We present an exact black hole solution surrounded by massive vector fields predicted by Kaluza–Klein (KK) gravity. KK gravity in four dimensions (4D) is of particular interest, as it predicts a tower of particle states, including gravitons with spin-0 and spin-1 components, in addition to the massless spin-2 gravitons of general relativity. The extra degrees of freedom in the gravitational sector modify the law of gravity, allowing the theory to explain the effects attributed to dark matter in the universe. In this paper, we construct a black hole solution surrounded by massive spin-1 gravitons within KK theory. In addition to the influence of the massive vector fields, we incorporate an interaction term between the black hole and the massive vector field. The black hole solution is affected by the mass of the spin-1 graviton and an additional parameter that encodes corrections to Newton’s constant, as well as the coupling between the massive vector field and the black hole mass. We find that the coupling between the massive vector field and the black hole mimics the effect of an electric charge. To this end, we investigate the accretion disk, quasinormal modes (QNMs), and the stability of the black hole spacetime. Finally, we use Event Horizon Telescope (EHT) observations of Sgr A* to constrain the black hole parameters.

North Macedonia

Kimet Jusufi

India

Ankit Anand

Iran

Sara Saghafi

Brazil

B. Cuadros-Melgar

Kourosh Nozari

Black holes surrounded by massive vector fields in Kaluza–Klein gravity

We introduce a novel Einstein–Rosen BTZ wormhole metric as a solution to the Einstein field equations with a negative cosmological constant and explore in detail its various phenomenological aspects. We show that the wormhole metric is characterized by a horizon at the throat, resembling a black hole horizon. This implies that our wormhole metric describes a one-way traversable wormhole at the throat, with Hawking radiation observed by an observer located at some distance from the wormhole. It is also found the same Hawking temperature using the BTZ-like coordinates and Kruskal-like coordinates. This temperature is invariant not only on the type of coordinates but also the nature of the spin of quantum fields. Importantly, we find that at the wormhole throat, the spacetime is not a pure vacuum solution, but rather contains an exotic string matter source with negative tension, which may stabilize the wormhole geometry. To this end, we found that the size of the wormhole throat is proportional to the number of quantum bits suggesting a possible implications on ER=EPR. Further we studied the particle dynamics and, finally, we tested the ANEC with a test scalar and vector fields. For the double null-component computed in BTZ coordinates, we found an apparent divergence at the wormhole throat, which is then shown to be regularized by means of Kruskal-like coordinates. The ANEC for such a scalar/vector field is violated at the wormhole throat.

Germany

Mendrit Latifi

Exploring a novel Einstein–Rosen BTZ wormhole

We address the galaxy rotation curves through the Yukawa gravitational potential emerging as a correction of the Newtonian potential in extended theories of gravity. On the one hand, we consider the contribution of the galactic bulge, galactic disk, and the dark matter halo of the Navarro–Frenk–White profile, in the framework of the standard  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model. On the other hand, we use modified Yukawa gravity to show that the rotational velocity of galaxies can be addressed successfully without the need for dark matter. In Yukawa gravity, we recover MOND and show that dark matter might be seen as an apparent effect due to the modification of the law of gravitation in terms of two parameters: the coupling constant  $$\alpha $$  <math> <mi>α</mi> </math>   and the characteristic length  $$\lambda $$  <math> <mi>λ</mi> </math>  . We thus test our theoretical scenario using the Milky Way and M31 rotation velocity curves. In particular, we place observational constraints on the free parameters of Yukawa cosmology through the Monte Carlo method and then compare our results with the predictions of the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM paradigm by making use of Bayesian information criteria. Specifically, we find that  $$\lambda $$  <math> <mi>λ</mi> </math>   is constrained to be of the order of kpc, while cosmological data suggest  $$\lambda $$  <math> <mi>λ</mi> </math>   of the order of Gpc. To explain this discrepancy, we argue that there is a fundamental limitation in measuring  $$\lambda $$  <math> <mi>λ</mi> </math>   due to the role of quantum mechanics on cosmological scales.

