**Symposium: Black Holes and Gravitational Waves **

**Plenary lectures (1 hour): **

1.- Claus Laemmerzahl (laemmerzahl@zarm.uni-bremen.de)

*Accretion disks as probes of Black Hole physics *

*Claus Laemmerzahl. ZARM, University of Bremen *

With accretion discs one can probe the strong gravity regime in the near vicinity of Black Holes. In this talk the general formalism for accretion disks in stationary axially symmetric Black Hole space-times is developed. In the case of matter models based on ideal fluids analytic solutions fort the density and pressure can be found. The formalism can be extended to charged fluids. In addition, also the issue of viscosity will be addressed.

2.- Deirdre Shoemaker (deirdre.shoemaker@physics.gatech.edu) – USA

*Numerical Relativity in the Age of Gravitational Wave Observations *

*Deirdre Shoemaker. Georgia Institute of Technology *

The advent of gravitational wave astronomy has created opportunities to probe strong-field gravity as black holes merge. Numerical relativity provides the means to confront the measurements with theoretical prediction from general relativity, allowing us to interpret the sources of gravitational waves and to test whether general relativity is the theory governing these events. This talk will talk about what demands will be placed on this field to maximize the science output of the new era.

3.- Jorge Cervantes (jorge.cervantes@inin.gob.mx): --- MX

*A Brief History of Gravitational Waves *

*Jorge Cervantes. ININ *

This review describes the discovery of gravitational waves. We recount the journey of

predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the subsequent successful discovery.

4.- Omar López-Cruz (omarlx@inaoep.mx) – MX

*Optical Follow-up of Gravitational Wave Sources *

*Omar López-Cruz. INAOE *

Detecting the electromagnetic (EM) counterpart of gravitational waves (GW) sources gives us with a wealth of information to understand the properties of the GW precursors. The fusion of neutron stars (NS) binaries has been identified as sources of GW. NS-NS fusions are also strong sources of EM radiation,they are called kilonovae. The light produced by kilonovae is mostly red, due to the high opacity of f-shell lanthanide-group elements, and broad spectroscopic features, resulting from the high velocities and many atomic transitions of the heavy r-process elements can be seen. Optical observations also provide information about outflows. In this talk I review what we have learned about the GW170817 event. I also describe the follow-up program of LIGO-VIRGO events using optical telescopes in Mexico, Spain, Chile, Argentina and United States.

5.- Carlos Herdeiro (carlosherdeiro@tecnico.ulisboa.pt) --- PT

*Black holes and ultralight bosonic fields*

*Carlos Herdeiro. Instituto Superior Técnico, University of Lisboa*

Hypothetical ultralight bosonic particles have been suggested as (fuzzy) dark matter candidates. Such particles will spontaneously form macroscopic bosonic halos around spinning astrophysical black holes (BH), via an energy extraction process called superradiance, transferring part of the mass and angular momentum of the BH into the halo. I consider the phenomenology of this process, and of the equilibrium state attained. The latter is metastable. It may decay via gravitational wave emission, or via the growth of new superradiant modes. I discuss the opportunities to test these models with Gravitational Wave searches or black hole imaging. I also discuss the dynamics of relativistic bosonic stars, that describe self-gravitating lumps of these ultralight bosonic particles.

6.- Volker Perlick (perlick@zarm.uni-bremen.de) – DE

*Influence of a cosmic expansion on the shadow of a black hole *

*Volker Perlick. ZARM, University of Bremen *

If a black hole is seen against a backdrop of light sources, it shows a black disc known as the ``shadow'' of the black hole. In the first part of the talk I recall how the boundary curve of the shadow can be analytically calculated for an isolated (Schwarzschild or Kerr) black hole. Then I discuss how the cosmic expansion, in the simplest case just driven by a cosmological constant, would influence the size of the shadow and if this influence could be of any relevance for actual observations of black-hole shadows.

