Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Evaluating gravitational path integrals in the Lorentzian has been a long-standing challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour into the complex, the sign fluctuations can be suppressed, for instance using the holomorphic gradient flow algorithm. Working through simple models, we show that this algorithm enables efficient Monte Carlo simulations for Lorentzian simplicial quantum gravity. In order to allow complex deformations of the integration contour, we provide a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads to a complex version of simplicial gravity that generalizes the Euclidean and Lorentzian cases. Outside the context of numerical computation, complex simplicial gravity is also relevant to studies of singularity resolving processes with complex semi-classical solutions. Along the way, we prove a complex version of the Gauss-Bonnet theorem, which may be of independent interest.

Bounding Greybody and Weak Deflection Angle of NED Black Holes with Many Horizons

In this project, our foremost intention is to analyze the angle of deflection of photon by NED black holes with many horizons in the context of non-linear electrodynamics. For the accomplishment of our intention at first we manipulated the optical metric of the desired black holes for the calculation of Gaussian curvature. After that, the angle of deflection in leading orders is attained from the desired black holes in weak field limit by using the famous Gauss-Bonnet theorem. Moreover, we evince the effect of plasma medium on the angle of deflection. At last, the graphical impact of the angle of deflection for NED black holes with many horizons is examined with respect to black hole charge and impact parameter in both the plasma and non plasma medium. In addition, we discuss the rigorous bound for grey body factor of the desired black hole and also observer its graphical behavior.

Bounding Greybody and Deflection Angle of Improved Schwarzschild Black Hole

We explore the deflection angle in the framework of improved Schwarzschild Black hole utilizing the most advance geometrical path adopted by Gibbon-Werner. To investigate deflection angle of the photon ray by weak gravitational lensing for this black hole, we derive the optical curvature and perform the application of Gauss-Bonnet theorem on the optical metric. Moreover, we study the impacts of the plasma medium in context of the weak gravitational lensing in relate to this black hole. Further, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Also, we find the rigorous bound base upon the greybody factor for improved Schwarzschild black hole. A while later, we contrast our conclusions about deflection angle with the deflection angles of Schwarzschild black hole within plasma and non-plasma mediums.

Effect of the Magnetic Charge on Weak Deflection Angle and Greybody Bound of the Black Hole in Einstein-Gauss-Bonnet Gravity

The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.

Geometrization of light bending and its application to SdS w spacetime

The mysterious dark energy remains one of the greatest puzzles of modern science. Current detections for it are mostly indirect. The spacetime effects of dark energy can be locally described by the SdS$_w$ metric. Understanding these local effects exactly is an essential step towards the direct probe of dark energy. From first principles, we prove that dark energy can exert a repulsive dark force on astrophysical scales, different from the Newtonian attraction of both visible and dark matter. One way of measuring local effects of dark energy is through the gravitational deflection of light. We geometrize the bending of light in any curved static spacetime. First of all, we define a generalized deflection angle, referred to as the Gaussian deflection angle, in a mathematically strict and conceptually clean way. Basing on the Gauss-Bonnet theorem, we then prove that the Gaussian deflection angle is equivalent to the surface integral of the Gaussian curvature over a chosen lensing patch. As an application of the geometrization, we study the problem of whether dark energy affects the bending of light and provide a strict solution to this problem in the SdS$_w$ spacetime. According to this solution, we propose a method to overcome the difficulty of measuring local dark energy effects. Exactly speaking, we find the lensing effect of dark energy can be enhanced by 14 orders of magnitude when properly choosing the lensing patch in certain cases. It means that we can probe the existence and nature of dark energy directly in our solar system. This points to an exciting direction to help unraveling the great mystery of dark energy.