General Relativity and Quantum Cosmology (gr-qc)

Abstract: There are two free coupling parameters $c_{13}$ and $c_{14}$ in the Einstein-\AE ther metric describing a non-rotating black hole. This metric is the Reissner-Nordstr\"{o}m black hole solution when $0\leq 2c_{13}<c_{14}<2$, but it is not for $0\leq c_{14}<2c_{13}<2$. When the black hole is immersed in an external asymptotically uniform magnetic field, the Hamiltonian system describing the motion of charged particles around the black hole is not integrable. However, the Hamiltonian allows for the construction of explicit symplectic integrators. The proposed fourth-order explicit symplectic scheme is used to investigate the dynamics of charged particles because it exhibits excellent long-term performance in conserving the Hamiltonian. No universal rule can be given to the dependence of regular and chaotic dynamics on varying one or two parameters $c_{13}$ and $c_{14}$ in the two cases of $0\leq 2c_{13}<c_{14}<2$ and $0\leq c_{14}<2c_{13}<2$. The distributions of order and chaos in the binary parameter space $(c_{13},c_{14})$ rely on different combinations of the other parameters and the initial conditions.

Abstract: We show how to find exact black hole solutions in bumblebee gravity with cosmological constant including BTZ black holes.

Abstract: A way to test electromagnetic field and spacetime properties around black holes is by considering the dynamics of test particles. In fact, in real astrophysical scenarios, it is hard to determine spacetime geometry which is dominating due to degeneracy gravitational effects in parameters of gravity theories. In this work, we study for the first time the dynamics of spinning particles that have magnetic dipole moments around Schwarzschild black holes immersed in an external asymptotically uniform magnetic field using the Mathisson-Papapetrou-Dixon (MPD) equation. There are two combined interactions: gravitational interaction between the spin of the particle and (electro)magnetic interaction between the external magnetic field and the magnetic dipole moment of the particle to be taken into account. First, we derive the effective potential of the test spinning magnetized particles in motion around the black hole. We also study the combined effects of spin and magnetic interactions on innermost stable circular orbits (ISCOs), the energy, and angular momentum of the particles at ISCO together with superluminal bounds. We investigated the collision of the particles and evaluated the center-of-mass energy in the collisions. Finally, we consider various cases in which neutron stars and rotating stellar mass black holes can be treated as spinning magnetized particles, evaluating the effects of the spin and magnetic moment of objects around supermassive and intermediate-mass black holes.

Abstract: We consider static and spherically symmetric wormhole solutions in extended metric-affine theories of gravity supposing that stability and traversability of these objects can be achieved by means of the geometric degrees of freedom. In particular, we consider $f(R)$ metric, $f(T)$ teleparallel, and $f(Q)$ symmetric teleparallel models where curvature, torsion, and non-metricity rule entirely the background geometry without invoking any exotic energy-momentum tensor as matter field source. Starting from the flaring out and null energy conditions, we gather together a series of constraints which allow us to state that stable and traversable wormholes can be derived in a purely geometric approach resorting to modified gravity theories with more degrees of freedom than general relativity.

Abstract: This study explores the plausibility of an interacting tachyonic scalar, homogeneous in nature, as a promising candidate for dynamic dark energy, offering insights into the observed accelerated expansion of the universe. The parameterization of the interaction between the tachyonic field, matter, and Hubble's parameter is performed linearly. The analysis focuses on fundamental cosmological parameters in a flat universe $(K = 0)$: expansion rate, universe age, energy density evolution for matter and the tachyonic field. The study also examines the coupling strength between the tachyonic field and matter, revealing a maximum value of unity when the interaction depends solely on their energy densities. Combining them also yields an upper limit of unity (precisely 0.7) for the coupling strength.

Abstract: The abundance of dark matter in the actual universe motivates us to construct the black hole spacetime enveloped by dark matter. In this paper, we present a new spherically symmetric black hole surrounded by the pseudo-isothermal dark matter halo, and then explore the effects of the pseudo-isothermal halo profile on a rotating black hole at the M87 galactic center, aiming to achieve a black hole solution that aligns with those found in the real universe. Using the Newman-Janis method, we derive a rotating black hole solution encompassed by the pseudo-isothermal halo, which is consistent with observations of actual black holes that are believed to possess spin. Our investigation focuses on the impact of the pseudo-isothermal halo on the black hole event horizon, time-like and null orbits, as well as the black hole shadow. We find that as the spin parameter $a$ increases, the interval between the inner event horizon and the outer event horizon of the rotating black hole surrounded by the pseudo-isothermal halo in M87 diminishes. This leads to the formation of an extreme black hole. The presence of dark matter, however, has minimal effect on the event horizon. Moreover, in the M87 as the spin parameter $a$ increases, the black hole shadow deviates increasingly from a standard circle, with larger spin parameters causing more pronounced distortion relative to the standard circle. Surprisingly, we observe that the dark matter density has very little influence on the shadow of the black hole surrounded by the pseudo-isothermal halo in the M87. This study contributes to a deeper understanding of black hole structures and the role of dark matter in the universe.