7.- Mario Díaz (mario.diaz@utrgv.edu) U Texas, gravitational waves --- USA

*How heavy are stellar mass black holes? *

*Mario Díaz. University of Texas *

Very soon the gravitational wave ground based detectors will hit the 50 binary Black Hole mergers detection milestone. This means that in less than five years, our knowledge about the existence of BHs have increased fivefold compared to what we have learned in the previous 40 years before the first gravitational wave detection.

What have we learned from gravitational wave astronomy about their masses? How is this knowledge constraining stellar evolution and what we know about it?

In this talk I will present a review of the detections (and detection candidates -alerts-) made by gravitational wave detectors, compare it with our knowledge from electromagnetic astronomy and discuss the implications for theories of stellar evolution.

8.- Stefanie Komossa (skomossa@mpifr-bonn.mpg.de) --- DE

*The quest for supermassive black holes: singles, binaries, and mergers *

*Stefanie Komossa. Max Planck Institut for Radioastronomy *

Supermassive black holes with their extreme gravitational fields are at the forefront of research in extragalactic astrophysics. This talk outlines some of the major discoveries in black hole astrophysics, from early ideas to the most recent breakthroughs.

9.- Pablo Laguna (pablo.laguna@physics.gatech.edu) --- USA

*Space-time Curiosities: Inside the Final Black Hole and Geometrorobotics *

*Pablo Laguna. Georgia Institute of Technology *

Modeling black hole as punctures in space-time is common in binary black hole simulations. As the punctures approach each other, a common apparent horizon forms, signaling the coalescence of the black holes and the formation of the final black hole. In the first part of the talk, I will present results about the fate of the merging punctures inside the final black hole. While most studies of locomotion treat the environment and the locomotor separately, there exist a class of self-propelled systems which change the environment so dramatically that a treatment of them as a single entity is more natural. In the second part of the talk, I will present results from a study of the dynamics of a robophysical car driving around a central depression in a deformable membrane showing that the robot propulsion can be recast as geodesics of a test particle in a fiducial space-time.

10.- Miguel Alcubierre (malcubi@nucleares.unam.mx) -- MX

*Gravitational waves *

*Miguel Alcubierre. ICN-UNAM *

The theory of General relativity was postulated by Albert Einstein at the end of 1915. One of its main predictions was the existence of gravitational waves, that is perturbations of the geometry of space-time that travel at the speed of light, and are produced by violent astrophysical phenomena, as supernova explosions or the collisions of compact objects. However, gravitational waves are generally so weak that it took over a hundred years to detect them. The first confirmed detection happened in September 2015 at the Laser Interferometer Gravitational Observatory (LIGO), and was identified as the collision of two black holes. The 2017 Nobel Prize was awarded to three scientists for their crucial contribution to the development of LIGO. To date, 10 such detections have been confirmed, and there are over 20 new candidate events. At the end of 2017 the first detection of the collision of two neutron stars was announced, which coincided with a detection of a gamma ray burst, and was subsequently observed in the whole electromagnetic spectrum by many observatories both in space and around the world. In this talk I will give a brief introduction to the concept of gravitational waves, as well as the exiting results related to the first detections and the Nobel Prize.

**Short talks (30 minutes): **

1.- Hernando Quevedo (quevedo@nucleares.unam.mx)

*Geometrodynamics of Black Holes *

*Hernando Quevedo. ICN-UNAM *

I present the fundamentals of geometrothermodynamics (GTD), a formalism that represents in an invariant way thermodynamic laws and properties in terms of geometric concepts. The GTD of black holes is considered as a particular example and it is shown that a Legendre invariant metric, in which the mass, angular momentum and electric charge are considered as coordinates, can be used to describe the equilibrium space of black holes. As a consequence, black hole phase transitions can be described as curvature singularities of the equilibrium space. Moreover, GTD implies that black holes should be considered as quasi-homogeneous systems and, therefore, additional physical quantities like the cosmological constant should be considered as thermodynamic variables.