Italy

Rocco D’Agostino

Salvatore Capozziello

Testing Yukawa cosmology at the Milky Way and M31 galactic scales

Using the zero-point length effect, we construct a new class of charged black hole solutions in the framework of three-dimensional Gauss–Bonnet (GB) gravity with Maxwell electrodynamics. The gravitational and electromagnetic potentials and the spacetime curvature are finite and regular everywhere; however, the computation of scalar curvature invariants suggests the presence of a singularity at the origin. We also explore the thermodynamics of the solutions obtained and reveal that the entropy of the black hole decreases due to the stringy effects. The thermodynamics and conserved quantities are computed, and the validity of the first law of thermodynamics on the black hole horizon is verified. Finally, the spinning black hole solution is reported.

Pakistan

Mubasher Jamil

Ahmad Sheykhi

Three-dimensional charged black holes in Gauss–Bonnet gravity

In this paper we explore the topological classes of thermodynamics of a family of black holes. In particular we investigate the influence of distinct fields, including the electric field, non-linear magnetic field, along with the perfect fluid matter background that can mimic dark matter in large distances. In light of these considerations, we shall henceforth denote this fluid as perfect fluid dark matter (PFDM). Our analysis reveals that the winding and topological numbers for the Schwarzschild and Kerr black holes in PFDM background are the same as the Schwarzschild and Kerr black holes, however for the Kerr-AdS background in PFDM we obtain a different topological number compared to the Kerr black hole in PFDM. Furthermore, we explore in details the interplay of electric charge and nonlinear magnetic charge, impacting the topological classes of thermodynamics both in the absence and presence of PFDM. Interestingly, it is demonstrated that the topological numbers associated with the static Hayward black holes, both in the absence and presence of PFDM, deviate from those of the Schwarzschild black hole. This observation shows that the presence of a magnetic charge introduces an additional role and can alter the topological numbers. Finally, our study culminates with the comprehensive analysis of the topological numbers pertaining to the Hayward black hole, considering the combined effects of PFDM and rotation.

Muhammad Rizwan

Topological classes of thermodynamics of black holes in perfect fluid dark matter background

We use the recently modified Friedmann equations obtained from string T-duality effects that encode the zero-point length (Jusufi and Sheykhi (2023) [132]) to study the phase space analyses of a bouncing early universe. An important implication of such stringy effects is that they can alleviate the initial singularity since the Raychaudhuri equation is modified. We investigate if the Universe can undergo an accelerated expansion phase for a specific domain of the equation of state parameter. The stringy effects are encoded in the parameter Γ, which depends not only on the zero-point length but also on the state parameter ω. We construct two dynamical systems depending on whether <math><mo>−</mo><mn>1</mn><mo>&lt;</mo><mi>ω</mi><mo>≤</mo><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></math> and <math><mi>ω</mi><mo>≥</mo><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></math>, and we classify the equilibrium points of each system. Exact solutions and cosmological implications are discussed.

Chile

Alfredo D. Millano

South Africa

Genly Leon

Phase space analysis of the bouncing universe with stringy effects

We use a string T-duality corrected pair of regular black holes to construct an Einstein-Rosen (ER) bridge with the wormhole throat proportional to the zero-point (Planck) length. This may be a geometric realization of quantum entanglement for particle/antiparticle pairs. We point out that for an extreme mass configuration consisting of a black hole pair, one can have an ER bridge with a horizon area that coincides with the Bekenstein minimal area bound along with a wormhole mass proportional to the Planck mass. This could be related to gravitational self-completeness with quantum mechanical mass limits. We also discuss the ER bridge for sub-Planckian mass horizonless wormholes and show this admits a region of negative energy at the throat, which we posit to be related to a particle of negative mass generated by quantum fluctuations or the Casimir effect. We argue that Hawking radiation could be the best way for the geometric realization of quantum entanglement for particle/antiparticle pairs emitted by black holes. This sheds new light on the ER=EPR conjecture.