Abstract: In this work, we have studied the behavior of null geodesics within a rotating wormhole space-time in non-magnetized pressure-less plasma. By focusing on the dispersion relation of the plasma and disregarding its direct gravitational effects, we examine how light rays traverse in the mentioned space-time. A key highlight of the work is the necessity of a specific plasma distribution profile to establish a generalized Carter's constant, shedding light on the importance of this parameter. Furthermore, we have derived analytical formulas to distinguish the shadow boundary across various plasma profiles, uncovering a fascinating trend of diminishing shadow size as plasma density increases. Intriguingly, certain limits of the plasma parameters result in the complete disappearance of the shadow. When calculating the deflection angle by a wormhole in plasma space-time, we observe a distinct pattern: the angle decreases as the plasma parameter rises in non-homogeneous plasma space-time, diverging from the behavior observed in homogeneous plasma space-time. Also, leveraging observational data from M$87^{\ast}$, we establish constraints on the throat radius. Furthermore, minimum shadow diameters provide valuable constraints for the radial and latitudinal plasma parameters.

Abstract: Beginning with the Everett-DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might split at any instant into orthogonal branches, each of which exhibits approximately classical behavior. In an earlier version of the present work, we proposed a decomposition of a state vector into branches by finding the minimum of a measure of the mean squared quantum complexity of the branches in the branch decomposition. Here we define a formulation of quantum complexity for quantum electrodynamics on a lattice in Minkowski space. With respect to a particular Lorentz frame, for a system beginning in a state of low complexity, branching occurs repeatedly over time with each branch splitting successively into further sub-branches among which the branch followed by the real world is chosen according to the Born rule. Alternatively, in an explicitly Lorentz covariant formulation, the real world is a single random draw from the set of branches at asymptotically late time, which can then be restored to finite time in a particular Lorentz frame by sequentially retracing the set of branching events implied by the late time choice. The earlier version here is simplified by replacing a definition of complexity based on the physical vacuum with a definition based on the bare vacuum. As a consequence of this replacement, the physical vacuum itself is predicted to branch yielding branches with energy densities slightly larger than that of the unbranched vacuum. If the vacuum energy renormalization constant is chosen as usual to give 0 energy density to the unbranched vacuum, vacuum branches will appear to have a combination of dark energy and dark matter densities but no additional particle content.

Abstract: Kastor and Traschen constructed totally anti-symmetric conserved currents that are linear in the Riemann curvature in spacetimes admitting Killing-Yano tensors. The construction does not refer to any field equations and is built on the algebraic and differential symmetries of the Riemann tensor as well as on the Killing-Yano equation. Here we give a systematic generalization of their work and find divergence-free currents that are built from the powers of the curvature tensor. A rank-4 divergence-free tensor that is constructed from the powers of the curvature tensor plays a major role here and it comes from the Lanczos-Lovelock theory.

Abstract: In some modified theories of gravity, gravitational waves can contain up to six different polarizations, which can travel at speeds different from that of light. Searches for these different polarizations in gravitational wave data are important because any detection would be clear evidence of new physics, while clear non-detections could constrain some modified theories. The first step toward searching the data for such gravitational wave content is the calculation of the amplitudes of these different polarizations. Here we present a model-independent method to obtain the different polarizations of gravitational waves directly from the metric perturbation in theories where these polarizations are allowed to travel at different speeds. We develop our calculations so that the same procedure works with either the metric perturbation itself or its trace-reversed form. Our results are in agreement with previous work in the limit that all polarization speeds are the speed of light. We demonstrate how our model-independent method can be used with two specific modified theories of gravity, suggesting its wide applicability to other theories that allow for different gravitational wave propagation speeds. We further extend the ppE formalism to apply to such theories that travel with different speeds. Finally, we discuss how the different speeds of different polarizations may affect null stream tests of general relativity with gravitational wave observations by multiple interferometers. Differences in propagation speeds may make null streams ineffective or lead to the detection of what seem to be isolated scalar or vector modes.

Abstract: In this work, we present a thermodynamical study of a Rindler modified Schwarzschild black hole under the consideration of small thermal fluctuations. In particular, we compute various stable macroscopic thermodynamic variables such as Hawking temperature, entropy, Helmholtz free energy, internal energy, enthalpy, and Gibbs free energy. To explore the effects of small statistical thermal fluctuations on stable thermodynamical parameters, we estimated the corrections to the various thermodynamical potentials of Rindler modified Schwarzschild black hole upto the first (leading) order and do a comparative study for the different values of correction parameter and Rindler acceleration parameter for fixed values of a cosmological constant. We study the stability of black holes under the consideration of thermal fluctuations and notice that the small-sized black hole is stable and the large-sized black hole is unstable for a negative value of correction parameter. For the positive value of the correction parameter, both the small and large black holes become unstable.

Abstract: We study the dynamical stability of hairy dyonic black holes in the Einstein-Maxwell-scalar gravity system against the massless scalar field perturbation. We numerically obtain the corresponding quasinormal modes (QNMs) using the series solution and shooting methods for various black hole parameters. We find that the numerical values obtained from these two methods agree well with each other. The imaginary part of the QNM is always negative, indicating the stability of the dyonic hairy black hole against the scalar perturbation. We find that the decay and oscillatory modes of the scalar field perturbation increase linearly with the horizon radius for large black holes. We thoroughly investigate the behaviour of QNMs for different values of black hole parameters, including the electric charge, magnetic charge, horizon radius and hairy parameter, etc. Moreover, we also analyse the QNM near the small/large black hole phase transition and find that the nature of the QNMs is different for large and small black hole phases, suggesting QNMs as the possible probe of black hole phase transition.