2.- Nora Breton (nora@fis.cinvestav.mx)

*Regular Black Holes *

*Nora Breton. CINVESTAV-IPN *

In this talk I address Regular Static Spherically Symmetric Black Holes (BH) constructed by introducing a de Sitter core, like the Hayward BH (HBH), then I compare the different trajectories in free fall, in the interior of the horizon, between a regular (HBH) and a

singular (Reissner-Nordstrom) BH; the energy conditions are discussed as well as for the Regular Black Holes sourced by nonlinear electrodynamics (NLED). Finally, I give some comments on the procedure by Newman-Janis(NJ) to obtain stationary Regular BH starting from a static one, adding some words on the failure of the NJ technique.

3.- Roberto Sussman (sussman@nucleares.unam.mx)

*Towards a relativistic covariant interpretation of Milgrom’s acceleration *

*Roberto Sussman. ICN-UNAM *

We propose in this letter a relativistic coordinate independent interpretation for Milgrom's acceleration $a_{0}=1.2 \times 10^{-8}\hbox{cm/s}^{2}$ through a geometric constraint obtained from the product of the Kretschmann invariant scalar times the surface area of 2--spheres defined through suitable characteristic length scales for local and cosmic regimes, described by Schwarzschild and Friedman--Lema\^\i tre--Robertson--Walker (FLRW) geometries, respectively. By demanding consistency between these regimes we obtain an appealing expression for the empirical (so far unexplained) relation between the accelerations $a_0$ and $c H_0$. Imposing this covariant geometric criterion upon a FLRW model, yields a dynamical equation for the Hubble scalar whose solution matches, to a very high accuracy, the cosmic expansion rate of the $\Lambda$CDM concordance model fit for cosmic times close to the present epoch. While these results are ery preliminary and strictly valid only at a toy model level, we believe that they could provide relevant information in the search of alternative gravity theories or even within General Relativity itself.

4.- Alfredo Herrera-Aguilar (aherrera@ifuap.buap.mx)

*Estimation of mass and spin parameters of a Kerr black hole: Newton vs. Einstein *

*Alfredo Herrera-Aguilar. IF-BUAP *

A new general relativistic method for estimating the mass and spin parameters of a Kerr black hole (BH) from observational data is presented, i.e. from the red/blueshift of photons emitted by certain bodies orbiting around the BH, and the parameters characterizing their orbits (the radius and the polar angle for generic elliptical trajectories). With this method one can predict, and eventually look for, new relativistic effects related to the curvature of spacetime generated by the mass and the spin of black holes (this is in contrast to the Newtonian approach that is usually used to estimate the mass, for instance). In addition, this method allows us to clearly visualize which Newtonian and general relativistic contributions enter in the expression for the redshifts, and therefore for the mass and the spin parameters. So far we have managed to obtain analytical formulas to calculate both quantities (M and a) in the case of circular orbits that lie in the equatorial or galactic plane. These formulas are relatively simple and can be used very easily in this case. We are currently working on the confrontation with observations of a system that presents the aforementioned characteristics. In the case of more realistic orbits (elliptical orbits that lie outside the equatorial plane), we need to develop the method further. This more refined version of our formalism could be used to make very precise estimations of the parameters

that characterize a Kerr black hole hosted in the galactic center of the systems that have been studied so far with the Event Horizon Telescope, in particular that of the Milky Way.

5.- Eloy Ayón-Beato (ayon-beato@fis.cinvestav.mx)

*On the consistent thermodynamics of Lifshitz black holes *

*Eloy Ayón-Beato. CINVESTAV-IPN *

In arbitrary dimension, we consider a theory described by the most general quadratic curvature corrections of Einstein gravity together with a self-interacting nonminimally coupled scalar field. This theory is shown to admit five different families of Lifshitz black holes dressed with a nontrivial scalar field. The entropy of these configurations is microscopically computed by means of a higher-dimensional anisotropic Cardy-like formula where the role of the ground state is played by the soliton obtained through a double analytic continuation. This involves calculating the correct expressions for the masses of the higher-dimensional Lifshitz black hole as well as their corresponding soliton. The robustness of this Cardy-like formula is checked by showing that the microscopic entropy is in perfect agreement with the gravitational Wald entropy. Consequently, the calculated global charges are compatible with the first law of thermodynamics as well as an anisotropic higher-dimensional version of the Smarr formula. Some of these configurations exist on Lifshitz critical points of the theory where all their extensive thermodynamic quantities vanish.

