We study nonsingular black holes viewed from the point of view of Ayon-Beato–Garcia (ABG) nonlinear electrodynamics (NLED) and present a complete study of their corresponding strong gravitational lensing. The NLED modifies the the photon’s geodesic, and our calculations show that such effect increases the corresponding photon sphere radius and image separation, but decreases the magnification. We also show that the ABG’s shadow radius is not compatible with bound estimates of Sgr A* from Keck and VLTI (Very Large Telescope Interferometer). Thus, the possibility of Sgr A* being a nonsingular ABG black hole is ruled out.

Indonesia

H. Ramadhan

M. Ishlah

F. Pratama

I. Alfredo

Strong lensing and shadow of Ayon-Beato–Garcia (ABG) nonsingular black hole

In this work, we study thermodynamics of generalized Ayon-Beato and Garcia (ABG) black hole metric which contains three parameters named as mass <math id="M1"><mi>m</mi></math>, magnetic charge <math id="M2"><mi>q</mi></math>, and dimensionless coupling constant of nonlinear electrodynamics interacting field <math id="M3"><mi>γ</mi></math>. We showed that central regions of this black hole behaves as dS (AdS) vacuum space by setting <math id="M4"><mi>q</mi><mo>&lt;</mo><mn>2</mn><mi>m</mi><mfenced><mrow><mi>q</mi><mo>&gt;</mo><mn>2</mn><mi>m</mi></mrow></mfenced></math> and in the case <math id="M5"><mi>q</mi><mo>=</mo><mn>2</mn><mi>m</mi></math> reaches to a flat Minkowski space. In the large distances, this black hole behaves as a Reissner-Nordstrom BH. However, an important role of the charge<math id="M6"><mi>q</mi></math> appeared in the production of a formal variable cosmological parameter which will support pressure coordinate in the thermodynamic perspective of this black hole in our setup. We should point that this formal variable cosmological parameter is different with cosmological constant which comes from AdS/CFT correspondence, and it is effective at large distances as AdS space pressure. In our setup, the assumed pressure originated from the internal material of the black hole say <math id="M7"><mi>q</mi></math> and <math id="M8"><mi>m</mi></math> here. By calculating the Hawking temperature of this black hole, we obtain equation of state. Then, we plotted isothermal P-V curves and heat capacity at constant pressure. They show that the system participates in the small to large phase transition of the black hole or the Hawking-Page phase transition which is similar to the van der Waals phase transition in the ordinary thermodynamics systems. In fact in the Hawking-Page phase transition disequilibrium, evaporating generalized ABG black hole reaches to a vacuum AdS space finally.

Iran

Hossein Ghaffarnejad

Elham Ghasemi

Thermodynamic Phase Transition of Generalized Ayon-Beato Garcia Black Holes

We formulate positivity bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable <math><mi>s</mi></math>. In general, validity of these bounds requires the cancellation of divergences in the forward limit of the amplitude, proportional to <math><msup><mi>t</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> and <math><mi>log</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>. We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously suggested in the literature, and that the concrete UV behavior of the amplitude is uniquely determined by the structure of IR divergences. We thus extend previous results by including a subleading logarithmic term, which we show to be universal. The bounds that we present here have the potential of constraining very general models of modified gravity and effective field theories of matter coupled to gravitation.

Italy

Mario Herrero-Valea

Spain

Raquel Santos-Garcia

Finland

Russia

Anna Tokareva

Massless positivity in graviton exchange

The persistence of a suitable notion of black hole thermodynamics in Lorentz breaking theories of gravity is not only a non-trivial consistency test for such theories, it is also an interesting investigation per se, as it might help us identifying the crucial features at the root of these surprising laws governing such purely gravitational objects. In past investigations, controversial findings were presented in this sense. With the aim of settling this issue, we present here two complementary derivations of Hawking radiation in geometries endowed with universal horizons: a novel feature of back holes in Lorentz breaking theories of gravity which reproduces several properties normally characterizing Killing horizons. We find that both the derivations agree on the fact that the Hawking temperature associated to these geometries is set by the generalized universal horizon peeling surface gravity, as required for consistency with extant derivations of the first law of thermodynamics for these black holes. We shall also comment on the compatibility of our results with previous alternative derivations and on their significance for the survival of the generalized second law of black hole thermodynamics in Lorentz breaking theories of gravity.

Stefano Liberati

Hawking radiation from universal horizons

We discuss the weight of vacuum energy in various contexts. First, we compute the vacuum energy for flat spacetimes of the form <math><msup><mi>T</mi><mn>3</mn></msup><mo>×</mo><mi>R</mi></math>, where <math><msup><mi>T</mi><mn>3</mn></msup></math> stands for a general 3-torus. We discover a quite simple relationship between energy at radius <math><mi>R</mi></math> and energy at radius <math><mfrac><msubsup><mi>l</mi><mi>s</mi><mn>2</mn></msubsup><mi>R</mi></mfrac></math>. Then we consider quantum gravity effects in the vacuum energy of a scalar field in <math><msub><mi>M</mi><mn>3</mn></msub><mo>×</mo><msup><mi>S</mi><mn>1</mn></msup></math> where <math><msub><mi>M</mi><mn>3</mn></msub></math> is a general curved spacetime, and the circle <math><msup><mi>S</mi><mn>1</mn></msup></math> refers to a spacelike coordinate. We compute it for general relativity and generic transverse diffeomorphisms theories. In the particular case of unimodular gravity vacuum energy does not gravitate.

Enrique Alvarez

Jesus Anero

Weighing the vacuum energy

Unimodular Gravity is normally assumed to be equivalent to General Relativity for all matters but the character of the Cosmological Constant. Here we discuss this equivalence in the presence of a non-minimally coupled scalar field. We show that when we consider gravitation to be dynamical in a QFT sense, quantum corrections can distinguish both theories if the non-minimal coupling is non-vanishing. In order to show this, we construct a path integral formulation of Unimodular Gravity, fixing the complicated gauge invariance of the theory and computing all one-loop divergences. We find a combination of the couplings in the Lagrangian to which we can assign a physical meaning. It tells whether quantum gravitational phenomena can be ignored or not at a given energy scale. Its renormalization group flow differs depending on if it is computed in General Relativity or Unimodular Gravity.

Non-minimal tinges of Unimodular Gravity

A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal isometry group is of maximal rank and the conformal Killing vectors in conformally flat coordinates are exactly the same as the ones of flat spacetime. In this work, a new concept of distance is introduced, the conformal distance, which transforms covariantly under all conformal isometries of the CF space. It is shown that precisely for CF spacetimes, an adequate power of the said conformal distance is a solution of the nonminimal d’Alembert equation.

CFT in conformally flat spacetimes

The most general Lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations.

Conformal invariance versus Weyl invariance

We formulate a unimodular = 1 = 4 supergravity theory off shell. We see that the infinitesimal Grassmann parameters defining the unimodular supergravity trans- formations are constrained and show that the conmutator of two infinitesinal unimodular supergravity transformations closes on transverse diffeomorphisms, Lorentz transforma- tions and unimodular supergravity transformations. Along the way, we also show that the linearized theory is a supersymmetric theory of gravitons and gravitinos. We see that de Sitter and anti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular supergravity theory.

Carmelo Martin

Off-shell unimodular

We have recently undergone an analysis of gravitational theories as defined in first order formalism, where the metric and the connection are treated as independent fields. The physical meaning of the connection field has historically been somewhat elusive. In this paper, a complete spin analysis of the torsionless connection field is performed, and its consequences are explored. The main properties of a hypothetical consistent truncation of the theory are discussed as well.