theories such as f(R) there are also torsion or non-metricity teleparallel modifications like f(T), where T the torsion scalar and f(Q), where Q is the non-metricity scalar both of them playing a role...
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Adrian del RioPoster
Axial-type anomalies predicted by quantum field theory in curved spacetime are determined by the Chern-Pontryagin invariant of the spacetime background. I will show that this geometric quantity is non-zero in spacetimes admitting gravitational radiation that propagates to future null infinity with an excess of one polarization mode over the other. I will further argue that typical scenarios...
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Giulio ScelfoPoster
Cross-correlations between galaxy catalogs and gravitational wave maps can provide useful information regarding open questions in both cosmology and astrophysics. The detection of binary black hole mergers through gravitational waves by the LIGO-Virgo instrument sparked the discussion on whether they have astrophysical or primordial origin. According to a model whose popularity revived after...
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Prof. Partha Sarathi Majumdar (School of Physical Sciences, Indian Association for the Cultivation of Science)Poster
Using concomitantly the Generalized Second Law of black hole thermodynamics and the holographic Bekenstein entropy bound embellished by Loop Quantum Gravity corrections to quantum black hole entropy, we show that the boundary area of the remnant from the binary black hole merger in GW150914 is bounded from below. This lower bound is more general than the bound from application of Hawking's...
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Lorenzo Annulli (Instituto Superior Tècnico)Poster
Scalar fields can give rise to confined structures, such as Q-balls or boson
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tars, which can serve as interesting models for cold dark-matter. The existence and stability of objects in a given theory is relevant for a wide range of topics, from planetary science to a description of fundamental particles. Taking as starting point a theory describing a time-dependent scalar field, in this... -
Mr Rodrigo Vicente (CENTRA - Instituto Superior Técnico)Poster
We consider the interaction between a plane wave and a (counter-moving) black hole. We show that energy is transferred from the black hole to the wave, giving rise to a negative absorption cross-section. Moving black holes absorb radiation and deposit energy in external radiation. Due to this effect, a black hole hole of mass $M$ moving at relativistic speeds in a cold medium will appear...
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Suvodip Mukherjee (IAP)Poster
Cosmic microwave background and large scale structure missions have played a crucial role in constructing the standard model of cosmology. The upcoming missions in astrophysics and cosmology are going to explore the Universe over a wide range of redshifts using both electromagnetic waves and gravitational waves. I will introduce a few new frontiers in cosmology which will open-up from the...
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Stoytcho Yazadjiev (Sofia University)Poster
In this talk I will present new solutions describing neutron stars and black holes in the tensor-multi-scalar theories of gravity. Some astrophysical implications of the solutions will be also discussed.
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Mr Georgios Antoniou ( University of Nottingham )Poster
Novel wormholes are obtained in Einstein-scalar-Gauss-Bonnet theory for several coupling functions. The wormholes may feature a single-throat or a double-throat geometry. The scalar field may asymptotically vanish or be finite, and it may possess radial excitations. The domain of existence is fully mapped out for several forms of the coupling function.
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Prof. Sudipta Sarkar (IIT Gandhinagar)Poster
The study of the effects of higher curvature terms is a major research theme of contemporary gravitational physics. In this talk, I will present a comprehensive study of the higher curvature gravity and various observational & theoretical constraints. The inclusion of these terms leads to exciting new possibilities, e.g., gravitational and electromagnetic perturbations following different...
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Sourabh Nampalliwar (Eberhard Karls University of Tuebingen)Poster
Einstein’s theory has been the standard theory of gravity for nearly a century. Alternatives to and extensions of it have been proposed to address various issues. With advances in technology, these theories are becoming testable, especially in the strong field regime around black holes. In this talk, I will describe a theory agnostic approach to probe the nature of black holes. I will provide...
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Victor Eugen Ambrus (West University of Timisoara)Poster
The experimental confirmation of the polarization of the Lambda hyperons observed in relativistic heavy ion collisions experiments [1] has renewed the interest in anomalous transport of fermions due to the spin-orbit coupling (e.g., through the chiral vortical effect [2]). Using a non-perturbative technique [3], exact expressions are derived for the thermal expectation values of the...
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Prof. Anupam MazumdarPoster
I will discuss the physics of non singular compact objects which is primrily made up of gravitons, and it is as compact as that of the Buchdahl star. I will discuss how to construct such a system within higher derivative theories of gravity which incorporates nonlocal effects at the level of gravitational ingeractions. I will construct in fact both static and rotating solutions in this regard...