6.- Daniel Amaro (amarosanchez94@gmail.com)

*Geodesic Structure of the Einstein-Euler-Heisenberg Black Hole Spacetime *

*Daniel Amaro. UAM-Iztapalapa *

We derive the electrically charged static black hole spacetime of the Einstein-Euler-Heisenberg theory, in terms of the Plebański dual variables. This solution is a non-linear electromagnetic generalization of the Reissner-Nordström solution and it is characterized by three parameters: mass M, electric charge Q_e , and Euler-Heisenberg non-linearity parameter A. We study the trajectories of massive (charged and uncharged) and massless test particles in this spacetime. We also study the propagation of light, where the orbits of photons are analyzed by means of the effective Plebański pseudo-metric related to the geometrical metric and to the electromagnetic energy-momentum tensor. The shape of the shadow of the black hole is also presented and discussed.

7.- Leonardo Patiño (leopj@ciencias.unam.mx)

** Thermodynamics of D7-branes in supergravity warped black holes**.

*Leonardo Patiño. FC-UNAM *

A way to construct a warped black hole in IIB supergravity will be presented. The two parameters that characterize the resulting solution are the size of the horizon and the warping factor. A D7-brane will be embedded in this background in such a way that a particular asymptotic behavior is achieved. Depending on the value of the parameters of the black hole, the embedding of the D7-brane can be of two different types that are

distinguish from each other by their thermodynamic properties, corresponding to separate phases of the D7 in this family of backgrounds. The computation of some of the aforementioned thermodynamic quantities will be presented, along with a phase diagram over the parameter space of the black hole.

8.- Dennis Philipp (philipp@zarm.uni-bremen.de)

*General Relativistic Geodesy: concepts and effects *

*Dennis Philipp. ZARM, University of Bremen *

The Earth's geoid is one of the most important fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including the geoid) within Einstein's theory of General Relativity is inevitable.

Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential as a generalization of known (post-)Newtonian notions. This potential exists for any stationary configuration and observers who rigidly co-rotate. It is the same as realized by local plumb lines. In a second step, we employ this gravity potential to define the relativistic geoid in direct analogy to the Newtonian understanding. In the respective limits, it allows to recover well-known (post-)Newtonian results. However, the framework does not involve any approximation regarding the field strength and we can, thus, also speak of the geodesy of other (compact) objects.

Further generalizations such as relativistic normal gravity, height measures, and the proper time of observers on the geoid w.r.t. IAU resolutions will be discussed as well. To illustrate the concepts, some particular exact solutions of Einstein’s field equation as well as a parametrized post-Newtonian metric will be investigated. Moreover, a comparison to the Newtonian results sheds light on the magnitude of relativistic effects.

9.- Elías Castellanos (ecastellanos@mctp.mx)

*Bose-Einstein condensates as dark matter halos *

*Elías Castellanos. MCTP-UNACH *

Scalar Fields in the form of Bose-Einstein condensates (BEC's), seem to be a good candidate to describe dark matter in the universe. Even more, the existence of black holes in the center of some galaxies could be astrophysical phenomena that lead to the so-called quasi-bound states for the condensate that, in this scenario, can be interpreted as a galactic dark matter halo. By using the Thomas-Fermi approximation, we analyze the density distribution of the condensate in a Schwarzschild black hole space time, which we assumed as the BEC-dark matter halo. Additionally, from a simple and concise form we are able to confront the predictions of the Tomas-Fermi approximation with some data of rotation curves in galaxies. We set constraints on the parameters related to the halo, i.e., the mass parameter, the self-interaction coupling constant and the mass of the black hole (the only astrophysical parameter). We found that we could have a good fitting to the galaxies rotation curve, making to the Bose-Einstein condensate model a strong candidate to explain the fundamental nature of dark matter.