France

Emmanuel Moulay

United States

Jonas Mureika

Egypt

Ahmed Ali

Einstein-Rosen bridge from the minimal length

We employ Verlinde's entropic force scenario to extract the modified Friedmann equations by taking into account the zero-point length correction to the gravitational potential. Starting from the modified gravitational potential due to the zero-point length, we first find the logarithmic corrections to the entropy expression and then we derive the modified Friedman equations. Interestingly enough, we observe that the corrected Friedmann equations are similar to the Friedmann equations in braneworld scenario. In addition, from the corrected Friedmann equations, we pointed out a possible connection to the GUP principle which might have implications on the Hubble tension. To this end, we discuss the evolution of the scale factor under the effect of zero-point length. Finally, having in mind that the minimal length is of the Planck order, we obtain the critical density and the bouncing behavior of the universe with a critical density and a minimal scale factor of the order of Planck length.

Entropic corrections to Friedmann equations and bouncing universe due to the zero-point length

We construct a novel class of spherically symmetric and asymptotically flat black holes and naked singularities surrounded by anisotropic dark matter fluid with the equation of state (EoS) of the form     $$P_t=\omega \rho $$  <math> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <mo>=</mo> <mi>ω</mi> <mi>ρ</mi> </mrow> </math>  . We assume that dark matter is made of weakly interacting particles orbiting around the supermassive black hole in the galactic center and the dark matter halo is formed by means of Einstein clusters having only tangential pressure. In the large distance from the black hole we obtain the constant flat curve with the upper bound for the dark matter state parameter     $$\omega \lesssim 10^{-7}$$  <math> <mrow> <mi>ω</mi> <mo>≲</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> </mrow> </math>  . To this end, we also check the energy conditions of the dark matter fluid outside the black hole/naked singularity, the deflection of light by the galaxy, and the shadow images of the Sgr A    $$^\star $$  <math> <msup> <mrow></mrow> <mo>⋆</mo> </msup> </math>   black hole using the rotating and radiating particles. For the black hole case, we find that the effect of dark matter fluid on the shadow radius is small, in particular the angular radius of the black hole is shown to increase by the order     $$10^{-4}\, \upmu $$  <math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> <mspace width="0.166667em"></mspace> <mi>μ</mi> </mrow> </math>  arcsec compared to the vacuum solution. For the naked singularity we obtain significantly smaller shadow radius compared to the black hole case. Finally, we study the stability of the S2 star orbit around Sgr A    $$^\star $$  <math> <msup> <mrow></mrow> <mo>⋆</mo> </msup> </math>   black hole under dark matter effects. It is argued that the motion of S2 star orbit is stable for values     $$\omega \lesssim 10^{-7}$$  <math> <mrow> <mi>ω</mi> <mo>≲</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> </mrow> </math>  , however further increase of     $$\omega $$  <math> <mi>ω</mi> </math>   leads to unstable orbits. Using the observational result for the shadow images of the Sgr A    $$^\star $$  <math> <msup> <mrow></mrow> <mo>⋆</mo> </msup> </math>   reported by the EHT along with the tightest constraint for     $$\omega $$  <math> <mi>ω</mi> </math>   found from the constant flat curve, we show that the black hole model is consistent with the data while the naked singularity in our model can be ruled out.

Black holes surrounded by Einstein clusters as models of dark matter fluid

From a geometric point of view, we show that the unitary symmetries  $${{\,\textrm{U}\,}}(1)$$  <math> <mrow> <mrow> <mspace width="0.166667em"></mspace> <mtext>U</mtext> <mspace width="0.166667em"></mspace> </mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </math>   and  $${{\,\textrm{SU}\,}}(2)$$  <math> <mrow> <mrow> <mspace width="0.166667em"></mspace> <mtext>SU</mtext> <mspace width="0.166667em"></mspace> </mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </math>   stem fundamentally from Schwarzschild and Reissner–Nordström wormhole geometry through spacetime complexification. Then, we develop quantum tunneling which makes these wormholes traversable for particles. Finally, this leads to wormhole thermodynamics.