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Lucas Gardai CollodelPoster
In the context of a special class of tensor-multi-scalar theories of gravity for which the target-space metric admits as a Killing field a generator of a one-parameter group of point transformations under which the theory is invariant, we present rotating vacuum solutions, namely with no matter fields. These objects behave like nontopological solitons, whose primary stability is due to the...
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Mrs Martina ToscaniPoster
My poster is focused on two topics. The main one is related to intermediate mass black holes (IMBHs). Some recent observations suggest that IMBHs exist in our Universe. Yet, none of them has been confirmed so far. A possible way to prove the existence of these elusive objects can be the study of tidal disruption events of white dwarfs (WDs). Indeed, if a WD wanders too close to an IMBH, it...
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Raquel Santos GarciaPoster
Unimodular Gravity is an infrared modification of General Relativity where the cosmological constant is replaced by an integration constant, thus free from radiative corrections and effectively solving one piece of the cosmological constant problem. Apart from this, both theories enjoy the same classical
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dynamics, dictated by Einstein equations, and they were thought to be equivalent for any... -
Igor Bogush (Lomonosov Moscow State University)Poster
We generalize the recent derivation http://arxiv.org/abs/arXiv:1908.10617 of the Smarr formulas for Einstein-Maxwell stationary axisymmetric asymptotically locally flat spacetimes with line singularities to the Einstein-Maxwell-dilaton (EMD) theory with an arbitrary dilaton coupling constant. The line singularities include the Dirac and Misner strings for spacetimes with magnetic and NUT...
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Mr Nuno M. Santos (CENTRA, Instituto Superior Técnico, Universidade de Lisboa)Poster
Kerr black holes are known to support massive bosonic test fields whose phase angular velocity fulfills the synchronization condition, i.e. the threshold of superradiance. The presence of these real-frequency bound states at the linear level, commonly dubbed stationary clouds, is intimately linked to existence of Kerr black holes with bosonic hair at the non-linear level. These configurations...
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Kyriakos Destounis (Theoretical Astrophysics, University of Tübingen)Poster
The strong cosmic censorship conjecture has recently regained a lot of attention in charged and rotating black holes immersed in de Sitter space. Such spacetimes possess Cauchy horizons in the internal region of the black hole. The stability of Cauchy horizons is intrinsically connected to the decay of small perturbations
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exterior to the event horizon. As such, the validity of strong cosmic... -
Dennis Hansen (ETH Zürich)Poster
In this talk I will discuss the ultra-relativistic expansion of general relativity. The ultra-relativistic expansion in the speed of light captures very strong gravitational field effects and extreme astrophysical phenomena in a simplifying setting compared to full GR. Surprisingly it also turns out that the ultra-relativistic expansion is closely related to the non-relativistic expansion,...
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Partha Sarathi Majumdar (School of Physical Sciences, Indian Association for the Cultivation of Science)Poster
We use loop quantum gravity inspired holographic thermal stability criteria to establish the existence of regions in parameter space of charged rotating black holes away from extremality, where partial fulfillment of the stability criteria is possible. Physical implications of our results will be discussed.
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Taishi Ikeda (Instituto Superior Tecnico)Poster
Axion and axion-like particle are the candidates of the dark matter. Due to the super-radiant instability, these fields are amplified, and can localize around Kerr BH, as axion clouds. Since the axion clouds emit gravitational waves, it is important to analyze several properties of the axion cloud around BHs. Here, we study the axion cloud around binary BH (BBH). The axion cloud around a BH of...
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Mr Oliver Long (University of Southampton)Poster
Historically the Teukolsky equation corresponding to gravitational perturbations is solved for the Weyl scalars. However, reconstructing the metric from these scalars involves solving a fourth order PDE to obtain the Hertz potential and then another second order PDE to construct the metric perturbation. Solving the (adjoint) Teukolsky equation for the Hertz potential directly simplifies the...
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Diana-Cristiana Popescu (West University of Timisoara)Poster
We are illustrating a procedure for computing the total probabilities corresponding to the processes of fermion pair production in electric fields and in the field of a magnetic dipole on de Sitter space-time. The total probabilities are preserving the dependence on the expansion parameter, proving the fact that the results are consistent with the ones obtained for probability densities. The...
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Pradyumn Sahoo (Birla Institute of Technology and Science-Pilani, Hyderabad Campus)Poster
We propose, as a novelty in the literature, the modelling of wormholes within the particular case of the $f(R,T)$ gravity, namely $f(R,T)=R+\alpha R^{2}+\lambda T$, with $R$ and $T$ being the Ricci scalar and trace of the energy-momentum tensor, respectively, while $\alpha$ and $\lambda$ are constants. Although such a functional form application can be found in the literature, those concern to...
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