10.- Hugo Morales (hugo@xanum.uam.mx)

*Polymer Quantum Field Theory in the High Energy Regime *

*Hugo A. Morales-Técotl. UAM-Iztapalapa *

The proposal of loop (polymer) quantization of general relativity can be adapted to systems with finite number of degrees of freedom like each one of the infinite modes (harmonic oscillators) forming a scalar field to give rise to the Hosain-Husain-Seahra (HHS) model. This model crucially relies on the properties of the Mathieu solutions of the quantum pendulum that corresponds to the polymer oscillators and its generalization to interacting field theories is difficult. In this work we provide a a different perspective of the HHS model based on Feynman approach within the polymer scheme that relies on a perturbative expansion valid for high energies and which is amenable to include interactions.

11.- Román Linares (lirr@xanum.uam.mx)

*α' corrections of Black Holes *

*Román Linares. UAM-Iztapalapa *

In this talk we review some characteristics of the $\alpha$' corrections of black holes in the context of Heterotic Superstring effective field theory. In particular we will discuss the corrections to non-extremal 4-dimensional dyonic Reissner-Nordström Black Holes. We argue that to first order in α', consistency with the equations of motion of the Heterotic Superstring demands additional scalar and vector fields become active. We determine analytically the position of the event Horizon of the black hole, as well as the corrections to the extremality bound, to the temperature and to the entropy, checking that they are related by the first law of black holes thermodynamics.

12.- Mario Rodríguez (marioalberto.rodriguez@inin.gob.mx)

*A code for perturbation theory in modified gravity *

*Mario A. Rodriguez-Meza. ININ *

In this work we present a new code to study perturbation theory in modified gravity. The code is based on the computation of the Lagrangian Perturbation Theory (LPT) kernels. From these kernel functions we can compute the correlation function in Convolution-LPT (CLPT) and the power spectrum in Standard Perturbation Theory (SPT). We applied the code to compute the correlation function in CLPT and the power spectrum in SPT for LCDM, f(R) Hu-Sawicky and DGP braneworld models. We have made public the code to compute these statistics.

13.- Antonio García (garcia@nucleares.unam.mx)

*Relativistic Runge-Lenz Vector *

*Antonio García. ICN—UNAM *

We consider the construction of a S0(4) scalar field theory non minimally coupled to a Couloumb potential. Using the symmetry we calculate the hydrogen atom spectrum. We find that the symmetry have among its generators a constant of motion that we can identify with a Relativistic Runge-Lenz vector.

14.- Yuri Bonder (bonder@nucleares.unam.mx)

*Symmetries in theories with nondynamical fields *

*Yuri Bonder. ICN-UNAM *

I will first present a formalism to study symmetries in the context of diffeomorphism-invariant gauge theories. With it, I will show a universal symmetry algebra that contains the gauge symmetry and a covariant version of the diffeomorphisms. Then, I will include nondynamical fields that are supposed to describe effects associated with more fundamental degrees of freedom. Typically, these objects reduce/break the symmetries of the theory, and I will present a method to find the residual symmetries. I will present some results obtained with this method in theories with explicit Lorentz invariance and for the Unimodular Theory of Gravity, which is only invariant under a subgroup of diffeomorphisms.

15.- Marco Maceda (mmac@xanum.uam.mx)

*Noncommutative inspired black holes *

*Marco Maceda. UAM-Iztapalapa *

We review the idea of noncommutative smeared distributions of mass and charge as a tool for the construction of noncommutative inspired black holes. These models are free of singularities and possess interesting properties; we discuss some of their applications in different physical scenarios.

16.- David Vergara (vergara@nucleares.unam.mx)

*Quantum Geometry from a Noncommutative C*-twisted Poincaré algebra *

*David Vergara. ICN-UNAM *

We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from quantum gravity. Specifically we consider a two-parameter class of twisted Poincaré algebras, from which Lie-algebraic noncommutativities of the translations are derived as well as associative star-products, deformed Riemannian geometries, Lie-algebraic twisted Minkowski spaces, and quantum effects that arise as noncommutativities. Applying the GNS construction we derive the extremal pure states

and corresponding local convexes and combined convex hull and we describe the associated topological structure of the convex hull.

17.- Miguel Sabido (msabido@fisica.ugto.mx)

*Noncommutative Cosmology and the Cosmological Constant *

*Miguel Sabido. IF-UGTO *

In this work we explore the possibility of a noncommutative origin to the cosmological constant. The results are derived in the context of noncommutative cosmology, where noncommutativity is introduced by a deformation on the minisuperspace variables. These ideas are explored in several examples, the main result is an effective cosmological constant in terms of the deformation parameters.

18.- Hugo Compeán (compean@fis.cinvestav.mx)

*Deformation quantization of superstrings *

*Hugo Compeán. CINVESTAV-IPN *

In this work the quantization of the superstring is performed via the deformation quantization formalism in the Neveu-Schwarz- Ramond approach. We use the Weyl-Wigner-Moyal-Groenewold formalism to carry out the quantization. The Stratonovich-Weyl operator, the Moyal star product and the Wigner function of the ground state for the superstring are obtained. The spectrum of states is also obtained in the light-cone gauge of the superstring. Finally we give some remarks of a generalization to string field theory.

19.- Francisco Turrubiates (fturrubiates@esfm.ipn.mx)

*Uncertainty relations in arbitrary phase spaces *

*Francisco Turrubiates. FM-IPN *

Uncertainty relations define one of the main differences between classical mechanics and quantum mechanics and are of fundamental importance in the description of quantum systems. In this talk the construction of uncertainty relations for systems with arbitrary phase spaces by means of deformation quantization formalism is discussed. In particular, the expressions of the so-called Heisenberg-Robertson and Robertson-Schrödinger uncertainty relations for an arbitrary number of observables are obtained. Finally, the conditions to minimize Robertson-Schrödinger's uncertainty relations are analyzed, which allows us to introduce the concept of intelligent states in deformation quantization.

20.- Francisco Guzmán (guzman@ifm.umich.mx)

*Estimates of black hole parameters in astrophysical systems *

*Francisco Guzmán. IF-Universidad Michoacana *

We describe the inverse method approach to determine parameters of astrophysical systems involving black holes. In the first case we review the reconstruction of binary black hole parameters out of the gravitational wave signal. In a second case we estimate parameters of a black hole out of the image observed, produced by matter around the black hole. In the two scenarios we describe the state of the art in the solution of the direct problem and the consequent complexity of the future challenges of the resulting inverse problems.

21- 22.- Daniel Sudarsky (sudarsky@nucleares.unam.mx)

*A novel account for the nature and magnitude of the Dark Energy *

*Daniel Sudarsky. ICN-UNAM *

I will discuss some ideas about the interface between the quantum and gravitational realms, and the emergence of space-time itself, which led us to specific speculations about the way in which anticipated discrete aspects of quantum gravity might become manifest at the macroscopic level. We then will discuss an alternative description of gravitation, initially explored by Einstein, and known as Unimodular Gravity which can, under suitable conditions, incorporate such novel effects. The result is a mechanism for the generation an effective cosmological constant, that turns out to be naturally of the same order of magnitude as that dictated by observations. If this turns out to be correct the empirical case for the presence of a dominant dark energy component in the present day universe would turn out to be the first concrete evidence of a discreetness in the fabric of space-time. I will end with some comments about how the approach might also help in resolving the so called " $H_0$ tension".